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UBC Theses and Dissertations

Application of operations research in the airline industry Alexander, Arthur 1971

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APPLICATION OF OPERATIONS RESEARCH IN THE AIRLINE INDUSTRY - by ARTHUR ALEXANDER B . S c , U n i v e r s i t y of A l b e r t a , 1954 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF BUSINESS ADMINISTRATION i n the F a c u l t y of COMMERCE AND BUSINESS ADMINISTRATION We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1971 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree a t the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . ARTHUR ALEXANDER Department of Commerce and Business A d m i n i s t r a t i o n The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada 23 A p r i l 1971 ABSTRACT The problem was to review and e v a l u a t e o p e r a t i o n s r e s e a r c h techniques and models t h a t had been a p p l i e d i n the a i r l i n e i n d u s t r y and to d i s c o v e r problem areas where f u r t h e r r e s e a r c h i s needed. The method was to review management and o p e r a t i o n s r e s e a r c h l i t e r a t u r e p e r t a i n i n g to a i r l i n e s , and to formulate the t h e s i s o u t l i n e on the b a s i s of l i t e r a t u r e c o n s u l t e d . More s p e c i a l i z e d l i t e r a t u r e was then sought under each of the main chapter headings:, Marketing, P r o d u c t i o n , A i r p o r t s , Finance. In Marketing, l i t t l e was found t h a t o r i g i n a t e d from a i r l i n e companies, except i n the area of f o r e c a s t i n g . Adver-t i s i n g and p r i c i n g models s t u d i e d were c h i e f l y from manufactur-i n g i n d u s t r i e s . A i r l i n e P r o d u c t i o n , the revenue-earning p a r t of a i r -l i n e o p e r a t i o n , has been e x t e n s i v e l y s t u d i e d by o p e r a t i o n s r e s e a r c h e r s i n the a i r l i n e i n d u s t r y . R e s e r v a t i o n s systems, manpower p l a n n i n g , s c h e d u l i n g of a i r c r a f t and crews and passenger c h e c k - i n and baggage h a n d l i n g were main t o p i c s of study. A i r p o r t models d e a l i n g w i t h t r a f f i c c o n g e s t i o n , A i r T r a f f i c C o n t r o l , a i r c r a f t , maintenance, and i n v e n t o r y c o n t r o l F i n a n c i a l models have been developed l a r g e l y by a i r f r a m e manufacturers as s e l l i n g t o o l s f o r new a i r c r a f t , and f o r market r e s e a r c h by the plane b u i l d e r s . Cash flow models and models t h a t a i d f i n a n c i a l c o n t r o l have been a p p l i e d . General c o n c l u s i o n s are t h a t o p e r a t i o n s r e s e a r c h has been i n v e s t i g a t e d as a means t o b e t t e r a i r l i n e management i n most departments of a i r l i n e o p e r a t i o n . Much remains t o be done t o develop p r a c t i c a l o p e r a t i o n s r e s e a r c h competence i n the f o l l o w i n g areas: 1. A d v e r t i s i n g and P r i c i n g . 2. Routing and Sch e d u l i n g of a i r c r a f t and crews. 3. F i n a n c i a l Investment. The volume of the l i t e r a t u r e on o p e r a t i o n s r e s e a r c h i s growing r a p i d l y . T h i s t h e s i s i n c l u d e s o n l y a s m a l l sampling of the work done p r i o r to 1971. For more i n t e n s i v e study, b i b l i o g r a p h i e s of c u r r e n t and past work should be c o n s u l t e d . An e x c e l l e n t source of b i b l i o g r a p h i c a l data i s the I n t e r n a t i o n a l A b s t r a c t s i n Operations Research, by the I n t e r n a t i o n a l Feder-a t i o n o f O p e r a t i o n a l Research S o c i e t i e s , (IFORS). CHAPTER PAGE I. DEFINITIONS OF OPERATIONS RESEARCH 1 Operations Research a t Aer Lingus 5 Survey of Operations Research i n Ten A i r l i n e s . . . . . 8 Pl a n n i n g and C o n t r o l — P r o b l e m A n a l y s i s . . . 10 Operations Research as an A i r l i n e Product 12 I I . OPERATIONS RESEARCH IN AIRLINE MARKETING . . . 15 OPERATIONS RESEARCH IN AIRLINE FORECASTING . . . 19 Demographic S t u d i e s 21 E x p o n e n t i a l Smoothing 2 8 S i m u l a t i o n 29 C o n c l u s i o n s : Market F o r e c a s t i n g . . . . . . . 34 OPERATIONS RESEARCH IN ADVERTISING . . 35 A d v e r t i s i n g Reach 3 8 A d v e r t i s i n g Response 39 Media, S e l e c t i o n . 45 OPERATIONS RESEARCH IN AIRLINE PRICING . . . . . 48 C o n c l u s i o n s : Operations Research i n A i r l i n e Marketing . . . . 55 I I I . PRODUCTION 57 INFORMATION SYSTEMS 60 J u s t i f i c a t i o n f o r Upgrading the System . . . 64 A i r l i n e R e s e r v a t i o n s Systems . . . 72 P r o d u c t i o n Information Systems . 77 SCHEDULING 84 A Review of Scheduling Models 85 F l e e t S c h e d u l i n g a t A i r Canada 95 A i r c r a f t R o t a t i o n 99 Sch e d u l i n g of Personnel and Cargo . . . . . . 104 CUSTOMER SERVICE . . . I l l C o n c l u s i o n : A i r l i n e P r o d u c t i o n Models \ 121 IV. AIRPORT OPERATIONS 125 F a c i l i t i e s Design C o n s i d e r a t i o n s . . . . . . 127 A i r T r a f f i c C o n t r o l 136 F l e e t Maintenance 141 Maintenance Shop Scheduling 148 Operations Research i n Shop Methods 15 6 V. AIRLINE FINANCE . . . . . . . . . 169 The C u r r e n t F i n a n c i a l P i c t u r e 169 F a c t o r s A f f e c t i n g Money Supply t o A i r l i n e s 173 Investment D e c i s i o n s . . . 175 Cash Flow Models 183 F i n a n c i a l C o n t r o l 189 Future F i n a n c i n g 193 VI.-' CONCLUSION 195 BIBLIOGRAPHY 200 LIST OF FIGURES 1.1 Operations Research S t a f f a t Aer Lingus . . . 6 1.2 Operations Research S t a f f s i n Ten A i r l i n e s . 11 1.3 Judgement Elements i n Model A p p l i c a t i o n 13 2.1 F o r e c a s t i n g - E x p o n e n t i a l Smoothing . . . . . . 29 2.2 Simple Route Network . . . . . . 31 2.3 A d v e r t i s i n g D e c i s i o n F a c t o r s 37 2.4 Net P r o f i t R e l a t i o n s h i p 53 3.1 P i l o t P r o g r e s s i o n 81 3.2 Schematic S c h e d u l i n g Model R e l a t i o n s h i p s W i t h i n the A i r l i n e System 86 3.4 A i r Canada Passenger Flow Model 97 3.5 A i r c r a f t R o t a t i o n Model 100 3.6 Reserve Crew Sch e d u l i n g 109 3.7 I n i t i a l Pan American 747 Experience 113 3.8 Sample S h i f t S c heduling Program . . 118 4.1 Cargo A i r p o r t E v o l u t i o n . . . . . 131 4.2 Schematic A i r p o r t T r a f f i c Flows 134 4.3 Engine P r o v i s i o n i n g by Dynamic Program-ming. . . . . . . . . . . 155 4.4 S t r a t e g i e s f o r S t o c k i n g Insurance Spares . . 165 5.1 C a p a c i t y vs Revenue Growth U.S. A i r l i n e s . . 170 5.2 Lockheed A i r l i n e System Simulator 177 5.3 Lockheed Simulator Outputs 180 ACKNOWLEDGEMENT For g i v i n g me an o p p o r t u n i t y t o w r i t e t h i s t h e s i s , I owe warmest thanks t o Howard Stewart and Dorothy Stewart. For innumerable cups of c o f f e e and f o r her p e r s i s t e n t encouragement, I thank my w i f e , M a r i l y n Jean Alexander. For a s s i s t a n c e i n p r e p a r a t i o n of the m a t e r i a l and f o r many h e l p f u l s u g g e s t i o n s , I am indebted t o Dr. Bernard Schwab, t o Dr. K a r l Ruppenthal, and t o Dr. W i l l i a m Ziemba. For t y p i n g the f i n a l d r a f t , much p r a i s e i s deserved by Maryse E l l i s . DEFINITIONS OF OPERATIONS RESEARCH I n 1970, a i r l i n e s b e g a n t o e c o n o m i z e . A b o u t 10,000 emp l o y e e s were l a i d o f f and many i n - f l i g h t a m e n i t i e s were w i t h d r a w n . Economy c l a s s p a s s e n g e r s p a i d t o s e e m o v i e s , and i n most m o r n i n g f l i g h t s , t h e t r e n d was t o s a n d w i c h e s i n s t e a d o f h o t m e a l s , f i r s t c l a s s m e a l s w i t h o u t s o u p , h i g h e r c h a r g e s f o r c o c k t a i l s , and cream o r s u g a r f o r c o f f e e o n l y i f r e q u e s t e d . Washroom t o w e l s were changed f r o m c l o t h t o p a p e r . U n i t e d A i r L i n e s was s a i d t o s a v e a b o u t $300,000 a n n u a l l y by t h e u s e o f l e s s e x p e n s i v e p a p e r and f e w e r c o l o u r s f o r t i c k e t s , t i m e t a b l e s and e n t e r t a i n m e n t p r o g r a m s . On a l a r g e r s c a l e , U n i t e d A i r L i n e s c a n c e l l e d e i g h t o r d e r s and f i f t e e n o p t i o n s f o r DC-10 a i r b u s e s , and p o s t p o n e d d e l i v e r y o f f o u r B o e i n g 747's. Over 1971 and 1972 t h i s was e x p e c t e d t o s a v e t h e company $130 m i l l i o n . 1 M o s t l a r g e a i r l i n e s and t h e t h r e e l a r g e U. S. a i r -c r a f t m a n u f a c t u r e r s use. o p e r a t i o n s r e s e a r c h , (O/R). Was t h e u s e o f O/R a f a c t o r i n - t h e 1970-71 d o w n t u r n i n a i r l i n e f o r t u n e s ? I f O/R i s u n a b l e t o p r e v e n t s e r i o u s m i s j u d g e m e n t s TIME M a g a z i n e , F e b r u a r y 8, 1971, p. 53. i n corporate po l i c y , what use i s i t ? P r a c t i c a l men i n high positions may well ask questions l i k e these. The proper use of O/R improves corporate perform-ance i n many ways, some of which are discussed i n the chapters that follow. The great decisions that deal with market prediction and major .policy are far from academic formality. If O/R was a factor i n choosing poor p o l i c y , then the O/R was misapplied, perhaps from faul t y assumptions, from careless analysis of the problem, or from l i t e r a l acceptance of model r e s u l t s . A stringent set of assumptions i s needed to go from the r e a l world to a manageable model. Naturally these assumptions do not describe the r e a l world; i f they did, there would be l i t t l e purpose i n making them at a l l . A model should be examined to see i f i t i s consistent with the assumptions made. The useful-ness of the model, then, depends on whether the re-sul t s given by the model w i l l hold when the assumptions underlying the model are modified to f i t the many facts e x i s t i n g i n the r e a l world. 2 The O/R model i s a to o l and not a substitute for judgement*Models provide l o g i c a l means for u t i l i z i n g available information to narrow the range over which decisions are 3 made. Users of O/R should be aware that output i s a function of input provided,. . Managers may not follow d e t a i l s of the mathematics but they can understand the factors used E.M. Bass, et a l . (eds.), Mathematical Models and  Methods i n Marketing, Homewood, Irwin, 1961, p. 173. Ibid., "The Uses and Limitations of Mathematical Models for Market Planning," by R.S. Weinberg, p. 34. and the assumptions made. A i r l i n e s i z e , t r a f f i c d e n s i t y , degree of c o m p e t i t i o n , or mean stage l e n g t h a l l a f f e c t 4 p r o f i t a b i l i t y , but the b i g f a c t o r i s o f t e n management. Study Routine u s u a l l y f o l l o w s a p a t t e r n approximately as f o l l o w s : 1. Formulate the Problem. (What are we t r y i n g to do?) 2. Model the system math e m a t i c a l l y . (How do we go about i t ? ) 3. D e r i v e model s o l u t i o n s . 4. T e s t model and s o l u t i o n s . (What d i d we f i n d out?) 5. E s t a b l i s h c o n t r o l s f o r s o l u t i o n s . (What do we conclude? 6. Implement the s o l u t i o n . ^ (What do we recommend?)'' Steps 2 and 3 above u s u a l l y i n v o l v e one or more of .the standard o p e r a t i o n s r e s e a r c h t e c h n i q u e s . However, when new problems are encountered,.unsolved d i f f i c u l t i e s o f t e n l e a d t o the development of new t h e o r y . I f a model i s a poor r e p r e s e n t a t i o n of the world, i t may have been the r e s u l t of t r y i n g to f o r c e a r e a l world s i t u a t i o n i n t o a s t e r e o t y p e mould. G. Burck, "A New F l i g h t P l a n f o r the A i r l i n e s , " Fortune, A p r i l 1969, p. 206. ^F.S. H i l l i e r , and G.J. Lieberman, I n t r o d u c t i o n To  Operations Research, San F r a n c i s c o , Holden Day, 1967, p. 12. g R.E. Jacks, "Passenger Check-in and Information System," AGIFORS Proceedings, 1969. A new engineer has. a rather naive b e l i e f i n the t r a d i t i o n a l advisory concept of s t a f f . He bel ieves he w i l l be ca l led .upon because of h i s superior t r a i n -ing and knowledge. Most i n d u s t r i a l engineering super-v i s o r s , however, envis ion the department not as a consultant or service group, but as a c a t a l y s t , a questioner of e x i s t i n g procedures and a force i n i n s t i t u t i n g new methods. 7 B r i e f l y , O/R techniques are as fo l lows: 1. Mathematical Programming. L inear programming and spec ia l cases, inc lud ing the t ransporta t ion problem, the transhipment problem, and the assignment problem. Non-l inear programming, inc lud ing integer , s tochas t i c , and quadratic programming. 2. Combinatorial Analys i s the C r i t i c a l Path Method. (CPM) PERT 3. Dynamic Programming 4. Game Theory. 5. Queueing Theory. In the discuss ions that fo l low, the Kendal l c l a s s i f i c a t i o n for queueing systems i s used: A / B / S : ( d / e ) , where A.= a r r i v a l pat tern , B = service pa t tern , S = number of servers , d = maximum number wait ing or being served, e = queue d i s c i p l i n e . 7 R.A. Webber, "Innovation and C o n f l i c t i n I n d u s t r i a l Eng ineer ing , " Journal of Ind. Engineer ing. V o l . XVIII , No. 5, May 1967, pp. 306-313. 7. S i m u l a t i o n . g Operations Research a t Aer Lingus 0/R i s the a p p l i c a t i o n of q u a n t i t a t i v e a n a l y s i s and s c i e n t i f i c concepts t o the c o n s t r u c t i o n of d e c i s i o n models as an a i d i n s o l v i n g management problems. Aer Lingus i n 196 8 had a mixed f l e e t comprised of Boeing.707 and 720, BAC-111 and V i s c o u n t s . B737 and B747 a i r c r a f t were planned f o r the f u t u r e . The use of O/R a t Aer Lingus began i n 1961. By 1968 the r e were nine management s c i e n c e s p e c i a l i s t s . A p a r t i a l o r g a n i z a t i o n c h a r t , shown i n F i g u r e 1, i l l u s t r a t e s the company O/R c o n f i g u r a t i o n o f 1968. Three management s c i e n -t i s t s i n the economic p l a n n i n g group focused on c o r p o r a t e p l a n n i n g such as investment o r i e n t e d models of company o p e r a t i o n s . The s i x under the systems manager worked on t a c t i c a l problems. Some of the main a p p l i c a t i o n s of O/R a t Aer Lingus were the f o l l o w i n g : M.A. F o l e y , "O/R a t Aer Lin g u s , " The A e r o n a u t i c a l  J o u r n a l , V o l . 72, No. 691, J u l y , 1968, pp. 596-602. General Manager Economic Planning Manager (3 Mgmt. Scientists) Deputy Gen. Manager n _. A s s i s t Gen. Manager 1 - F Systems Manager I "1 1 1 1 1 . Tele Computer Computer Methods Workforce Operation Communic Ops. Systems Evaluation Research (6 people) Figure 1 Operations Research at Aer Lingus. (from The Aeronautical Journal, July 19T8, p. 597.) Inventory ControI d i f f i c u l t i e s arose from the number of items, (125,000 part numbers), infrequent and i r r e g u l a r demand, short consumption history, very high shortage costs, long and variable lead times, and the need to purchase large i n i t i a l stocks before operating experience was obtained. Problems of implementation, were i n weaving decision models into p r a c t i c a l computer systems that served many other needs. Fleet Planning 3 subject to peaked demand character-i s t i c s . A i r c r a f t mix depended.on types of a i r c r a f t available, t r a f f i c loads, and route c h a r a c t e r i s t i c s . Selection of the B 7 3 7 for short haul work was based on t h i s model. A second model evaluated Supersonic Transport and Jumbo j e t e f f e c t s on the trans- A t l a n t i c routes. A t h i r d model gave as output the number of a i r c r a f t required to f l y a given schedule for given route structures. Fleet Simulations required detailed schedules of f l i g h t s nine to eighteen months ahead. Weather, Unscheduled maintenance, a i r p o r t congestion, random fluctuations i n turn around time . . . dictated a requirement for slack. Monte Carlo simulations were used to evaluate a l t e r n a t i v e s . Tradeoffs were made between punctuality and a i r c r a f t productivity. Computer Systems3 r e a l time passenger name records and reservations should be handled on the most suitable equipment. O/R was used to solve s p e c i f i c problems, for example the c a p a b i l i t i e s of al t e r n a t i v e f a c i l i t i e s , or passenger service standards as a function of the number of agent sets. Manpower Planning i n sales o f f i c e s to give a s p e c i f i e d l e v e l of service, included queueing problems based on expected c a l l - a r r i v a l s , hourly over the year. Manpower for passenger and a i r c r a f t handling at the a i r p o r t . A queueing model by week, to accommodate demand flu c t u a t i o n s , and to provide acceptable service levels at reasonable manpower costs,, the model was used to assess some of the costs of adding extra f l i g h t s . Aircrew Rostering3 an a l l o c a t i o n problem using mathe-matical programming to minimize the number of crews assigned to f l i g h t s . T r a f f i c Forecasting by exponential smoothing was used for short term, and multiple regression analyses for medium ranges of up to two years. U n t i l 196 8, few useful models 9 rewarded a l l the e f f o r t . P i l o t Training. Deterministic simulations provided valuable insights into the costs of t r a i n i n g p i l o t s . Air Hostess Recruitment by dynamic programming methods attempted to accommodate fluctuations i n need and i n a t t r i t i o n , within the l i m i t s of available t r a i n i n g f a c i l i t i e s . Hiring and t r a i n i n g i s cheapest i f spread out over time, but th i s may produce surplus hostesses at off-peak times. Survey of Operations Research i n Ten A i r l i n e s . In response to a 1967 survey by Japan A i r Lines, ten a i r l i n e s were asked to give data with respect to t h e i r O/R a c t i v i t i e s . Names of O/R groups varied from company to 9 I b i d . Japan A i r Lines, "Operations Research Organization, Functions and A c t i v i t i e s , " AGIFORS Proceedings, 1967, p. 123. company. The main functions d e s c r i b e d i n response t o the survey are l i s t e d below. P l a n , develop, a s s i s t other departments by p r o v i d -i n g mathematical techniques. Research and develop O/R techniques. A d v i s e management of O/R approach. C a r r y out s t u d i e s , a n a l y s e s , and p r o j e c t i o n s . Improve p r o f i t a b i l i t y by the use of s c i e n t i f i c t e c h n i q u e s . Advise or a s s i s t management u s i n g O/R and s i m i l a r t e c h niques. S c i e n t i f i c programming. Provi d e c o n s u l t i n g s e r v i c e . O/R A c t i v i t i e s 3 p a s t , present, or f u t u r e i n the ten a i r l i n e s i n c l u d e d v a r i a t i o n s of the f o l l o w i n g : 1. Survey of O/R a p p l i c a t i o n s . 2. Market demand a n a l y s i s and f o r e c a s t i n g . 3. A i r c r a f t r o u t i n g , s c h e d u l i n g , and f l e e t s i m u l a t i o n . 4. Inventory c o n t r o l and spares l o c a t i o n . 5 . Maintenance r e c o r d i n g , s c h e d u l i n g . 6. Manpower requirements, r o s t e r i n g . 7. Crew r e c r u i t m e n t , t r a i n i n g , s c h e d u l i n g . 8. A i r p o r t f a c i l i t i e s s i m u l a t i o n . 9. Passenger s e r v i c i n g a t a i r p o r t s , booking p o l i c y . 1 0 . Corporate p l a n n i n g — l o n g range s t a f f p l a n n i n g . (a) model o f . t h e f i r m (b) accounting methods, sampling 11. Computer c a p a c i t y e v a l u a t i o n — s y s t e m e v a l u a t i o n , (a) r e s e r v a t i o n s system F i g u r e 2 shows the composition of ten a i r l i n e O/R groups as surveyed i n 1967. The f o l l o w i n g a b b r e v i a t i o n s are used i n the F i g u r e 2. AA American A i r l i n e s AF A i r France BA 30AC SK Scandinavian UA U n i t e d A i r L i n e s AC A i r Canada AR Aer Lingus LH L u f t h a n s a SR S w i s s a i r JL Japan A i r L i n e s P l a n n i n g and C o n t r o l — P r o b l e m A n a l y s i s The man who - i n s i s t s on seeing with -perfect clearness before he decides, never decides. H e n r i F r e d e r i c k Amiel A d e s c r i p t i v e c l a s s i f i c a t i o n of a i r l i n e problems i s i l l u s t r a t e d i n F i g u r e 3. A i r l i n e s , l i k e other forms of e n t e r p r i s e , are faced w i t h the need t o make d e c i s i o n s with l e s s i n f o r m a t i o n than they would l i k e . N. R. Tobin, i n s p i r e d by R., W. L i n d e r , 1 1 suggested t h a t d e c i s i o n s are based on knowledge and understanding. Knowledge i s u s u a l l y p a r t i a l , and based on h i s t o r i c a l o b s e r v a t i o n . Understanding i s an 1 1 L i n d e r , R.W., "Models f o r P l a n n i n g and C o n t r o l , " A'GIFORS Proceedings, 1969. //. 1 A, / Ak U 5 V ? (/A 6o $7 S& & 47 ?9 ss 4s Sr i /Z f 4 4 3 3 3 M\A7> A/ f i i 1 ${TA\-rtS-r r I f 0 3 'oca n : 9-r. 1 / / z ?\ 3 3 3 — — Si -At. 3 4 3 Z 2 — —-no. 'cs 2 i f / 3 er I Sr. - 3 0 '\ 4 4- 31 ±_ i *f 3 o 4o 2, 4 z 2 £> / j. i z. i 4-o - So z / z 1 1 So - l OP 0 z / / 5 Z 1 1 4 z 5 3 4_ £ 2 Y 3 - s • — S 2 _ 1 ~7 . . . . [ F x ; re) - 9 / 2 — V /o - — i — t\ TOVA c /tt 9 4 S] C s A is i • t/o • i f-t/res y y 3x educ at In n •/ • — • * A-Ti/OAT i • V < >s Ye S • < ( \ LS *> r vj • • > J rarnmer • • • • '1 !! Ft au re / • Z o fe Sn r T A s * ro m / ffOR •>cee hi 3 9 oh J — f — \ outgrowth of p a r t i a l knowledge. Understanding i s t h e r e f o r e incomplete, p a r t i c u l a r l y when a p p l i e d t o f u t u r e events. Yet d e c i s i o n s must.be made, and are being made very l a r g e l y on bases of judgement and experience. F i g u r e 3 i l l u s t r a t e s the importance of judgement i n model a p p l i c a t i o n . While many long-run d e c i s i o n s are somewhat f l e x i b l e , investment d e c i s i o n s made today are reasonably b i n d i n g and i n many cases w i l l not a f f e c t o p e r a t i o n s f o r two or three y e a r s . A novel view of a i r l i n e management problems i s taken i n B e l g r a y ' s comparison between I s r a e l ' s A i r Force and 12 a i r l i n e o p e r a t i o n . In an i n t e r e s t i n g breakdown of a i r f o r c e c h a r a c t e r i s t i c s and f u n c t i o n s , the I s r a e l i A i r Force i s s e t as an example i n management e f f e c t i v e n e s s . The l e s s o n i s t h a t any w e l l run o p e r a t i o n can p r o v i d e u s e f u l i d e a s . O/R as an A i r l i n e Product BOAC, a latecomer to c o m p u t e r i z a t i o n , became a le a d e r i n the f i e l d of r e a l - t i m e systems, and i n 1971 s o l d hardware and software as a s i d e l i n e . E a s t e r n A i r L i n e s and C o n t i n e n t a l i n the U n i t e d S t a t e s a l s o s o l d software. Although BOAC developed more than f i f t y programs f o r a i r l i n e o p e r a t i o n , B e l g r a y , D.C, "The I s r a e l i A i r Fo r c e , The S i x Day War, and T h e i r Relevance t o A i r l i n e Management," AGIFORS Proceedings, 1968, pp. 464-482. — 13 * to W LL Cm fr S ) € •/7<5 • r\ ^ / 7ft > 'AM k fa r/S A e&fions In ter '/7C J acft'qns ! • ctan of e/7 •to #: r cu'/ cn So/ r? -the tortg Co | ar\e Me zrt ^t/ *> he >;// tfpetii » C-to rs Corribex Cpmhet iters i. r)e*f ; /ear * in tpnf run 7 1 iS the S-o V/ra* are^ -t> he * c me she tjtt ' A 70--- • — 7 1 Si '** e */ '-the col e COJ 1 p at, lie 7 1 m Cc \u~at "i \i?tbs t/uz ?£ 5 'S | | C "or/trot r tio rt i _ e _1 ac rrerit %l k, Wits k/trZt ca na .( tions aV/e ct r^aJte Jo i vtectst 'on ep.er&ti'r. ?kos ts €> j clst{s ?\ l/^q rentes 7\ Jive* •r mkt s ha* •el /rrs ?rft /fyod/ Jo r , i ei/erri/ e. Wo. / cto ntraJ-JC^ Corn} >ei ve actions fTect & service retaX e? — 1 shaft ?s \retare & ctema-n 7 * I | com fret L-tirs • j C^f»F Mat- fit^tva mt\ M 4'/t mark //o ijf tsr ma f t 7 ,/,' z. te A ?a,tt fa/be reta/e / % i .! 7CIO -i <a TecteatAy Spct o -ni to * 1 fie 1 Vat uajfte^s ? on) i/ l Xl'i 'ajotes i -7 m | 2 "C | C on •(ro, tie lo rrc » / Web £& XJA ter rra / we o ct, j l roster fettUs . ^ j - run t'nVe otoW 7 9 ertfs | 7 outfit K/e rV/tat sche* itvt 'e? '&t\ is; oUi >et* ptft en a ?t VtUre /onf- run ^nJar/^e.t' At At 7 W aim 7 1 I u/e c Scfye^cte/i 'el p&rskntj er bl IC ce/ft ^ « wot it mkt^ti reet •1 / i c / (nx /on* ' this an </7 Vr? ? ti/fyre ? 1 | j \ 1 1 1 i [f/f ur-e. » Cwet#e\rre/7t 1 Ft ?m en rts if ate /fa* orr n 'Pol fr ?. ) many real-time systems such as reservations and departure control were largely routine a c t i v i t i e s . On the tougher problems such as forecasting, scheduling and routing, BOAC was i n the same s i t u a t i o n as others who have struggled to develop s a t i s f a c t o r y m o d e l s — s t i l l looking for better answers. By 1970, ..BOAC' s computer system, BOADICEA, - was credited with improving.load factors by two per cent, equiv-alent to $9 m i l l i o n i n extra annual revenues. The roles of middle and top management were not eliminated, nor was t h i s expected. A i r l i n e Management and Marketing, Vol. 2, No. 12, December 1970, p. 23. OPERATIONS RESEARCH IN AIRLINE MARKETING The product of.an a i r l i n e , the movement of passengers or cargo, i s not usually.wanted f o r i t s own sake. Time saved, or a r r i v a l a t . d e s t i n a t i o n are the r e a l p r o d u c t s — products t h a t are e s s e n t i a l l y u n d i f f e r e n t i a t e d among a i r l i n e s . S e v e r a l f a c t o r s promote the growth of a i r t r a f f i c . Over long d i s t a n c e s a i r t r a n s p o r t i s f a s t e r than a l t e r n a t i v e modes f o r t r a v e l or f o r cargo shipment. A i r l i n e f a r e s and cargo r a t e s , w h i l e u s u a l l y more expensive than s u r f a c e t r a n s p o r t r a t e s , are n e v e r t h e l e s s c o m p e t i t i v e when c o s t s of time i n t r a n s i t are s i g n i f i c a n t . I n c r e a s i n g c o n c e n t r a t i o n s of urban p o p u l a t i o n s put more people w i t h i n convenient reach of a i r p o r t s at both ends of t h e i r journey. Growing p o p u l a t i o n and i n c r e a s e d n a t i o n a l p r o d u c t i v i t y g r a d u a l l y i n c r e a s e per-s o n a l d i s c r e t i o n a r y income. The r e s u l t i s i n c r e a s e d p e r s o n a l spending on a i r l i n e t ourism. 2 While t o t a l a i r l i n e c o s t s are r i s i n g , u n i t c o s t s are f a l l i n g i n some areas. For example, d i r e c t c o s t s f o r """J.L. Grumbridge, Marketing Management i n A i r T r a n s p o r t , London: George A l l e n and Unwin L t d . , 19 66, p. 2 4~T 2 A v i a t i o n Week and Space Technology, January 11, 1971, p. 23. ' ' f l y i n g f r e i g h t have f a l l e n from about twenty cents per ton m i l e w i t h DC-3 a i r c r a f t t o about three cents per ton m i l e 3 w i t h the Boeing 747. Marketing concern f o r c o s t s i s i m p l i c i t i n the l o g i c a l search f o r p r o s p e c t i v e demand. T h i s can o r i g i n a t e two ways. E i t h e r a demand i s r e c o g n i z e d , and the problem i s to f i n d f e a s i b l e s o l u t i o n s t h a t meet c o s t c o n s t r a i n t s , or the means f o r low c o s t t r a n s p o r t a t i o n are a v a i l a b l e , and the problem i s to seek out the demand. The Lockheed company was faced w i t h the l a t t e r problem i n seeking 4 p o t e n t i a l c i v i l i a n uses f o r the C5 t r a n s p o r t a i r c r a f t . A i r p o r t development has tended .to l a g behind needs f o r longer and s t r o n g e r runways f o r l a r g e r a i r c r a f t , f o r 5 passenger f a c i l i t i e s and f r e i g h t h a n d l i n g c a p a c i t y . R e s u l t -i n g c o n g e s t i o n and delay are n e g a t i v e f a c t o r s t h a t tend to d i s c o u r a g e p r o s p e c t i v e a i r l i n e customers. A i r l i n e s g e n e r a l l y are bound by r e g u l a t i o n i n t h e i r own n a t i o n a l t e r r i t o r i e s , and on i n t e r n a t i o n a l routes by 3 C.W. Foreman, "The Hidden B e n e f i t s of A i r F r e i g h t , " Business H o r i z o n s , V o l . 11 , No. 6, December 1968, pp. 27 -34 . 4 A v i a t i o n Week and Space Technology, January 12, 1970, p. 30. 5 S t a n l e y H. Brewer, The Environment of I n t e r n a t i o n a l  A i r C a r r i e r s i n the Development of F r e i g h t Markets, S e a t t l e : U n i v e r s i t y of -Washington, Gradua"Ee School of Business A d m i n i s t r a t i o n , 1967, p..54. I n t e r n a t i o n a l A i r T r a n s p o r t A s s o c i a t i o n (IATA), and I n t e r -n a t i o n a l C i v i l A v i a t i o n O r g a n i z a t i o n (ICAO) standards, as w e l l as by b i l a t e r a l agreements. In 1970 the U n i t e d S t a t e s C i v i l A e r o n a u t i c s Board (C.A.B.), became aware of excess c o m p e t i t i o n on some.national r o u t e s , but the C.A.B. was r e l u c t a n t t o allow j o i n t c a p a c i t y r e d u c t i o n s because t h i s would be c o l l u s i o n (that v i o l a t e d a n t i - t r u s t laws and Un i t e d S t a t e s a v i a t i o n p o l i c y ) ; Predetermined c a p a c i t y a t home i m p l i e s acceptance o f predetermined c a p a c i t y on i n t e r n a t i o n a l r o u t e s , c o n t r a r y t o U n i t e d S t a t e s p o l i c y of the past two decades.^ The c a r d i n a l s i n s of the r e g u l a t o r s have been i n l e g i s l a t i n g , i n e f f e c t , w a s t e f u l ruinous over-c o m p e t i t i o n along a i r routes and then i n t e r v e n i n g unwisely to f o r e s t a l l the n a t u r a l adjustments f o r o v e r - c o m p e t i t i o n — m e r g e r , s t a t e s m a n l i k e agreement, or b u s i n e s s f a i l u r e . 7 T h i s was demonstrated i n 1969 when f i v e c a r r i e r s were p e r m i t t e d by the C.A.B. t o j o i n t hree a l r e a d y - c e r t i f i c a t e d g c a r r i e r s i n f l y i n g the Hawaii r o u t e . Marketing p r o v i d e s the found a t i o n t h a t supports the business s t r u c t u r e . Market surveys u s u a l l y precede b u s i n e s s A v i a t i o n Week and Space Technology, February 2 , 1 9 7 0 , p. 3 6 . 7 Tom Alexander, "Is There Any Way to Run an A i r l i n e ? " Fortune V o l . LXXXII, No. 3 , September 1 9 7 0 , p. 1 1 7 . a c t i v i t i e s , and success depends upon f l e x i b i l i t y and inno-v a t i o n i n adapting to market changes. E a s t e r n A i r L i n e s ' " A i r Bus" s e r v i c e i s an example of i n n o v a t i o n i n the American market f o r a i r t r a v e l . There are no r e s e r v a t i o n s , no food, no refund w i t h i n twenty-four hours, and passengers c a r r y 9 t h e i r own baggage.to the gate. Marketing i s demand-oriented and i s concerned w i t h a c t u a l or p o t e n t i a l revenues from f a r e s , excess baggage, m a i l , f r e i g h t , c h a r t e r and other s e r v i c e s t o the p u b l i c or to o t h e r a i r l i n e s . A i r l i n e market-i n g o r g a n i z a t i o n s are s u b j e c t to change, as i n U n i t e d A i r L i n e s ' t r a n s f e r of s a l e s promotion to a d v e r t i s i n g , or Trans World A i r l i n e s ' . e l i m i n a t i o n of i t s a d v e r t i s i n g department (but not of advertising)."*"^ E x p erimental s e r v i c e s , f o r example, suburban c h e c k - i n f o r the New York m e t r o p o l i t a n area, w i t h w a i t i n g rooms, p a r k i n g space, baggage and t i c k e t c h e c k i n g , have been t r i e d i n an attempt to generate t r a f f i c and t o r e l i e v e a i r p o r t congestion."'""*' to meet com p e t i t i o n from c h a r t e r o p e r a t i o n s , scheduled t r a n s a t l a n t i c European. c a r r i e r s began p o o l i n g marketing data t h a t were for m e r l y 12 c o n f i d e n t i a l . Feedback from the t r a v e l l i n g p u b l i c i s of 9 M.A. M c l n t y r e , "Managerial I n i t i a t i v e and Government R e g u l a t i o n , " P e r s p e c t i v e s i n T r a n s p o r t a t i o n , e d i t e d by K a r l M. Ruppenthal, S t a n f o r d ~ C a l i f o r n i a , S t a n f o r d U n i v e r s i t y Graduate School of Business, 1 9 6 3 , pp. 1-8. " ^ A v i a t i o n Week and Space Technology, September 7, 1 9 7 0 , p. 3 0 . 1 : L I b i d . 1 2 I b i d . , 26 A p r i l 1 9 7 0 , p. 3 5 . g r e a t i n t e r e s t t o the a i r l i n e s . Immediately f o l l o w i n g Pan American Airways' i n t r o d u c t i o n of B747 s e r v i c e , passenger surveys were conducted to t e s t r e a c t i o n t o the new a i r -13 c r a f t . The 1969 i n c r e a s e s i n passenger complaints r e g a r d -in g s e r v i c e i r r e g u l a r i t i e s and o v e r s a l e s c o u l d not be ignored. Ground h a n d l i n g problems w i t h " b e l l y " f r e i g h t , ( f r e i g h t c a r r i e d below the passenger deck), came with the j e t age. B e t t e r s e r v i c e and h i g h e r p r o f i t s depend on b e t t e r knowledge of a i r f r e i g h t u s e r s , t h e i r reasons f o r u s i n g a i r f r e i g h t , 15 types of cargo and o r i g i n - d e s t i n a t i o n p a t t e r n s . Operations r e s e a r c h i n marketing w i l l be c o n s i d e r e d under three headings: (1) F o r e c a s t i n g , (2) Promotion, and (3) P r i c i n g . I. OPERATIONS RESEARCH IN AIRLINE FORECASTING T r u n k l i n e . lo a d f a c t o r s (domestic U n i t e d S t a t e s and i n t e r n a t i o n a l r o u t e s ) , averaged f o r t y - s i x per cent i n November .1969. The U n i t e d States.domestic average load 13 I b i d . , August 3, 1970, p. 21.. 14 I b i d . , January 12, 1970, p. 33. D. H. Reeher, " A i r F r e i g h t Has Problems on the Ground," Business Horizons, V o l . 11, No. 1, February, 1968, pp. 33-38. f a c t o r was o n l y f o r t y - t h r e e p e r c e n t , r a n g i n g between t h i r t y -s e v e n and f i f t y - t h r e e p e r c e n t . T h e s e low a v e r a g e s r e f l e c t e d a d i p i n t r a f f i c g r o w t h f r o m e i g h t e e n p e r c e n t p e r annum i n 1 9 6 8 t o t e n p e r c e n t p e r annum i n 1 9 6 9 , and t h e a d d i t i o n o f 16 s i g n i f i c a n t new c a p a c i t y . D u r i n g 1 9 6 9 a v a i l a b l e s e a t m i l e s i n c r e a s e d by a b o u t s i x t e e n p e r c e n t . S c a n d i n a v i a n A i r l i n e S y s t e m r e q u e s t e d p o s t p o n e m e n t o f t h e d e l i v e r y o f f i v e DC-9 a i r c r a f t f r o m M c D o n n e l l D o u g l a s b e c a u s e a c t u a l t r a f f i c g r o w t h was below t h e e x p e c t e d t w e n t y p e r c e n t f o r 1 9 6 9 . 1 7 F o r s w o o d C. W i s e r J r . , p r e s i d e n t o f T r a n s W o r l d A i r l i n e s w a s q u o t e d as s a y i n g t h a t i n t r o d u c t i o n o f t h e B o e i n g 7 47 was p r e m a t u r e , and t h a t t h e t r i - j e t s , t h e L o c k h e e d L - 1 0 1 1 and t h e M c D o n n e l l D o u g l a s DC-10 s h o u l d have come 1 8 f i r s t . By t h e end o f 1 9 7 0 t h e a i r l i n e s f a c e d s e r i o u s o v e r c a p a c i t y . However, d e c i s i o n s t o buy t h e 7 4 7 and t r i - j e t a i r c r a f t were made d u r i n g a p e r i o d o f o p t i m i s m . I n 1 9 6 7 p a s s e n g e r t r a f f i c f o r e c a s t s f o r 1 9 7 5 p r e d i c t e d t h r e e o r f o u r t i m e s t h e 1 9 6 5 volume. F r e i g h t t r a f f i c was e x p e c t e d t o 19 m u l t i p l y by a f a c t o r o f s e v e n o r e i g h t . 16 A v i a t i o n Week and Spa c e T e c h n o l o g y , J a n u a r y 1 2 , 1 9 7 0 , p . 29"7 1 7 I b i d . , J a n u a r y 1 9 , 1 9 7 0 , p. 3 1 . I 8 I b i d . , F e b r u a r y 2, 1 9 7 0 , , p. 3 7 . 19 K n u t H a m m a r s k j o l d , " E c o n o m i c I m p l i c a t i o n s o f H i g h C a p a c i t y J e t s and S u p e r s o n i c A i r c r a f t , " F i n a n c i a l A n a l y s t s  J o u r n a l , M a r c h - A p r i l , 1 9 6 7 , p. 6 7 . In 1971,. worries at a i r l i n e s head o f f ices resul ted from over-capaci ty . Ev ident ly t r a f f i c growth forecasts were h igh . Does t h i s mean that the forecast ing models were incorrect? W i l l there be rev i s ions i n forecast ing techniques to prevent a recurrence of such errors? Perhaps the,answers to these questions are best given by examination of some forecast ing methods. Demographic Studies. and Regression Analys i s attempt to re l a te a i r l i n e a c t i v i t y to market condi t ions . Character-i s t i c s of the market such.as geographic d i v i s i o n s , economic a c t i v i t y and growth, t ransportat ion economics wi th in the market area, per capi ta wealth, and so on, are assumed to a f fect a i r l i n e t r a f f i c . Regression analys i s indicates how a i r l i n e t r a f f i c i s . a f f ec t ed ,by selected market c h a r a c t e r i s t i c s . Regression analyses can usua l ly specify degrees of confidence that may be placed i n the re su l t s obtained. Proper forecast ing depends upon. inc lus ion of a l l s i g n i f i c a n t f ac tor s , (to which the model i s s e n s i t i v e ) , but omission of s i g n i f i c a n t factors may be acceptable i n the model provided that the omitted factors remain constant during the forecast per iod . Government monetary p o l i c i e s and the consequent economic slow-down were s i g n i f i c a n t between 1967 and 1971. This affected business genera l ly , inc lud ing a i r -l i n e t r a f f i c . Actua l events i n 1970 should have been i n c loser accord with 1967 forecasts were i t not for changes t h a t o c c u r r e d xn v a r i a b l e s omitted from f o r e c a s t c o n s i d e r - . a t i o n . New markets may l a c k adequate h i s t o r i e s from which t o develop r e g r e s s i o n a n a l y s e s . Two s t u d i e s by S t a n l e y H. Brewer i l l u s t r a t e methods of e s t i m a t i n g market needs from 20 21 d a t a a v a i l a b l e . ' In 1956, the Boeing company commissioned a study of the Europe-Asia market f o r a i r f r e i g h t . As a p o t e n t i a l t r a d i n g zone, Europe-Asia had long d i s t a n c e s and p r o s p e c t s of r a p i d economic growth, p a r t i c u l a r l y i n high - v a l u e commodities. U n f o r t u n a t e l y , o r g a n i z e d a i r t r a n s p o r t a t i o n 22 i n f o r m a t i o n was c o n s i d e r e d inadequate. Model f o r m u l a t i o n was t h e r e f o r e achieved p a r t l y by analogy. The h y p o t h e s i s was t h a t there should be a c l o s e and p o s i t i v e c o r r e l a t i o n between economic growth and growth of a i r t r a n s p o r t . I f t h i s proved v a l i d f o r any t r a d i n g zone, i t might be assumed v a l i d f o r the Europe-Asia t r a d i n g zone. P u b l i s h e d data on trade and economic growth i n post war Europe p r o v i d e d a r e c o r d of commodity movements i n Europe and commodity movements between Europe and the U n i t e d S t a t e s . 20 S t a n l e y H. Brewer, J . Rosenzweig, and J . Warren, B r i t i s h Columbia's Need f o r a U n i f i e d R e g i o n a l A i r Trans-p o r t a t i o n , S e a t t l e : U n i v e r s i t y of Washington, Graduate School of Business, 1965. 21 S t a n l e y H. Brewer, E.K. Fremont, and J.E. Rosenzweig, The Europe-Asia Market f o r A i r F r e i g h t , S e a t t l e : U n i v e r s i t y o f Washington, C o l l e g e of Business A d m i n i s t r a t i o n , 1963." The h y p o t h e s i s was confirmed f o r post-war Europe, 2 3 c h i e f l y by r e g r e s s i o n a n a l y s i s of data a v a i l a b l e . A model was developed, e x p r e s s i n g a i r t r a n s p o r t as a f u n c t i o n of economic a c t i v i t y . As a i r cargo c o n s t i t u t e d l e s s than one per cent of t o t a l cargo shipments, i t was necessary to r e -l a t e the use o f a i r t r a n s p o r t t o the value and type of commodity, r a t h e r than merely t o e x t r a p o l a t e a i r t r a f f i c as a f u n c t i o n of t o t a l t r a d e growth. Using t h i s model a f o r e -c a s t o f Europe-Asia a i r t r a f f i c was d e r i v e d , g i v i n g p r o j e c t e d a i r cargo p o t e n t i a l s f o r . 1 9 6 5 , 1 9 7 0 , and 1 9 7 5 . In 1 9 6 3 the annual r a t e of growth f o r a i r cargo t r a f f i c between Europe and A s i a was p r e d i c t e d at n e a r l y t h i r t y per cent. These r e s u l t s were r e l a t e d t o c o s t - p r i c e developments i n a i r t r a n s p o r t by f o r e c a s t statements i n the form of graphs f o r p o t e n t i a l f r e i g h t i n each d i r e c t i o n over a range of con-c e i v a b l e charges per t o n - m i l e . Europe-Asian development was p r o j e c t e d i n terms of p o p u l a t i o n and gross n a t i o n a l product, based on U n i t e d Nations e s t i m a t e s . Two qu e s t i o n s are suggested by the growth assumptions. What are the e f f e c t s of p o p u l a t i o n growth on gross n a t i o n a l product i n c o u n t r i e s t h a t are a l r e a d y h e a v i l y populated? What e f f e c t s on trade p a t t e r n s c o u l d be expected from p o t e n t i a l p o l i t i c a l realignments? These que s t i o n s may have been o u t s i d e the study terms of r e f e r e n c e . In e v a l u a t i n g t r e n d s , s e v e r a l methods are a v a i l a b l e . The s i m p l e s t method i s t o p l o t a b s o l u t e demand data a g a i n s t time and to draw a v i s u a l approximation of a b e s t f i t s t r a i g h t l i n e . Greater p r e c i s i o n of f i t can be obtained 2 4 u s i n g the method of l e a s t .squares. C u r v i l i n e a r trends can be f i t t e d i n s i m i l a r f a s h i o n by p l o t t i n g logarithms of the f u n c t i o n s , or by means of Gompertz f u n c t i o n s of three v a r i a b l e s , . s e l e c t e d by hypothesis or by t r i a l and e r r o r 25 methods. M u l t i p l e l i n e a r r e g r e s s i o n expresses a dependent v a r i a b l e such as demand, i n terms of up to f i f t e e n independent v a r i a b l e s (such as e x p o r t s , imports and p o p u l a t i o n ) , but f o r e c a s t i n g the independent v a r i a b l e s may be as d i f f i c u l t 2 6 as f o r e c a s t i n g demand i t s e l f . Mr. R.W. -Linder has d e s c r i b e d A i r Canada's econometric 27 model f o r long term f o r e c a s t i n g : m a l a2 a3 , r b l „b2 T = cx^ * x 2 * x 3 "* * * 1 * 2 * * * * ' ' where T = A i r Canada t o t a l . . t r a f f i c volume x^ = p o l i c y v a r i a b l e i Yj = socio-economic or c o m p e t i t i v e v a r i a b l e j c = a constant a.,b. = e l a s t i c i t i e s of T with r e s p e c t to the i n d e -1 -1 pendent v a r i a b l e s 24 Taro Yamane,.. S t a t i s t i c s : An I n t r o d u c t o r y A n a l y s i s , New York: Harper & Row, 2nd e d i t i o n , 1967, p. 339. 2 5 W i n f r i e d Grassman, "The I n t r i c a c i e s of F o r e c a s t i n g , " AGIFORS Proceedings, 1967, p. 244. T h i s m u l t i p l i c a t i v e model i s updated a n n u a l l y by r e g r e s s i o n a n a l y s i s of A i r Canada and other d a t a . S e l e c t i o n of v a r i a b l e s i s fundamental t o v a l i d i t y of the model, both f o r i n c l u s i o n of s i g n i f i c a n t v a r i a b l e s and f o r e x c l u s i o n of redundant v a r i a b l e s . The presence i n the model of c o r r e l a t e d v a r i a b l e s i s c a l l e d m u l t i c o l i n e a r i t y , a c o n d i t i o n t h a t may b i a s model output. A r e g r e s s i o n a n a l y s i s w e l l known to a i r l i n e s i s the McDonnell Douglas Econometric Passenger Demand F o r e c a s t i n g Model, a complex s t r u c t u r e comprised of s i x main p a r t s t h a t 2 8 are b r i e f l y d e s c r i b e d below. P a r t One i s an a d d i t i v e l i n e a r m u l t i p l e r e g r e s s i o n t h a t f o r e c a s t s c i t y p a i r revenue passengers by r e l a t i n g c i t y p a i r a i r t r a f f i c growth t o the t o t a l domestic a i r l i n e s i n d u s t r y growth. C i t y p a i r trends are assumed t o h o l d r e l a t i v e l y f i x e d r e l a t i o n s h i p s w i t h t o t a l market t r e n d s . These r e l a t i o n s h i p s can change over time,, and are t e s t e d and 2 6 T b i d . 27 Roger W. L i n d e r , "Models f o r P l a n n i n g and C o n t r o l , " AGIFORS Proceedings, 1969. 2 8 Ronald J . Schmidt, "Econometric Passenger Demand F o r e c a s t i n g Model," Long Beach, C a l i f o r n i a , Douglas  Paper 5057, May 1968. redefined i f necessary. The qu a l i t y of forecast data obtained at t h i s stage, i s . r e f l e c t e d i n a c o e f f i c i e n t of v a r i a t i o n for each c i t y p a i r : V. = S. /X. c o e f f i c i e n t of v a r i a t i o n for c i t y p a i r i standard deviation of the estimate for c i t y pair i mean of the estimates for c i t y p air i . Part Two predicts c i t y p a i r t r a f f i c by extrapolation of h i s t o r i c a l c i t y p air t r a f f i c data, using a geometric progression technique. This procedure i s independent of the approach taken i n Part One. Part Three i s a microanalytic approach that forecasts c i t y p air t r a f f i c by measurement of pertinent h i s t o r i c a l 29 variables such as per capita disposable income. The resultant equation resembles A i r Canada's econometric model. Part Four i s an alternative forecasting routine used instead of parts one, two, and three when market growth i s negative. I t i s a. microanalytic approach based on disposable income d i s t r i b u t i o n , population household d i s t r i b u t i o n , and q u a l i t y factors such as service frequency,•and type of Ibxd. where V. = I S. = l X. = l a i r c r a f t . The procedure i s c a l l e d c r o s s - s e c t i o n a n a l y s i s . P a r t F i v e i s an averaging process by which the r e s u l t s of P a r t s One> Two, and Three are weighted i n v e r s e l y i n p r o p o r t i o n t o the c o e f f i c i e n t s of v a r i a t i o n . T h i s procedure i s not r e q u i r e d i n the circumstance of a c r o s s -s e c t i o n a n a l y s i s , when only the P a r t Four f o r e c a s t i s a v a i l a b l e . P a r t S i x a l l o c a t e s market share among competitors. In 1968, Douglas c o u l d o f f e r no v i a b l e o b j e c t i v e f u n c t i o n f o r d e t e r m i n a t i o n of market share. The d i f f i c u l t i e s of f o r m u l a t i n g such a f u n c t i o n are many. Market share i s a f f e c t e d by e n t r i e s and e x i t s of c a r r i e r s i n c i t y p a i r markets, changes i n numbers and types of a i r c r a f t used, market growth and d e n s i t y changes, through s e r v i c e or s t o p - s e r v i c e a u t h o r i z -a t i o n s , and h i s t o r i c a l market share r a t i o n a l i z a t i o n . Conse-q u e n t l y , the th r e e approaches most o f t e n used are as f o l l o w s : 1. Subject w e i g h t i n g of h i s t o r i c a l market shares. 2. H i s t o r i c a l revenue passenger m i l e s weighted market shares. 3. I n t u i t i v e e x t r a p o l a t i o n of l a s t year's share. Although the Douglas model c o n t a i n s much s o p h i s t i c a t e d s t a t i s t i c a l . a nalysis, output i s h i g h l y dependent upon i n t u i t i o n and judgement both i n the assessment of competitors' a c t i o n s and i n proper i n t e r p r e t a t i o n of ge n e r a l economic c o n d i t i o n s . ExponentiaI.Smoothing. Without a demand h i s t o r y , f o r e c a s t i n g can be done by i n t u i t i v e weighting of known demo- • g r a p h i c f a c t o r s . A f t e r a p e r i o d of scheduled o p e r a t i o n , a c t u a l demand may e x h i b i t seasonal and t r e n d p a t t e r n s . The si m p l e s t form of e x p o n e n t i a l smoothing, however, assumes no knowledge of tr e n d or seasonal f a c t o r s and i s given by the f o l l o w i n g : ~ = AS + (l-A)S. , & t + l t t where S f c = a c t u a l demand i n p e r i o d t S^_ = f o r e c a s t demand f o r p e r i o d t , (made i n p e r i o d t - l ) 0 < A < 1. Small v a l u e s f o r A make the model l e s s s e n s i t i v e t o c u r r e n t demand. F o r e c a s t s based on the simple e x p o n e n t i a l smoothing model are e a s i l y compiled. F i g u r e 1 compares a c t u a l and f o r e c a s t demand f o r a s i n u s o i d a l demand p a t t e r n w i t h constant upward t r e n d . . The f o r e c a s t p a t t e r n resembles the p a t t e r n of a c t u a l demand, but the f o r e c a s t departs from r e a l i t y i n two r e s p e c t s . The amplitude of the f o r e c a s t i s l e s s than a c t u a l and the f o r e c a s t lags the a c t u a l demand curve, i n t h i s case by approximately one q u a r t e r c y c l e . Both o t these f a u l t s i n the f o r e c a s t can be reduced by i n c r e a s i n g the f o r e c a s t frequency, but some d e v i a t i o n and some l a g w i l l always be pr e s e n t . More s a t i s f a c t o r y c o r r e c t i o n s can be b u i l t i n t o the e x p o n e n t i a l smoothing -*N t o -e=-/ O O .O 0 Q A ft A <> -Or \ 'ff Y i d ' 0 I 4. v w \> 4 I CO 4***-i ,1 0 4 16' i t r 1^ model i f seasonal and t r e n d data are g i v e n . F o r e c a s t s obtained by these methods assume t h a t no f a c t o r of demand changes r a p i d l y . The model i s s e n s i t i v e t o g r a d u a l change, and i n e f f e c t , smooths out random f l u c t u a t i o n s . I f major changes are r e c o g n i z e d i n demand f a c t o r s , f o r e c a s t s should be a d j u s t e d a c c o r d i n g l y . E x p o n e n t i a l smoothing models are r e l a t i v e l y easy t o c o n s t r u c t . In o p e r a t i o n they r e q u i r e very l i t t l e computer storage c a p a c i t y . E x p o n e n t i a l smoothing was used to p r o j e c t t r a f f i c volumes f o r i n d i v i d u a l s e c t o r s of the A i r Canada route net-work. F o r e c a s t s f o r short.range up to two years were based on three e x p o n e n t i a l l y smoothed components: (1) c u r r e n t average t r a f f i c , (2) c u r r e n t t r e n d i n t r a f f i c volume, and (3) c u r r e n t monthly seasonal f a c t o r . T h i s model was d e s c r i b e d as crude, d e s c r i p t i v e and d e t e r m i n i s t i c , but was c o n s i d e r e d 31 p r a c t i c a l f o r s h o r t range p r o j e c t i o n s . Simulation i n market f o r e c a s t i n g was i l l u s t r a t e d by two Lockheed programs; A i r l i n e S i m u l a t i o n f o r A n a l y s i s of 32 3 Commercial A i r p l a n e Markets, and A i r l i n e System S i m u l a t i o n . P.R. Winters, " F o r e c a s t i n g Sales by E x p o n e n t i a l l y Weighted Moving Averages," Mathematical Models and Methods i n Marketing, Bass, F.M., e t a l . , (eds.), Homewood, Irwi n , 1961, pp. 482-513. 31 R.W. L i n d e r , op_. c i t . 32 Lee R. Howard and 0. Duane Eberhardt, A i r l i n e S i m u l a t i o n f o r A n a l y s i s of Commercial A i r p l a n e Markets, Trans-p o r t a t i o n S c i e n c e , V o l . 1, No. 3, 1967, pp. 131-157. Both models were based on s i m i l a r assumptions w i t h r e s p e c t to market f o r e c a s t i n g . Route i n t e r a c t i o n occurs when two or more scheduled routes connect a g i v e n c i t y p a i r . In the diagram below, two-d i r e c t i o n a l paths connect the p o i n t s LAX, CHI, and PIT. A passenger t r a v e l l i n g from LAX to PIT may go d i r e c t l y or by way of a one-stop route through CHI. S i m i l a r l y , a passenger going from LAX to CHI may use the one-stop route through PIT. Thus on the LAX-PIT route there are three components CHI F i g u r e 2 Simple Route Network of demand. For r e a l i s m i n t r a f f i c f o r e c a s t i n g these should be c o n s i d e r e d . U n f o r t u n a t e l y , n e i t h e r Lockheed paper e x p l a i n s how route i n t e r a c t i o n s are e v a l u a t e d and i n c o r p o r a t e d i n t o the models. F l i g h t frequency a f f e c t s demand except sometimes where no a l t e r n a t i v e form of t r a n s p o r t a t i o n i s a v a i l a b l e . The 33 W i l l i a m A. Gunn, " A i r l i n e System S i m u l a t i o n , " Operations Research, 1 2 , 1 9 6 4 , pp. 2 0 6 - 2 2 9 . assumptions of the model were t h a t (1) demand i s u n i f o r m l y d i s t r i b u t e d , (2) f l i g h t s are u n i f o r m l y spaced throughout the schedule p e r i o d , (3) p e r s i s t e n c e of passenger demand f o r a p a r t i c u l a r f l i g h t i s normally d i s t r i b u t e d about the passenger's d e s i r e d departure time, and (4) the standard d e v i a t i o n of the p e r s i s t e n c e of demand t i m e - d i s t r i b u t i o n w i l l be o ne-half of the . corresponding time t o t r a v e l by road. Demand i s not u n i f o r m l y d i s t r i b u t e d from the p o i n t of view of a s i n g l e c a r r i e r . . Connecting f l i g h t s can impose sharp demand break p o i n t s and time o f day demand f l u c t u a t i o n s are r e a l . F l i g h t s are not u n i f o r m l y spaced i n p r a c t i c e . There tend t o be p e r i o d s o f g r e a t e r a c t i v i t y between 8 and 34 10 AM and between 5 and 10 PM. The p e r s i s t e n c e of demand assumptions appear reasonable i f c o m p e t i t i v e a i r l i n e t r a f f i c i s i n c l u d e d i n the model. Fares a f f e c t demand i n two ways. A low f a r e generates demand by a t t r a c t i n g t r a f f i c t h a t otherwise would not have flown, and by d i v e r t i n g t r a f f i c from more expensive a l t e r n a t e f l i g h t s and from other modes of t r a n s p o r t a t i o n . The two e f f e c t s were not e v a l u a t e d p r e c i s e l y , mainly f o r l a c k of s u f f i c i e n t d a t a , but Lockheed estimated e x t e r n a l e l a s t i c i t i e s of demand f o r t r a v e l as f o l l o w s : M e l v i n A. Brenner, " P u b l i c Demand and A i r l i n e S c h eduling," A i r T r a n s p o r t a t i o n A s s o c i a t i o n paper, 1 9 6 8 , p. 2 4 . Business; 10 per cent. Non-business: 140 per cent. Speed i s a demand f a c t o r i n terms of both absolute and r e l a t i v e t r i p times. J e t a i r c r a f t have s h o r t a b s olute t r i p times compared w i t h p r o p e l l e r - d r i v e n a i r c r a f t . However, slow a i r c r a f t may have .a r e l a t i v e t r i p time advantage i f there i s a s i g n i f i c a n t w a i t i n g time b e f o r e the next scheduled j e t f l i g h t . A b s o l u te and r e l a t i v e t r i p time demands are i n c o r p o r a t e d i n t o model a l l o c a t i o n s of t r a f f i c . Passenger p r e f e r e n c e i s " s u r e l y a f a c t o r of ignorance, p r e j u d i c e and emotion as w e l l , as other more q u a n t i t a t i v e 35 f a c t o r s such as s i z e , number of engines," and although i t i s r e a l , passenger p r e f e r e n c e has been omitted form models f o r l a c k of q u a n t i f i a b l e and o b j e c t i v e d ata. The Lockheed A i r l i n e System S i m u l a t i o n has been i n use s i n c e 1961. During t h i s time the model was improved, but d e s p i t e the complex s i m u l a t i o n based on demand f a c t o r s d e s c r i b e d above, the r e s u l t a n t model may have been an o v e r s i m p l i f i c a t i o n . Perhaps t h i s would be.true of any f o r e c a s t t h a t o f f e r e d comprehensive assessment of a l l route t r a f f i c c h a r a c t e r i s t i c s . The main assumptions of the model appear to be those t h a t p e r t a i n t o f l i g h t frequency. Demand was assumed t o be u n i f o r m l y d i s t r i b u t e d . F l i g h t s were assumed to be u n i f o r m l y W i l l i a m A. Gunn, " A i r l i n e System S i m u l a t i o n , " L o c k h e e d - C a l i f o r n i a Company Paper, A p r i l 1962, p. 18. spaced i n time.. T h i s does not r e f l e c t the world of peak demands and a i r c r a f t r o t a t i o n s and connections t h a t prevent uniform time spacings between f l i g h t s . However, c e r t a i n a b e r r a t i o n s of i n p u t may be t o l e r a b l e . P r o f e s s o r Shaw's s i m u l a t i o n of schedule e f f e c t s on passenger volume i n d i c a t e s t h a t demand i s s e n s i t i v e to frequency but much l e s s s e n s i t i v e 3 6 t o time of d e p a r t u r e . C o n c l u s i o n s : Market F o r e c a s t i n g Three b a s i c techniques have been d e s c r i b e d : (1) r e -g r e s s i o n a n a l y s i s , (2) e x p o n e n t i a l smoothing, and (3) s i m u l a t i o n . A l l three approaches attempt to s t e e r by "watching the r e a r view m i r r o r , " and a l l r e q u i r e major c o n t r i b u t i o n s of human judgement. These o b s e r v a t i o n s prompt the q u e s t i o n of why models are used at a l l . Some j u s t i f i -c a t i o n s are as f o l l o w s : 1. Computer or manual models allow management.to con-c e n t r a t e on . the judgement aspects e x c l u s i v e l y . O p e r a t i o n a l d e t a i l s can be d e l e g a t e d t o a computer or to j u n i o r s t a f f . 2. Models serve to p i n p o i n t s p e c i f i c judgemental i n -puts and p r o v i d e e x p l i c i t e v a l u a t i o n of a l t e r n a t e i n p u t assumptions. 3 6 G.C. Shaw, "The S c h e d u l e — i t s E f f e c t on Passenger Volume," AGIFORS Proceedings, 1 9 6 8 , p. 1 6 0 . 3. Models remove some of the mystique of forecast-ing by the use of standard procedures, and at the same time treat . judgemental i n p u t s . i n a consis tent manner. 4 . Models can be adjusted or updated e x p l i c i t l y whereas human experience i s l a rge ly personal and non-transferrable , p a r t i c u l a r l y i n the short term. 5. Computer models should be fast and accurate. They can in te rpre t a number of inputs and ramify the output to include thousands of d e t a i l s contingent upon the input dec i s ions . I I . OPERATIONS RESEARCH IN ADVERTISING A i r l i n e markets can be considered under two main headings: 1. Business, and 2. Non-business. The business market buys transport presumably for economic reasons. Business demand -is presumed to be r e l a t i v e l y i n e l a s t i c . The "product" i s time saved. Pr ivate i n d i v i d u a l t r a v e l l i n g for urgent personal reasons could be included as part of the business market. The non-business market buys passenger transport for reasons that are par t ly non-economic The product i s a r r i v a l at a chosen d e s t i n a t i o n , r e u n i o n with f r i e n d s or f a m i l y , or other p l e a s u r e a c t i v i t y . Demand i s 37 r e l a t i v e l y e l a s t i c . Business market s u s c e p t i b i l i t y to a d v e r t i s i n g appeal i s c o n s i d e r e d somewhat s t o l i d . Business a d v e r t i s i n g then should be i n f o r m a t i v e , f a c t u a l , and h e l p f u l i n showing what s e r v i c e s are a v a i l a b l e (door to d o o r ) , and how to c a l c u l a t e economic s h i p p i n g q u a n t i t i e s to take advantage of p r i c e breaks. The aims of busi n e s s a d v e r t i s i n g would appear t o be: (1) r e a l i z a t i o n of f u l l e c o n o m i c a l l y j u s t i f i e d a i r t r a f f i c p o t e n t i a l , and (2) attainment of hi g h share of market f o r reasons of performance and s e r v i c e . The non-business market i s g e n e r a l l y more s u s c e p t i b l e t o emotional appeal than the business market, and market p o t e n t i a l i s not l i m i t e d e n t i r e l y by economic f a c t o r s . A d v e r t i s i n g should aim a t i n c r e a s i n g market demand, and a t c a p t u r i n g the b e s t p o s s i b l e share. G l a m o r i z i n g a p a r t i c u l a r r e s o r t may a t t r a c t more customers, but i f the a i r l i n e i s one of many s e r v i n g the same r o u t e , the b e n e f i t s of a d v e r t i s -i n g may go i n l a r g e p a r t t o compe t i t o r s . In concept, a d v e r t i s i n g d e c i s i o n requirements are s t r a i g h t f o r w a r d . Simple and p e r s u a s i v e messages are to be Lee R. Howard, and Duane 0..Eberhardt, op. c i t . , p. 137. d e l i v e r e d to everyone who may be i n t e r e s t e d , s u b j e c t t o the c o n s t r a i n t t h a t expenditures on a d v e r t i s i n g should y i e l d new p r o f i t s t h a t reward the a d v e r t i s e r a t h i s r e q u i r e d r a t e of r e t u r n on investment. A d v e r t i s i n g d e c i s i o n s may be rep r e s e n t e d d i a g r a m a t i c a l l y as f o l l o w s : GOALS \ APPEALS• BUDGET MEDIA• NET RETURN FORMAT FINAL SPECIFICATION F i g u r e 3 A d v e r t i s i n g Decion F a c t o r s P o t e n t i a l a d v e r t i s i n g reach i n c l u d e s a l l who may be exposed to a giv e n medium. Word of mouth i n c l u d e s everybody, but i s slow. Radio and t e l e v i s i o n messages are r e c e i v e d a t the i n s t a n t of d e l i v e r y or not at a l l . A d v e r t i s i n g i n j o u r n a l s and magazines may not be seen, or i f seen, may not be read. A c t u a l r e a c h i s l e s s than p o t e n t i a l reach, but a c t u a l reach can be measured by sampling methods. On the oth e r hand, a d v e r t i s i n g response i s d i f f i c u l t t o measure except i n s p e c i a l circumstances such as want-ads t h a t p u b l i c i z e a s i n g l e event, or a d v e r t i s e a s i n g l e a r t i c l e . Response t o a i r l i n e s advertisements may p e r s i s t f o r many months a f t e r d e l i v e r y of the message. Using aggregate data i t i s easy to confuse cause and e f f e c t i n c o n s t r u c t i n g 3 8 marketing models. A d v e r t i s i n g Reach A d v e r t i s i n g reach f o r r a d i o or t e l e v i s i o n can be estimated by means of telephone surveys. Magazine and j o u r n a l c i r c u l a t i o n f i g u r e s are known. However, i f • a d v e r t i s e m e n t s are i n s e r t e d i n s e v e r a l magazines, reach i s not the cumulative c i r c u l a t i o n but something l e s s because of d u p l i c a t i o n . Magazine a d v e r t i s i n g reach was found to be w e l l approximated 3 9 by M.M. A g o s t i n i ' s model: D _ A ( l ) (K • A ( 2 ) / A ( l ) + 1) I where A ( l ) = A^ = t o t a l t a r g e t group members i n audience of media 1, 2, A(2) = Z £ . = t o t a l of a l l p a i r w i s e i = l j = i + l -1 d u p l i c a t i o n of the I media K =. 1.125 3 8 A. Mercer, " O p e r a t i o n a l Research i n Marketing," O p e r a t i o n a l Research Q u a r t e r l y , V o l . 17, No. 3, p. 244. 39 .. David B. Montgomery, and Glen L. Urban, Management  Science in. Marketing, Englewood C l i f f s , P r e n t i c e H a l l , 1969 , p. 100. S i m u l a t i o n has been used to model the press and 40 t e l e v i s i o n r e a c h i n g a t a r g e t . A d e t a i l e d s i m u l a t i o n i n -c o r p o r a t e s many more v a r i a b l e s than say, A g o s t i n i ' s model. S i m u l a t i o n should o f f e r more r e a l i s m than simple models but d e s p i t e thousands of i n t e r v i e w s , assumptions are crude. Readership i s a f u n c t i o n . o f demography, and c h a r a c t e r i s t i c s of the t a r g e t w i t h r e s p e c t to the product and the a d v e r t i s e -ment . A d v e r t i s i n g Response A n a l y s i s of response has been attempted by s e v e r a l i n v e s t i g a t o r s . Four approaches t o the problem are d i s c u s s e d b r i e f l y i n the paragraphs f o l l o w i n g . Some impressive r e s u l t s have been obtained f o r s p e c i f i c i n d u s t r i e s , but response t o a d v e r t i s i n g remains a d i f f i c u l t task f o r a n a l y s i s . Benjamin, J o l l y and M a i t l a n d p o s t u l a t e d t h a t response 41 42 to a d v e r t i s i n g i s a l o g a r i t h m i c f u n c t i o n of the type: ' Response = a • l o g ( a d v e r t i s i n g spend) + b, where a, b, are c o n s t a n t s . E.M.L. Beale, P.A.B. Hughes, and S.R. Broadbent, "A Computer Assessment of Media Schedules," O p e r a t i o n a l  Research Q u a r t e r l y , V o l . 17, 1966, pp. 381-411. 41 B. Benjamin, J.W.P. J o l l y M a i t l a n d , " O p e r a t i o n a l Research and A d v e r t i s i n g : T h e o r i e s of Response," O p e r a t i o n a l  Research Q u a r t e r l y , XI, 1960, pp. 205-218. 42 B. Benjamin, J . M a i t l a n d , " O p e r a t i o n a l Research and A d v e r t i s i n g : Some Experiments i n the Use of A n a l o g i e s , " O p e r a t i o n a l Research Q u a r t e r l y , IX, September 1958, pp. 207-TTT. Marginal ef fect iveness of adver t i s ing decl ines as the adver t i s ing budget increases . The value for "a" depends on t o t a l industry sa les . Var iab le "b" i s a negative quantity that represents minimum expenditure for threshold response. J . Simon's assumption' was that revenues from advert is 43 ing dec l ine at a constant ra te . This i s a time re l a t ionsh that can be used to compare present values of adver t i s ing budget s t r a teg ie s . . Evaluat ion of response i t s e l f must be obtained by separate means. K. Palda studied a f i f ty- two year h i s tory of advert is 44 ing and sales for Lydia Pinkham's Vegetable Compound. A model for sales as a function of adver t i s ing was obtained by regress ion ana ly s i s . In t h i s case the regress ion analys i s accounts for ninety-two per cent of annual sales v a r i a t i o n , but to be re levant i n the a i r l i n e industry , the model might require extensive modi f i ca t ion . Assuming that the advert i s ing-sa les r e l a t i o n s h i p can be s p e c i f i e d , e i ther by analys i s or hypothesis , Gupta and Krishnan offered a d i f f e r e n t i a l equation approach to J . Simon, "A Simple Model for Determining Adver-t i s i n g Appropr i a t ions , " Journal of Marketing Research, August 1965, pp. 285-292. 44 K. Palda , The Measurement of Cumulative Adver t i s -ing E f f e c t s , Englewood" C l i f f s : Prent ice H a l l , 1964, pp. HF-J8T o p t i m i z a t i o n of s a l e s : T o t a l S a l e s = (market p o t e n t i a l ) ( 1 - e Y ) where y i s a constant A = a d v e r t i s i n g expenditure.. dS T h i s model y i e l d s the r e s u l t t h a t ^ = y ( a - S ) , where "a" i s market p o t e n t i a l . The e f f e c t i v e n e s s of a d v e r t i s i n g i s a v a r i a b l e t h a t d e c l i n e s as t o t a l s a l e s approach the market p o t e n t i a l . The model ignores time e f f e c t s i n response, and does not p r o v i d e f o r p r e s e n t - v a l u e a n a l y s i s of a l t e r n a t i v e s t r a t e g i e s . Perhaps the most impressive response a n a l y s i s model i s A.E. Amstutz's M i c r o a n a l y t i c S i m u l a t i o n . T h i r t e e n consumer c h a r a c t e r i s t i c s were r e l a t e d t o p r i c e , p e r s o n a l s e l l i n g e f f o r t , a d v e r t i s i n g and advertisement c h a r a c t e r i s t i c s , and 46 word of mouth communication. In one example, ten competing brands were ranked a c c o r d i n g to percentage market share. In a comparison between .actual r e s u l t s and model r e s u l t s , the sum of the ten a b s o l u t e f o r e c a s t e r r o r s was 5.1 per cent. T h i s was an impressive demonstration of s i m u l a t i o n c a p a b i l i t y combined wi t h s k i l l f u l assumptions i n the model s t r u c t u r e . 45 S.K. Gupta, and K.S. K r i s h n a n , "A D i f f e r e n t i a l E q u a t i o n Approach to Marketing," Ops. Res., V o l . 1 5 , No. 6, 1 9 6 7 , p. 1 0 3 0 . 46 A r n o l d E. Amstutz, Computer S i m u l a t i o n of Compet-i t i v e Market Response, Cambridge, Mass., M.I.T. Press~7 1 9 6 7 . I n c o n t r a s t w i t h m i c r o a n a l y t i c s i m u l a t i o n , d e c i s i o n t h e o r y o f f e r s s i m p l e m o d e l c o n s t r u c t i o n s f o r a d v e r t i s i n g b u d g e t s , b u t s i m p l i c i t y i n t h e model i s o f f s e t by t h e com-p l e x i t y o f t h e a s s u m p t i o n s i n v o l v e d . I f t h e d e c i s i o n maker i n company A i s w i l l i n g t o a s s i g n s u b j e c t i v e p r o b a b i l i t i e s t h a t c o m p e t i t o r s , s a y company B, w i l l s p e n d a t v a r i o u s p r e s c r i b e d l e v e l s , t h e n a p a y o f f t a b l e m i g h t be c o n s t r u c t e d f o r e a c h c o m b i n a t i o n o f company A and company B e x p e n d i t u r e s f o r a d v e r t i s i n g . A l t h o u g h ' company B's f u t u r e a c t i o n s a r e unknown, t h e s u b j e c t i v e p r o b a b i l i t y e s t i m a t e s , t r a n s f o r m t h e p r o b l e m o f u n c e r t a i n t y t o one o f r i s k . The f o l l o w i n g t a b l e shows t h r e e s t r a t e g i e s f o r company B, w i t h a s s o c i a t e d s u b -j e c t i v e p r o b a b i l i t i e s . T h r e e s t r a t e g i e s a r e a l s o shown f o r company A. The t a b l e i t s e l f c o n s i s t s o f e s t i m a t e d p a y o f f s f o r company A u n d e r t h e v a r i o u s c ombined s t r a t e g i e s . B u d g e t B: $100 $200 $300 E x p e c t e d ( P r o b a b i l i t y ) P a y o f f B u d g e t A (1/4) (1/2) (1/4) $100 400 200 160 $240 200 390 225 200 260 300 350 300 250 300 B a s e d on t h i s t a b l e , t h e h i g h e s t ( net) p a y o f f e x p e c t e d i s r e a l i z e d i f A sp e n d s $30 0 on a d v e r t i s i n g . A p a r t f r o m t h e d i f f i c u l t y o f a s s i g n i n g s u b j e c t i v e p r o b a b i l i t i e s t o t h e a c t i o n s o f c o m p e t i t o r s , p a y o f f v a l u e s t h e m s e l v e s must be assumed. Market share might be assumed p r o p o r t i o n a l t o company expenditure as a f r a c t i o n of t o t a l i n d u s t r y expenditure (on 47 a d v e r t i s i n g ) . T h i s assumes t h a t a d v e r t i s i n g e f f e c t i v e n e s s i s uniform throughout the i n d u s t r y , and t h a t ' c o m p e t i t o r s are d e f i n e d . In the non-business a i r l i n e market, c o m p e t i t i o n i s f o r d i s c r e t i o n a r y spending t h a t buys many t h i n g s other than a i r t r a v e l . At b e s t , c o m p e t i t i o n i s i l l - d e f i n e d . A c o n s t a n t sum game has a constant p r i z e . The p r i z e i s shared a c c o r d i n g to the success of the p a r t i c i p a n t s . An example i s g a s o l i n e s a l e s . T o t a l s a l e s are h a r d l y a f f e c t e d by promotional a c t i v i t y because consumers buy only what they need; they buy no more when p r i c e s are low. A i r l i n e s a l e s t o b u s i n e s s passengers might be a p a r a l l e l example. H.D. M i l l s developed t h r e e models, t h a t can apply to i n d u s t r i e s w i t h constant sum market c h a r a c t e r i s t i c s . In g e n e r a l , M i l l ' s models are of the f o r m : ^ E . P r o f i t s of brand i = V • „ 1 „ — • M - ,C -E E ± p f where V = p r e s e n t t o t a l market E^ = e f f e c t i v e promotional o u t l a y , f i r m i M = u n i t c o n t r i b u t i o n t o margin Cp =. p r o m o t i o n a l o u t l a y i n d o l l a r s = f i x e d c o s t s of p r o d u c t i o n and s e l l i n g 47 Montgomery and Urban, op. c i t . , p. 121. 4 8 H.D. M i l l s , "A Study i n Promotional Competition," Mathematical Models and Methods i n Marketing, Bass, F.M., e t a l . , (eds.) , Homewood") Irwin, 1961, pp. 271-301. Model v a l i d i t y depends h e a v i l y on the assessment of E^, a f a c t o r t h a t i n t u i t i v e l y can not be c o n s t a n t . Perhaps the value i n models of t h i s - type i s t h a t f o r m u l a t i o n r e q u i r e s an assessment of c o m p e t i t o r s ' a d v e r t i s i n g e x p e n d i t u r e s , and some s u b j e c t i v e e v a l u a t i o n of m a r g i n a l b e n e f i t from company investment i n a d v e r t i s i n g . S e v e r a l other game approaches have been developed. 49 L. Friedman has put forward a t l e a s t f i v e models. One model t h a t overcomes the d i f f i c u l t y with M i l l s ' model, (the e v a l u a t i o n of E . ) / was of the form: / a d v e r t i s i n g budget l / P r i c e l e s s 1. y Company A / = W. v a r i a b l e • S « B - B " c o s t s / u n i t 2 . A l l o c a t e budget to market " i " i n p r o p o r t i o n to market " i " as a f r a c t i o n of t o t a l s a l e s p o t e n t i a l where S = t o t a l market s a l e s p o t e n t i a l B = a d v e r t i s i n g budget, company B I f competitors a l l f o l l o w t h i s r u l e , the major determ-i n a n t of company a d v e r t i s i n g budgets i s : p r i c e minus v a r i a b l e c o s t s . T h i s i m p l i e s t h a t the company wi t h l e a s t c o s t s ( r e l a t i v e t o p r i c e ) w i l l a d v e r t i s e most and capture a L. Friedman, "Game Theory Models i n the A l l o c a t i o n of A d v e r t i s i n g Expenditure," Bass, e t a l . , (eds.), Mathematical Models and Methods i n Marketing, Homewood, Irwin, 1 9 6 1 , pp. 2 2 0 ^ 5 T : market share corresponding to i t s share of t o t a l industry advertising expenditure. The model yields a stable solution a f t e r several cycles (and adjustments) i n both companies. Media Selection I n t u i t i v e l y , an advertising budget should be spent on the best media f i r s t , and on successively less e f f e c t i v e media u n t i l the budget i s spent. On the other hand, the most expensive advertising i n any of the media could exhaust a large budget and leave l i t t l e or nothing to spend i n other media. Several l i n e a r programming models have been put forward for media se l e c t i o n . One of the simplest of these 50 models was proposed by Bass and Lonsdale: I maximize t o t a l exposure = ^ ^ R i X i i = 1 subject to ^ ^ C i X i — I B 1 1 — i = 1 0 < X. < L. for i = 1,2, ••• ,1 — l — l ' ' ' where R. = rated exposure value of an i n s e r t i o n i n medium " i " 50 F.M. Bass, and R.T.-Lonsdale, "An Exploration of L/P i n Media Selection," Journal of Marketing Research I I I , May 1966, pp. 179-187. X. = number of i n s e r t i o n s i n medium 11 i " 1 = c o s t per i n s e r t i o n i n medium " i " B = t o t a l a d v e r t i s i n g budget a v a i l a b l e L. = p h y s i c a l l i m i t of i n s e r t i o n s i n medium " i " T h i s f o r m u l a t i o n i s simple, but i t has shortcomings suggested above: . . . the r e s u l t i s o p t i m a l but i t r e p r e s e n t s c o n c e n t r a t i o n of the budget i n one or a few media. Since t h i s i s i n t u i t i v e l y i m p l a u s i b l e , users of the model were l e t t o s p e c i f y lower l i m i t s f o r the numbers of . i n s e r t i o n s i n each medium. These a r t i -f i c i a l c o n s t r a i n t s were added on the b a s i s of judgement. 51 P a r t of the t r o u b l e with t h i s l i n e a r programming approach i s t h a t the are c o n s t a n t s . A piecewise l i n e a r f o r m u l a t i o n of the L i n e a r Program co u l d be achieved by a s s i g n i n g two or more d i s c r e t e v a l u e s t o each of the R^, high v a l u e s f o r exposure valu e s of the f i r s t i n s e r t i o n s , and lower v a l u e s f o r succeeding (and l e s s e f f e c t i v e ) i n s e r t i o n s . T h i s would be, of course, f u r t h e r e x e r c i s e f o r s u b j e c t i v e judgement. Other approaches to media s e l e c t i o n i n c l u d e non-l i n e a r o p t i m i z i n g a l g o r i t h m s , s i m u l a t i o n , h e u r i s t i c programs * * . 5 2 and dynamic programming. "^Montgomery & Urban, op. c i t . , p. 144. 52 Pe t e r Langhoff, Models, Measurement and Marketing, Englewood C l i f f s , P r e n t i c e H a l l , 1965. L i t t l e and Lodish developed a dynamic programming model c a l l e d MEDIAC,. more complex than the Bass and Lonsdale 53 l i n e a r program. Included among factors considered were the population of each market segment, per capi ta sales p o t e n t i a l , exposure value of the media during spec i f i ed time in terva l s , , exposure e f f i c i e n c y and re tent ion from previous advertisements. Dozens of adver t i s ing models are i n the l i t e r a t u r e but , " u n t i l knowledge or f a i t h . increases , .mathematical soph i s t i c a t ion and elegance are l i k e l y to be of only secondary importance; they may even be a pos i t ive disadvantage i f they conceal or d i s t r a c t from the crudi ty of the underlying 54 s t r u c t u r e . " . U n t i l 1970, a i r l i n e operations research staffs appeared to be l i t t l e concerned with advert i s ing models. Perhaps, i n sympathy with Friedman's adver t i s ing model, they f e l t that long run success depends on favorable cos t -pr ice r e l a t i o n s h i p s , or perhaps a i r l i n e managements had l i t t l e fa i th, i n the adver t i s ing models proposed. The reason for the apparent lack of in te re s t i n adver t i s ing models may have been that current adver t i s ing p o l i c y and method are 5 J . D . C . L i t t l e and L . M . Lodi sh , "An Explorat ion of Linear Programming i n Media S e l e c t i o n , " Journal of Marketing  Research, I I I . May 1966, pp. 179-187. 54 M . H . J . Webb, "Adver t i s ing Response Functions & Media P lann ing , " O/R Quarterly, V o l . 19, No. 1, 1968, pp. 43-59. proprietary matters not f r e e l y discussed outside the company; a c t i v i t y may be greater than indicated by the l i t e r a t u r e . I I I . OPERATIONS RESEARCH IN AIRLINE PRICING The International A i r Transport Association i s largely instrumental i n setting rates and fares for i n t e r n a t i o n a l a i r l i n e services. T a r i f f s ; are set by unanimous agreement and enforced by a system of inspection which can levy heavy f i n a n c i a l penalties. After the IATA agreement, governmental approval of the fares generally i s required. Cargo rates are b u i l t to the following plan: (a) a basic rate per pound (b) s p e c i a l rates for s p e c i f i c commodities (c) incentive rates for shipments above a given minimum (d) minimum handling charge (e) volumetric surcharge for high bulk cargoes (f) value surcharge for precious cargoes. Passenger fare p r i c i n g can be modified to reduce peaking or to a t t r a c t more revenue. Price concessions may be permanent or "creative". Creative fares are below basic J.L. Grumbndge, op_. c i t . , p. 61. fares, designed to promote new t r a f f i c without d i v e r t i n g e x i s t i n g t r a f f i c . This i s achieved by means of r e s t r i c t i o n s such as: (a) reduced fares generally are return or round t r i p fares (b) excursion fares generally are sold only i n country of o r i g i n (c) s p e c i a l fares generally have limited v a l i d i t y , up to f o r t y - f i v e days (d) stay at destination i s usually a s p e c i f i e d minimum or maximum period of time. Special fares are sold to groups, fam i l i e s , or as packaged tours. Standby fares allow the passenger to f l y only when space i s not f i l l e d by regular passengers. In setting s p e c i a l or creative fares, two rules should be kept i n mind: 1. Tariff-making l o g i c must not outrage public l o g i c . If a service i s from A to C v i a B, then the low fare passenger bound for C who decides af t e r a l l to stop at B, w i l l resent having to pay extra for not f l y i n g to C. J.L. Grumbridge, op. c i t . , p. 214. 2. Complicated fares should be avoided. P r i c i n g should begin with a knowledge of costs. For breakeven, t o t a l revenues are equal to t o t a l costs. Breakeven quantity i s generally found by the following: Breakeven quantity = (Fixed costs)/(Price - C) where C i s variable costs per unit. Seasonal fluctuations may prevent continuous recovery of f u l l costs. In the short run, fixed costs may not be recovered, but under no circum-stances i s i t desirable to operate i f revenues are less than variable costs. The Lockheed company was interested i n the p o s s i b i l -i t i e s for use of the L-500 i n mass cargo applications. The 57 study of t h i s problem was i n f i v e steps: 1. Learn the problems faced by large-volume shippers and make in-depth studies of the economies of bulk.air shipments of marketable goods. 2. Prove the a b i l i t y of the L-500 a i r c r a f t to handle wide v a r i e t i e s of cargo, and to switch r e a d i l y from one to another. 3. Generate r e l i a b l e estimates of o v e r a l l costs, and not just d i r e c t transportation costs. Aviation Week and Space Technology, January 12, 1970, p. 307" 4. P r o v i d e data t o enable s h i p p i n g departments to c a l c u l a t e t h e i r own b e s t method. 5. Locate back-haul cargo. The study produced the f o l l o w i n g t a b l e comparing a i r and sea c o s t s f o r s h i p p i n g s m a l l c a r s : A i r Sea I t a l y to A t l a n t a $352 $377 Yokohama t o San, F r a n c i s c o $406 $303 The advantage of sea t r a n s p o r t between Yokohama and San F r a n c i s c o d e c l i n e d f o r i n l a n d d e s t i n a t i o n s , but low seaborne r a t e s from Japan were on s h i p s owned by the car manufacturers. T h i s i s not a p r i c i n g study as y e t . I t i s o n l y a f e a s i b i l i t y study but i t g i v e s an i d e a of the type of a n a l y s i s t h a t precedes a p r i c i n g d e c i s i o n . . A tremendous l e v e r i n p r i c i n g l a t i t u d e i s the a v a i l a b i l i t y of back haul cargo. A i r l i n e p r i c i n g problems i n some ways resemble the s t y l e goods problem, p a r t i c u l a r l y on a new s e r v i c e , where demand i s u n c e r t a i n . S t y l e goods are s u b j e c t to f a i r l y sharp c u t o f f , almost as abrupt as the l a s t c a l l t o board an outgoing f l i g h t . Reduced p r i c e s on outmoded s t y l e s " ; are r a t h e r s i m i l a r t o standby t i c k e t s at h a l f the normal f a r e . T.M. Whitin's s t y l e goods p r i c i n g model i s a con-58 c e p t u a l d e v i c e f o r r e t a i l markets. Although a p p l i c a b i l i t y o f t h i s model t o a i r l i n e s i s somewhat s t r a i n e d , the assumptions appear reasonable: 1. Inventory, (scheduled a v a i l a b i l i t y of s e a t s ) , i s on hand at the b e g i n n i n g of the p e r i o d . 2. I n v e n t o r i e s on hand at the end of the p e r i o d are l i q u i d a t e d a t a l o s s . Some standby s a l e s and some unsold seats occur. 3. Shortages y i e l d l o s t p r o f i t s and g o o d w i l l . Seats should be a v a i l a b l e t o a l l who w i l l pay f u l l f a r e . 4. The p r o b a b i l i t y of demand at v a r i o u s l e v e l s i s known from a c c u r a t e f o r e c a s t s . G + P + L where p = o p t i m a l p r o p o r t i o n o f stockout time G = u n i t l o s s of g o o d w i l l due to stockout P = u n i t p r o f i t on s a l e s a t r e g u l a r p r i c e , TT L = u n i t l i q u i d a t i o n l o s s . In r e t a i l i n g , t h i s i s the l o s s a s s o c i a t e d w i t h a marked down p r i c e . In a i r l i n e s i t would appear to be a p r o b a b i l i s t i c l o s s on standby or zero f a r e s T.M. W h i t i n , "Inventory C o n t r o l and P r i c e Theory," Management S c i e n c e , V o l . I I , No. 1, October 1955, pp. 61-68. Assuming that the functional relationships are known or that they can be estimated, a graphic representation would be as follows: Figure 4 Net P r o f i t Relationship f(x) - (probability of a s a l e ) • ( u n i t p r o f i t ) g(x) = (probability of. a l o s s ) • ( l i q u i d a t i o n loss) The shaded area i n the diagram represents t o t a l p r o f i t , Q l The objective i s to maximize: J (f(x) - g(x))dx 0 Given f(x) and g(x), the solution i s at Q , the optimal stock l e v e l . Functions f(x) and g(x), and the resultant are dependent upon pr i c e . These dependencies would be evaluated subjectively i n most cases. A similar s t y l e goods model was proposed by Hertz 59 and S c h a f f i r : P = ( s e l l i n g price) - (variable costs) P' = (reduced price) - (variable costs) P r o f i t on item i w i l l be: p^(P) + (1 - p^) P', where p^ i s the p r o b a b i l i t y of s e l l i n g unit i . No recognition of loss of goodwill i s . e x p l i c i t i n t h i s l a t t e r formulation. Despite c e r t a i n s i m i l a r i t i e s between s t y l e goods p r i c i n g and a i r l i n e p r i c i n g , the situations are obviously d i f f e r e n t . Style implies monopolistic features not s i g n i f i c a n t l y present i n a i r l i n e s . The timing and the amount of the price cut are matters of choice to s t y l e goods re-t a i l e r s , but not to a i r l i n e s that are regulated. However, non-business demand for a i r t r a v e l appears to be price e l a s t i c , and perhaps more predictable than the style.goods markets, so that i n concept at l e a s t , s t y l e goods models may be of value i n a i r l i n e p r i c i n g . G.L. Urban examined a m u l t i p l i c a t i v e model for packaged goods : ^ _ E l A l C21 X21 C31 X31 . q l " a l P l F l P2 F2 P3 F3 ( S 1 ) D.B. Hertz, and K.H. S c h a f f i r , "A Forecasting Method for Management of Seasonal Style Goods Inventories," Bass, F.M., et a l . , Mathematical Models and Methods i n Marketing, HomewoocT, Irwin^ 1961, pp. • 469-481. ^Montgomery and Urban, op. c i t . , p. 173. where = s a l e s of product 1 a^ = a c o n s t a n t P^ = p r i c e of product 1 E^ = i n d u s t r y e l a s t i c i t y f o r product 1 F^ = package f a c i n g s on s t o r e shelves A^ = i n d u s t r y s h e l f f a c i n g e l a s t i c i t y f o r product 1 C21 =.. c r o s s p r i c e e l a s t i c i t y between products 2 and 1 X21 = c r o s s s h e l f - f a c i n g e l a s t i c i t y between products 2 and 1 = observed market share of product 1 T h i s model c o u l d be a p p l i e d t o a i r l i n e s i f brands were v a c a t i o n t r i p s on competing a i r l i n e s and i f s h e l f f a c i n g s were p o s t e r s i n t r a v e l agents' windows. For the o r i g i n a l model, e v a l u a t i o n of e l a s t i c i t i e s was obtained from observa-t i o n o f q^/S^ r e l a t i v e to p r i c e and f a c i n g o b s e r v a t i o n s . The d i f f i c u l t y i n the a i r l i n e s i t u a t i o n i s i n experimenting w i t h p r i c e , p a r t i c u l a r l y where adjustments are made by o n l y , one competitor. C o n c l u s i o n s , Operations Research i n A i r l i n e Marketing Can management s c i e n c e be p r a c t i c a l l y and p r o f i t -a b l y employed i n marketing? Many top marketing men are f r a n k l y s k e p t i c a l about the p o s s i b i l i t i e s . They have heard p l e n t y of promises, but except f o r the area of marketing l o g i s t i c s — i n v e n t o r y c o n t r o l and the l i k e — they have y e t t o see much i n the way of performance. 61 C a r d w e l l , "Marketing and Management S c i e n c e — A Marriage on the Rocks?". C a l i f o r n i a Management Review, V o l . X, No. 4, Summer 1968, pp. 3-12. I n t h e same a r t i c l e f r o m w h i c h t h e above q u o t a t i o n i s t a k e n C a r d w e l l p o i n t s o u t t h a t i n t h e more c o n c r e t e a r e a s o f m a r k e t i n g a d m i n i s t r a t i v e s y s t e m s ( o r d e r p r o c e s s i n g , d e l i v e r y s c h e d u l i n g , i n v e n t o r y management, c o m m i s s i o n p l a n s ) , and i n f o r m a t i o n s y s t e m s , ( s a l e s a n a l y s e s , s a l e s b u d g e t s , f o r e c a s t i n g ) , o p e r a t i o n s r e s e a r c h has made a v a l u a b l e c o n -t r i b u t i o n . I n s u b j e c t i v e a r e a s , C a r d w e l l o b s e r v e s , t h e s u c c e s s o f o p e r a t i o n s r e s e a r c h h a s b e e n d i s a p p o i n t i n g . One o f t h e main r e a s o n s f o r d i s a p p o i n t m e n t has been i n t h e t e c h n i q u e o r i e n t a t i o n o f t r y i n g t o f i t m a r k e t i n g p r o b l e m s i n t o s t a n d a r d s o l u t i o n p a t t e r n s . A more s u c c e s s f u l a p p r o a c h has been t o c o n c e n t r a t e on t h e -problem, and t o u s e o p e r a t i o n s r e s e a r c h i f and when p r a c t i c a l , u s u a l l y on p a r t s i n s t e a d o f on t h e w h o l e . CHAPTER III PRODUCTION A i r l i n e production i s defined here as revenue earning a c t i v i t y , the transport of.passengers, mail and f r e i g h t . From the viewpoint of an a i r l i n e c l i e n t , production service begins with the reservation and ends with a r r i v a l at f i n a l destination. This chapter deals with operations research applications associated with f l i g h t bookings or reservations, loading, f l y i n g , and unloading of revenue-producing cargo. Ground handling, ground transportation and intermodal transfer of passengers and f r e i g h t are discussed i n Chapter IV as part of a i r p o r t operation. The term " a i r l i n e production" i s taken from W. S. Barry but where Barry includes a i r c r a f t maintenance as a production a c t i v i t y , maintenance was excluded from production i n t h i s chapter because i t i s not primarily a revenue-earning a c t i v i t y . 1 Many factors a f f e c t a i r l i n e production a c t i v i t y . Five of the most s i g n i f i c a n t factors are: W. S. Barry, A i r l i n e Management, London: A l l e n & Unwin Limited, 1965, pT 226. 1. p u b l i c demand f o r s e r v i c e . 2. a i r l i n e marketing and s e r v i c e p o l i c y . 3. a i r l i n e p h y s i c a l and f i n a n c i a l r e s o u r c e s . 4. a i r p o r t , government, and other r e g u l a t o r y c o n s t r a i n t s . 5. s t a t e s of na t u r e , i n c l u d i n g weather and mechanical f a i l u r e . In the long run, through p r e s s u r e or as a r e s u l t of management or government p o l i c y , a l l f i v e f a c t o r s may be a l t e r e d . Absolute demand f o r s e r v i c e i s perhaps the l e a s t f l e x i b l e of the f i v e f a c t o r s . E f f e c t i v e demand however, can be i n f l u e n c e d by a d v e r t i s i n g and p u b l i c i t y , by r e v i s e d s e r v i c e standards, or by government t a x a t i o n or subs i d y . In the scramble t o win routs and customers, a i r l i n e s c o l l e c t i v e l y have under-optimized t h e i r p o o l of r e s o u r c e s . T h i s was i l l u s t r a t e d by the f o l l o w i n g comment on r e v i s e d C i v i l Aeronau-t i c s Board p o l i c y under chairman Secor Browne: Browne i s attempting t o r e v e r s e p o l i c i e s of some of h i s predecessors and other government r e g u l a t o r y agencies, not only by encouraging a i r -l i n e mergers but by encouraging a i r l i n e n e g o t i a t o r s t o t a l k t o one another about swapping r o u t e s , a d j u s t i n g s c h e d u l e s o r otherwise r e d u c i n g d e s t r u c -t i v e d u p l i c a t i o n and o v e r c a p a c i t y . 2 Tom Alexander, "Is th e r e Any Way to Run an A i r l i n e ? " Fortune, September 1970, p. 211. P r o d u c t i o n d e a l s mainly w i t h short-term d e c i s i o n s , c o n t r o l a c t i v i t i e s and plans f o r the near f u t u r e . A n a l y s i s of s h o r t term problems p o i n t s i n the d i r e c t i o n of long term improvement, and i n t h i s sense p r o d u c t i o n a f f e c t s long term p o l i c y f o r m u l a t i o n . Although not e x c l u s i v e l y of a p r o d u c t i o n nature, long range f l e e t p l a n n i n g models were i n c l u d e d i n t h i s chapter. The chapter d e a l s w i t h three main t o p i c headings: 1. I n f o r m a t i o n S y s t e m s . The development of e l e c t r o n i c computers was concurrent w i t h the r a p i d growth of a i r l i n e t r a f f i c in' the decades f o l l o w i n g World War I I . Without computers f o r passenger booking, a i r l i n e s c o u l d not have grown as r a p i d l y as they d i d i n the years 1945 to 1970. 2. S c h e d u l i n g S y s t e m s . Scheduling Systems have a tremendous b e a r i n g on a i r l i n e revenues and c o s t s . Scheduling i s perhaps the most s i g n i f i c a n t s h o r t r u n a i r l i n e a c t i v i t y . 3- C u s t o m e r S e r v i c e s . Customer S e r v i c e s , i n c l u d e check-i n and baggage h a n d l i n g and::most of the p e r s o n a l c o n t a c t between an a i r l i n e and i t s c l i e n t e l l e . I. INFORMATION SYSTEMS Management i n f o r m a t i o n i s important to a l l business a c t i v i t i e s , but i t i s e s p e c i a l l y v i t a l to P r o d u c t i o n because: 1. A i r l i n e p r o d u c t i o n o p e r a t i o n s respond to huge inputs of c u r r e n t s t a t i s t i c s on passenger and cargo t r a f f i c , and on other d a t a such as weather c o n d i t i o n s and f a c i l i t i e s breakdown. 2. P r o d u c t i o n i n f o r m a t i o n i s extremely c u r r e n t and the r e s u l t a n t a c t i o n d e c i s i o n s must be r a p i d and a c c u r a t e . 3. E r r o r s i n some p r o d u c t i o n i n f o r m a t i o n may endanger human l i f e . For example, t a k e - o f f weight, weather and f l i g h t c l e a r a n c e i n f o r m a t i o n d i r e c t l y a f f e c t s a f e t y . At h i g h a l t i t u d e a i r p o r t s on hot summer days, a l l o w a b l e t a k e - o f f weight i s l e s s than t h a t p e r m i s s i b l e a t sea l e v e l , or w i t h c o o l e r temperatures. 4 . Expenditures on p r o d u c t i o n r e p r e s e n t the bulk of a i r l i n e c o s t s . Trans-World A i r l i n e s worked f o r months with s t a f f s of more than one hundred to develop a Burroughs system f o r passenger reservations.. The a i r l i n e became disc o u r a g e d w i t h the Burroughs system and began l o o k i n g a t PARS (programmed a i r l i n e r e s e r v a t i o n system), an IBM development. U n i t e d A i r L i n e s a f t e r s i m i l a r disappointment and problems w i t h t h e i r Univac program, signed w i t h IBM f o r a nationwide 4 passenger r e s e r v a t i o n s system f o r i n s t a l l a t i o n a t Denver. IBM s e r v i c e s and equipment were t o c o s t approximately f i f t y m i l l i o n d o l l a r s . In 1969 E a s t e r n A i r L i n e s opened a Systems Operations Center as a t r o u b l e - s h o o t i n g department geared t o look f o r p o t e n t i a l problems i n o p e r a t i o n s . The Center was t o t r y t o sta y f o u r t o s i x hours ahead of r e a l time, a n t i c i p a t i n g e f f e c t s of weather, a c c i d e n t s , and f o r e s e e a b l e d i s r u p t i o n s to the schedule or t o s e r v i c e needs. The main f u n c t i o n of the Center, apart from problem recognition, was t o translate emergencies i n t o a c t i o n plans and to d e l i v e r p lans to the d i s p a t c h e r . The Center occupied.twenty-one thousand square f e e t of f l o o r space, had i t s own Univac ComputerLand was 5 l i n k e d with E a s t e r n ' s v a s t passenger r e s e r v a t i o n s system. D e c i s i o n s are made at a l l l e v e l s i n an o r g a n i z a t i o n such t h a t the h i g h e r l e v e l s p r o v i d e goals or c o n s t r a i n t s f o r the lower l e v e l s . I n formation t r a v e l l i n g upwards i s u s u a l l y s e l e c t i v e , aggregated or condensed. Information t r a v e l l i n g downwards i s u s u a l l y expanded, d e t a i l e d and e x p l i c i t . The process i s i l l u s t r a t e d by the f o l l o w i n g diagram. 3 A v i a t i o n Week and Space Technology, 7 September, 1970, p. 24. 4 I b i d . , 25 May, 1970, p. 28. 5 I b i d , 1 June, 1970, p. 35 ^S.G.N. P r e s l e y , " C o n t r o l Information D i s t r i b u t i o n , " C P . A i r paper, unpublished, 1969. Policy Guidance Information Planning Information Control Information I Operating Conditions Pol i c y Decisions Planning Decisions Control Decisions. Operating Decisions Planning Directives Control Directives Operating Directives "Operating Actions Information Flow Diagram One could l i s t many questions concerning proposed information systems. For example: Who needs information? What information is.needed, and why? What i s the information source? How much information i s there to transmit? What growth rate? What form? (Verbal, hard copy, tape, et cetera.) When i s the information needed? What delays are permissible? How important i s sequence? Cost? Error? How accurately can the communications symbols be transmitted? How well do the symbols transmit desired meaning? How well does the received meaning a f f e c t desired conduct? 7 Transmission of information i s treated elsewhere and i s not the prime concern of t h i s paper. The answers to some of the s p e c i f i c questions raised above are of more immediate concern. P a y r o l l accounts, materials control, continuous process control, a i r l i n e passenger and cargo reservations, a l l provide examples of data treated mathematically and operat-ing with minimum human intervention. These applications are successful because they deal.mostly with i n t e r n a l data. Management, on the other hand, must rel a t e external and in t e r n a l information i n order to plan and control the organization. "Despite a l l the advances i n data processing, a breakdown i n . . . the preparation of managerial planning p and control reports i s a l l too frequently observed." The usual reason i s that data processing planners and information Harold Chestnut, Systems Engineering Methods, New York, John Wiley & Sons, 1967, pp. 1-69. 8 J.D. Gallagher, "Management Information Systems and the Computer," New York, American Management Association Inc., 1961, p. 13. systems people are unaware of management needs for reports on the t o t a l course of the business. The r e s u l t i s that data processing groups take refuge i n the preparation of data r e p o r t s — t a b u l a t e d reports which are only consolidations of raw data, and without,reference to the r e a l needs of management. An Operations Research man should be i d e a l l y trained 9 to i d e n t i f y management information needs. Operations research can make a healthy contribution i n laying the ground-work for operating decisions i n a c t i v i t i e s that a f f e c t more than one functional area of a business: 1. by helping to formalize the elements i n recurring decisions. 2. by helping to design the flow of information to concerned functional areas. 3. by helping to tes t a lternative p o l i c i e s for business operation. J u s t i f i c a t i o n for Upgrading the System Computer systems involve heavy f i n a n c i a l outlays. Before making a detailed development of costly system up-grades, pot e n t i a l benefits should be evaluated. I f the b e n e f i t s look a t t r a c t i v e , f u r t h e r e f f o r t s should be d i r e c t e d toward system development. A good example of such a b e n e f i t study i s found i n Dr. M a c A i r t ' s a n a l y s i s of the "no show" problem at Aer L i n g u s . A u t o m a t i c p a s s e n g e r r e s e r v a t i o n b e n e f i t s . No shows occur f o r s e v e r a l reasons: (1) e r r o r s i n a i r l i n e procedures, for example, f a i l u r e t o e f f e c t a c a n c e l l a t i o n , (2) l a t e passenger a r r i v a l , (3) agents misbooking, and other e r r o r o u t s i d e a i r l i n e c o n t r o l , (4) m u l t i p l e booking by the passenger t o a l l o w him t o s e l e c t h i s f l i g h t at the l a s t minute. The proposed automatic r e s e r v a t i o n symtem was con-s i d e r e d e f f e c t i v e i n e l i m i n a t i n g only e r r o r s of type (1), although e r r o r s of type (4) can a l s o be prevented. Type (1) e r r o r s were estimated by Aer Lingus to account f o r f o r t y -nine per cent of a l l no shows.^ N = uX - dX - vR where N =. a d j u s t e d e r r o r no shows from type (1) e r r o r s uX = t o t a l e r r o r no shows from type (1) e r r o r s dX = e r r o r no shows o c c u r r i n g too l a t e f o r r e s a l e vR = t o t a l e r r o r no r e c o r d s . (Passenger a r r i v e s w i t h v a l i d t i c k e t , but a i r l i n e has no r e c o r d of t i c k e t s a l e . ) J.G. M a c A i r t , " E s t i m a t i o n of the F i n a n c i a l Advan-tages of E l i m i n a t i n g E r r o r No Shows i n a Real Time PNR R e s e r v a t i o n System, AGIFORS Proceedings, 1967, p. 271. Assuming t h a t N i s u n i f o r m l y d i s t r i b u t e d over a l l f l i g h t s , then l o s t revenue i s given by: l o s t revenue = NpqrF where p = p r o b a b i l i t y t h a t a f l i g h t i s c l o s e d q = p r o b a b i l i t y of r e s e l l i n g a t i c k e t r = p r o b a b i l i t y t h a t a passenger r e f u s e d h i s f i r s t c h o i c e o f . f l i g h t w i l l t r a v e l other than by Aer Lingus F = average f a r e Much of the a n a l y s i s of t h i s problem i s i n the d e r i -v a t i o n of the parameters p, q, r . A c l e v e r a n a l y s i s of q i s g i v e n to determine the p r o b a b i l i t y of r e s a l e on c l o s e d f l i g h t s . S u p e r f i c i a l l y t h i s may appear a u s e l e s s e x e r c i s e because the p r o b a b i l i t y of a r e s a l e appears to be more or l e s s u n i t y . However, i f r e s a l e s r e p r e s e n t t r a n s f e r s of passengers from other f l i g h t s , they r e p r e s e n t no e x t r a revenue to the a i r l i n e . U n i t e d A i r L i n e s O n - L i n e C h e c k - I n . U n i t e d A i r L i n e s d e a l t w i t h a s i m i l a r , problem of r e c o g n i z i n g no shows, i n t h i s case a proposed o n - l i n e c h e c k - i n i n f o r m a t i o n system w i t h s t a t i o n s a t t i c k e t counters, baggage co u n t e r s , s e l e c t e d i n f o r m a t i o n c e n t r e s , and at the g a t e . 1 1 Manual c h e c k - i n R . E . Jacks, "Passenger Check-In and the Information System," AGIFORS•Proceedings, 1 9 6 9 . procedures are slow. No-shows are r e c o g n i z e d too l a t e f o r r e s a l e of t i c k e t s , say a t the next stop. The b e n e f i t of an o n - l i n e system would be e a r l y r e c o g n i t i o n of no-shows a t c h e c k - i n and e l i m i n a t i o n of manual counting and c a l c u l a t i o n by c l a s s of s e r v i c e and d e s t i n a t i o n . Due to d i f f i c u l t i e s t h a t the proposed c h e c k - i n procedure would have c r e a t e d i n the accounting department, it.was r e j e c t e d i n i t s o r i g i n a l form. A d e s c r i p t i o n of f i f t e e n systems a l t e r n a t i v e s e v o l v e s around r e a l c o n s t r a i n t s w i t h i n the framework of e x i s t i n g o p e r a t i o n s . T h i s study i s l a r g e l y of an i n d u s t r i a l e n g i n e e r i n g nature, with c o s t - b e n e f i t a n a l y s i s of a l l the a l t e r n a t i v e s . Operations r e s e a r c h combines w i t h i n d u s t r i a l e n g i n e e r i n g i n e v a l u a t i o n of s t o c h a s t i c v a r i a b l e s , ( t a k i n g i n t o account time of day, day of week and so on), and t h i s paper i s a p r a c t i c a l demon-s t r a t i o n of o p e r a t i o n s r e s e a r c h a p p l i e d to a r e a l s i t u a t i o n . Indirect benefits from upgraded systems. A booking l e v e l model was envisaged by American A i r l i n e s a f t e r implementation of the SABRE e l e c t r o n i c r e s e r v a t i o n s system. The enormous s e t of s t a t i s t i c s p r o v i d e d by SABRE and more re c e n t passenger booking systems are p r e r e q u i s i t e t o competent assessment of passenger a r r i v a l d i s t r i b u t i o n s . A l though r e s e r v a t i o n systems are designed to keep a c c u r a t e and c u r r e n t i n v e n t o r i e s of seats s o l d and seats a v a i l a b l e f o r every f l i g h t , e r r o r s a r i s e due to l a t e passenger a r r i v a l s or from t r a v e l agents' errors, and other reasons outside the control of the a i r l i n e s . One booking po l i c y would be to s e l l no more than the number of seats avai l a b l e . This would ensure that a l l passengers could be accommodated, and that none would be l e f t at the gate when the f l i g h t departed. On the other hand, because the expected numbers of passengers are fewer than the t o t a l booked, an a i r l i n e using t h i s p o l i c y would usually f l y with empty seats on f l i g h t s that were closed to further bookings. Thus a cert a i n amount of o v e r s e l l i n g should y i e l d higher revenues to the a i r l i n e , at the r i s k of increasing l i k e l i h o o d of surplus passengers who can not be accommodated, and at the r i s k of v i o l a t i n g the contract to carry each confirmed passenger. If o v e r s e l l i n g i s the policy chosen, then the amount of oversales can.be defined i n terms of the expected numbers of passengers l e f t at the gate. For 12 example, set 0^ as follows: expected oversales s p e c i f i e d 0. = 1 expected validated passengers Let L = number of passengers a r r i v i n g for departure out of the t o t a l N who were booked when the f l i g h t was closed Let K = number of passengers a r r i v i n g out of the t o t a l number of teletype bookings from other a i r l i n e s — r e c e i v e d af t e r normal bookings are closed M. Rothstein, and A. Stone, "Passenger Booking Levels," AGIFORS Proceedings, 1967, p. 392. Let H = the sum of no-record passengers a r r i v i n g at departure with validated t i c k e t s Then J, the number of passengers actually boarding, w i l l be: J = - L + K + H 13 Using Taylor's approach, the d i s t r i b u t i o n of J i s approximated by means of the Gram-Charlier method, (an i n f i n i t e series incorporating the moments of random variables 14 as i t s parameters). The method i s described elsewhere, and s h a l l not be discussed further except to say that i t was chosen because: 1. nothing better was suggested 2. res u l t s obtained seemed reasonable. A simulation could t e s t the accuracy of the Gram-Charlier approach, but i t was f e l t that the exercise was not worthwhile. The algorithm: 1. Let N be the number booked r days before departure of f l i g h t (Set N = capacity). 2. Calculate the f i r s t three moments of the d i s t r i b u t i o n of people from t h i s N who are available for f l i g h t at departure. C.J. Taylor, "The Determination of Passenger Book-ing Levels," AGIFORS Proceedings, 1962. 3. Using the Gram-Charlier series of type A as an approximation of the d i s t r i b u t i o n , calculate the expected oversales r a t i o 0 . 4. Compare 0 C with 0.. . . . the sp e c i f i e d r a t i o set. by Company po l i c y . 5. I f 0 >• 8., set N = N-1, or i f 6 < 6 . , set N = c j ' ' c j ' N+1. 6. Go to 2. and repeat u n t i l 0 q(N*) < 6 . < 6 c(N* + l ) . 7. Compute the pr o b a b i l i t y of one or more oversales, given N*. 8. Go to 1. and repeat for a l l 0 . . . 9. Go to 1. and repeat.for a l l r u n t i l r = 0, (day of departure). For various s p e c i f i e d oversales r a t i o s 0 ^ , the output gives the number of bookings to accept on each of the l a s t twelve days before departure, and the p r o b a b i l i t i e s of one or more oversales occurring at f l i g h t time. American A i r l i n e s performed f i e l d tests at Chicago, Cleveland, and Dallas. The f i e l d tests showed that the model indeed reduced the percentage of empty seats on closed f l i g h t s although the paper does not indicate numbers of passengers l e f t at the gate, except to say that s p e c i f i e d Maurice G. Kendall and Alan Stuart, The Advanced  Theory of S t a t i s t i c s , Vol. 1, 3rd ed., London"!! Charles G r i f f i n & Co. Ltd., 1969, pp. 156-163. passenger s e r v i c e l e v e l s were met. The i n f e r e n c e i s t h a t the model o f f e r s a p o s i t i v e revenue p o t e n t i a l . f l i g h t s normally favour the through passengers. The problem i s t o d e c i d e when to stop booking s h o r t f l i g h t s . The a r r i v a l r a t e s of passenger bookings was seen as the key t o the problem. The revenue from a s h o r t l e g f l i g h t must be weighed a g a i n s t the p r o b a b i l i t y of a l a r g e r revenue on a through f l i g h t . However, i f s h o r t bookings f i l l up each l e g , through bookings may not r e s u l t i n h i g h e r revenues, e s p e c i a l l y i f the f a r e s t r u c t u r e f u l l y r e f l e c t s the h i g h e r c o s t s of a 15 s h o r t f l i g h t . journey p a t t e r n s . The f a r e s f o r each p o s s i b l e journey and the p r o b a b i l i t i e s of bookings f o r each p o s s i b l e journey are needed f o r an LP s o l u t i o n t o the s e c t o r booking problem. Model f o r m u l a t i o n i n i t s s i m p l e s t form i s g i v e n by: B O A C S e c t o r C o n t r o l . Booking l e v e l s on m u l t i - s e c t o r A n i n e - s e c t o r f l i g h t can have f o r t y - f i v e p o s s i b l e 45 Maximize (revenue) = 1 s u b j e c t t o where r.. = revenue a s s o c i a t e d w i t h journey j c^ = c a p a c i t y remaining i n s e c t o r i f j = f o r e c a s t demand f o r journey j s^ = s e t of journeys i n v o l v i n g s e c t o r i Although t h i s method produces rough answers, i t s u f f e r s the l i m i t a t i o n of a s i n g l e estimate of demand f o r each journey. P r o b a b i l i t i e s of f u r t h e r bookings can be s p e c i f i e d a f t e r some bookings have been made, but t h i s leads to a l a r g e LP. To reduce computational procedures, the problem can be decomposed. T h i s r e s u l t s i n s u b - o p t i m i z a t i o n but s t i l l y i e l d s convenient s o l u t i o n . The method has been used e x p e r i m e n t a l l y by BOAC. Such a model should perform b e t t e r than human agents working by experience and i n t u i t i o n , or making random de-c i s i o n s . However, the f o r e c a s t elements w i t h i n the LP model are judgement items. Over time the model should do b e t t e r than the human o p e r a t o r s because i t c o n s i s t e n t l y f o l l o w s the r u l e s l a i d down. A i r l i n e R e s e r v a t i o n s Systems. E a s t e r n A i r L i n e s ' t h i r d g e n e r a t i o n computer system was one of the l a r g e s t i n the world. In March 1969, E a s t e r n r e c e i v e d about 125,000 telephone c a l l s each day. R e s e r v a t i o n 15 B. G r i f f i t h s , and J . T a y l o r , "Mathematical Formu-l a t i o n of the S e c t o r C o n t r o l Problem," AGIFORS Proceedings, 1967, p. 436. c a l l s v a r i e d f r o m n i n e t y s e c o n d s f o r an i n f o r m a t i o n c a l l t o o v e r s e v e n h u n d r e d s e c o n d s f o r a r o u n d t r i p b o o k i n g . The 16 a v e r a g e c a l l l a s t e d 237 s e c o n d s . A m e r i c a n A i r l i n e s ' SABRE s y s t e m k e p t t r a c k o f s e a t a v a i l a b i l i t y , p a s s e n g e r name r e c o r d s , m e a l c o u n t s , b o a r d i n g m a n i f e s t s , and a u t o m a t i c g e n e r a t i o n o f t e l e t y p e messages r e q u i r e d by o t h e r a i r l i n e s . The d i m e n s i o n s o f E a s t e r n ' s r e s e r v a t i o n s were l a r g e : 2,700 d a i l y f l i g h t segments between n i n e t y - e i g h t a i r p o r t s , w i t h i n v e n t o r y r e c o r d s up t o a y e a r i n a d v a n c e . The s y s t e m was c a p a b l e o f r a p i d r e s p o n s e t o a l l a g e n t r e q u e s t s r e g a r d i n g f a r e s , s c h e d u l e s and a v a i l a b i l i t y . The h a r d w a r e needed was i m p r e s s i v e : 3 IBM 360/65 p r o c e s s o r s e a c h w i t h 524K c o r e 3 c o r e s t o r a g e u n i t s e a c h t a k i n g s i x m i l l i o n c h a r a c t e r s 20 d i s c f i l e s , e a c h f o r two h u n d r e d m i l l i o n c h a r a c t e r s 676 m o b i l e d i s c p a c k s , e a c h f o r t w e n t y - f i v e m i l l i o n c h a r a c t e r s . I n 1969 E a s t e r n p l a n n e d t o u s e m i c r o f i l m f o r o f f - l i n e s t o r a g e o f r e l a t i v e l y s t a t i c i n f o r m a t i o n . The m i c r o f i l m s y s t e m was e x p e c t e d t o c o s t $3.3 m i l l i o n , b u t w o u l d s t r e a m -l i n e t h e $31.3 m i l l i o n computer s y s t e m by t a k i n g s t o r e d m a t e r i a l o f f l i n e . The m i c r o f i l m s y s t e m h a n d l e d 73,500 pa g e s W.E. J e n k i n s , " A i r l i n e s R e s e r v a t i o n s S y s t e m s , " D a t a m a t i o n , M a r c h 1969, p. 29. of i n f o r m a t i o n w i t h f o u r second access f o r whole-page d i s -p l a y s on cathode ray tubes. Savings were expected from reduced d a t a communications, r e d u c t i o n s i n telephone times (about twenty seconds per c a l l ) , reduced computer program-17 ming, storage requirements, and process times. In c o n t r a s t w i t h t h i s , CP A i r , w i t h about 5.6 per cent of E a s t e r n ' s volume i n 1970 had e s s e n t i a l l y a manual booking system,.using a " b i g board" t o keep t r a c k of f l i g h t s . P h y s i c a l l i m i t a t i o n s of board s i z e compound the r e s e r v a t i o n s problem as the s c a l e of o p e r a t i o n s m u l t i p l i e s . Aer Lingus i n A p r i l 1965 i n s t a l l e d an A l t a m a t i c r e a l time r e s e r v a t i o n system, and subsequently ordered an IBM PARS system. While Aer Lingus and CP A i r were approximately the same s i z e (both flew about 1.25 m i l l i o n passengers i n 1969) they chose r e s e r v a t i o n s systems t h a t were q u i t e d i f f e r e n t . I t i s c l e a r t h a t at s o m e p o i n t , manual systems must g i v e way to e l e c t r o n i c systems. S y s t e m E v a l u a t i o n . . In connection w i t h i t s SABRE system, American A i r l i n e s wanted to e v a l u a t e e f f e c t s on response time (time taken to answer q u e r i e s ) , caused by R.B. Parsons, " M i c r o f i l m R e t r i e v a l i n an A i r l i n e R e s e r v a t i o n System," Datamation,.Vol. 15, No. 9, September 1969, p. 103. A i r l i n e Management and Marketing, October, 1970, p. 45. v a r i a t i o n s i n system d e s i g n . A g e n e r a l model of the SABRE system was developed f o r use as a guide to system d e c i s i o n 19 making. The model was designed to e v a l u a t e the combined e f f e c t of a m u l t i t u d e of hardware components, software programs, systems s t r a t e g i e s , and communications i n t e r f a c e s . Response time was accepted as the standard by which to judge r e a l time systems. The path of a message through the SABRE system was as f o l l o w s : 1. Message "m" i s typed at a c o n s o l e . 2. "m" i s t r a n s m i t t e d on r e a l - t i m e channel t o c o r e . 3. A s e r i e s of t e s t s are performed on "m". 4. An o p e r a t i o n a l program s e t s up an e n t r y b l o c k . 5. The e n t r y i s processed. 6. A response i s t r a n s m i t t e d t o the c o n s o l e . There was no methods problem i n e v a l u a t i n g steps 2, 3, 4, and 6. These were d e a l t w i t h by SABRE p e r s o n n e l . In step 5, however, the i n t e r a c t i n g demands upon the c e n t r a l p r o c e s s i n g u n i t i n combination w i t h software f e a t u r e s of the system, presented a more d i f f i c u l t problem f o r a n a l y s i s . E n t r i e s went on a c e n t r a l p r o c e s s i n g u n i t (CPU) l i s t i n a f i r s t come f i r s t served manner. Each e n t r y was processed A. Weingarten, "Response Time i n a T o t a l A i r l i n e s Computer System," AGIFORS Proceedings, 1969. to completion u n l e s s the CPU was i n t e r r u p t e d . When the CPU was i n t e r r u p t e d , ( f o r example a w a i t i n g access t o d i s c f i l e ) , the e n t r y l e f t the CPU l i s t . A f t e r completion of the i n t e r r u p t i o n , (access t o d i s c e t c e t e r a ) , the entry was re t u r n e d t o the end of the CPU l i s t . I f no other e n t r i e s were i n pro c e s s , work on the o r i g i n a l e n try continued. I f , meanwhile, n e w e n t r i e s had a r r i v e d , a d e l a y " t " ensued before work on the o r i g i n a l e n t r y resumed. The random v a r i a b l e f o r each w a i t i n g time a t the CPU was r e p r e s e n t e d as t ^ . As the average entry had s i x accesses, there were s i x d e l a y s t ^ i n the course of p r o c e s s i n g the en t r y , p l u s an i n i t i a l d e l a y . Instead of e v a l u a t i n g each t ^ i n d i v i d u a l l y , t h i s model.evaluated T = t.^ + • t 2 + •••+ t ^ as a t o t a l d i s t r i b u t i o n . A r e l a t i o n s h i p between T and computer u t i l i z a t i o n was d e r i v e d . Thus, American A i r l i n e s o b t a i n e d r a p i d e v a l u -a t i o n of the SABRE system response time. The s i m p l i f i e d model was e a s i l y m o d i f i e d t o . s u i t proposed system changes, and the model p r o v i d e d f i r s t - c u t systems analyses without the expense or de l a y of f i e l d t r i a l s . P a s s e n g e r s y s t e m s o f t h e f u t u r e . I n i t i a l l y , computer systems kept t r a c k o f seats s o l d and seats a v a i l a b l e . In 1971, systems c o u l d handle r e s e r v a t i o n s i n v e n t o r i e s up t o one year i n advance, complete w i t h passenger name re c o r d s f o r more than a m i l l i o n bookings. Access times were f r a c t i o n s o f s e c o n d s . C a t h o d e r a y t u b e s s p e d i n p u t , h e l p e d e r r o r d e t e c t i o n i n i n p u t t i n g , and s p e d up r e t r i e v a l . One a i r l i n e c o u l d o b t a i n b o o k i n g a v a i l a b i l i t y d a t a f r o m most o t h e r a i r l i n e s . (About one t h i r d o f a l l p a s s e n g e r s u s e more t h a n S t a t e s a i r l i n e s had $250 m i l l i o n i n v e s t e d i n computer r e s e r v a t i o n s s y s t e m s t h a t made t h r e e h u n d r e d m i l l i o n b o o k i n g s f o r one h u n d r e d and f i f t y m i l l i o n p a s s e n g e r s f l o w n . A i r T r a f f i c C o n f e r e n c e s o f A m e r i c a i n A p r i l 1968 d e c i d e d t o p r o c e e d w i t h ATARS, a common a u t o m a t e d r e s e r v a -t i o n s s y s t e m f o r t r a v e l a g e n t s . More a m b i t i o u s were s p e c i f i -c a t i o n s b e i n g d e v e l o p e d by t h e A i r T r a n s p o r t a t i o n A s s o c i a t i o n ( A TA), and t h e I n t e r n a t i o n a l A i r T r a n s p o r t A s s o c i a t i o n ( I A T A ) , f o r documents i n a computer c o n t r o l l e d s y s t e m t h a t u l t i m a t e l y w o u l d d i s p l a y f a r e s f o r w o r l d w i d e i t i n e r a r i e s , c o n f i r m r e s e r v a t i o n s , p r o v i d e s e l f - s e r v i c e t i c k e t s f o r c r e d i t c a r d h o l d e r s , p e r m i t s e l f - s e r v i c e e x c h a n g e - o f f l i g h t s f o r c a r d h o l d e r s , p r o v i d e i n s t a n t no-show and s t a n d b y d a t a , p r o v i d e 21 a u t o m a t i c a l t e r n a t i v e r o u t i n g s . P r o d u c t i o n I n f o r m a t i o n Systems Manpower p l a n n i n g f o r e c a s t s p r o v i d e e s t i m a t e s o f f u t u r e manpower n e e d s . C o s t s a s s o c i a t e d w i t h v a r i o u s s t a n -d a r d s o f s e r v i c e may be compared. A i r Canada's A i r p o r t one a i r l i n e t o c o m p l e t e t h e i r f l i g h t s ) . 20 I n 1969, U n i t e d 20 G.A. Buchanan, "The O u t l o o k f o r Improved P a s s e n g e r D a t a m a t i o n , M a r c h 1969, p . 24. S y s t e m s , II I b i d p. 26. • t Manpower P l a n n i n g System was f o r c h e c k - i n , departure gate and a r r i v a l gate, but was to be extended t o i n c l u d e other 22 areas of the a i r p o r t . A i r C a n a d a M a n p o w e r P l a n n i n g . T h i s model was oper-a t i o n a l i n 1969 a t Montreal and Toronto f o r management p l a n n i n g purposes. The model was simple because i t was o r i e n t e d toward r e l a t i v e l y non-mathematical u s e r s . Implemen-t a t i o n of new procedures i s u s u a l l y the most d i f f i c u l t p a r t of an o p e r a t i o n s r e s e a r c h study, because i t r e q u i r e s new ways of t h i n k i n g , and because the r e s u l t s may be d i f f i c u l t t o v e r i f y . Unless the user has conf i d e n c e i n the r e s u l t s , the procedure w i l l be abandoned. User c o n f i d e n c e i s g r e a t l y i n c r e a s e d when the procedures are reasonably w e l l under-stood. E x t r a model complexity and p r e c i s i o n u s u a l l y imply e x t r a c o s t . Such c o s t s should be weighed a g a i n s t the a n t i c i p a t e d b e n e f i t s of p r e c i s i o n gained. Inputs t o the Manpower P l a n n i n g Model i n c l u d e d : 1. expected passenger t r a f f i c b oarding and d e p l a n i n g by f l i g h t . 2. f o r e c a s t of check - i n t r a f f i c by time of day. 3. s e r v i c e c h a r a c t e r i s t i c s a t each area s t u d i e d . V.K. Wozniuk, " A i r p o r t Manpower P l a n n i n g System," AGIFORS Proceedings, 1969. Outputs of the model: 1. Agents r e q u i r e d f o r each . f i f t e e n - m i n u t e i n t e r v a l through the day., f o r s e r v i c e l e v e l r e q u i r e d . : ( s h o r t i n t e r v a l requirement). 2. Agents r e q u i r e d f o r each eight-hour s h i f t through the day, f o r s e r v i c e l e v e l r e q u i r e d , ( s h i f t r e q uirement). 3. S l a c k agents. ( s h i f t requirement minus s h o r t i n t e r v a l requirement). The c h e c k - i n queue model i s M/M/2: (°°/FiFo) . T h i s was d e c i d e d p a r t l y t o f a c i l i t a t e the s o l u t i o n . The a c t u a l s e r v i c e d i s t r i b u t i o n was found t o be E r l a n g . R a t i o n a l i z i n g the need to be c o n s e r v a t i v e (to allow f o r i r r e g u l a r i t i e s not d i r e c t l y e v a l u a t e d ) , the M/M/2 model was chosen. Perhaps an a l t e r n a t i v e would be t o use an imbeded Markov c h a i n model mentioned on page 115. S e r v i c e standards were s p e c i f i e d as: N. hour Qmax + (1 - a) N Qave where N hour = h o u r l y agent requirements N Qmax maximum q u a r t e r hour requirement N, Qave = average q u a r t e r hour requirement I f a i s s e t a t zero, the requirement i s based on the average requirement. I f a i s s e t at u n i t y , the requirement i s based on the s h o r t i n t e r v a l requirement. By changing a between zero and u n i t y , management can e v a l u a t e the c o s t i m p l i c a t i o n s f o r any i n t e r p r e t a t i o n of s e r v i c e l e v e l . To i n c o r p o r a t e r e a l i s t i c o p e r a t i o n a l c o n s t r a i n t s , each agent works e i g h t hours c o n s e c u t i v e l y , w i t h lunch breaks, and i s s u b j e c t t o s i c k n e s s , v a c a t i o n and a t t r i t i o n f a c t o r s . The h e u r i s t i c procedure f o r f i n d i n g the number of agents i s q u i t e simple. The model enabled management to determine man-power needs, and to e x p l o r e p o l i c y a l t e r n a t i v e s . Pi-lot S e n i o r i t y and Salary Systems. P i l o t s a l a r i e s and t r a i n i n g c o n s t i t u t e d more than f i v e per cent of Aer L i n g u s 1 t o t a l c o s t s i n 196 8. A v a i l a b l e posts were o f f e r e d to the most s e n i o r p i l o t s f i r s t . S a l a r y was a f u n c t i o n of rank and type of a i r c r a f t flown. P r o g r e s s i v e bumping through the s e n i o r i t y sequence l e d to e x t r a t r a i n i n g c o s t s . A new Boeing 707 r e q u i r e d f i v e e x t r a crews. The f i v e most s e n i o r V i s c o u n t c a p t a i n s c o u l d e l e c t t o f l y the 707. They, i n t u r n would be r e p l a c e d by the most s e n i o r c o - p i l o t s — almost c e r t a i n l y j e t c o - p i l o t s . Thus th e r e would be ten j e t or V i s c o u n t c o - p i l o t v a c a n c i e s to be f i l l e d i n most cases by B707.th.ird p i l o t s . F i f t e e n V i s c o u n t c o - p i l o t s would be promoted to B 7 0 7 t h i r d p i l o t , and f i f t e e n new p i l o t s would be r e c r u i t e d . A p r o g r e s s i o n diagram i s shown i n 23 F i g u r e 1. 23 J.A; 0 ' C a r r o l l , "Note on a Computer S i m u l a t i o n Used to E v a l u a t e P i l o t S e n i o r i t y and S a l a r y Systems," AGIFORS Proceedings, 1968, p. 552. B747 Captain Zoo, B 707/720 Captain BAC 111 Captain B747 Copilot no B 707/720 Copilot Viscount Copilots Cadet Figure 3.1, P i l o t Progression, with Costs. (From AGIFORS Proceedings, 1968, p. 555). B e n e f i t s from t h r e e a l t e r n a t i v e s were ev a l u a t e d by s i m u l a t i o n . The a l t e r n a t i v e s : 1. Leave promotion scheme as i s . ( t h i r d p i l o t s on B 7 0 7 / 7 2 0 ) . 2. Replace t h i r d p i l o t s by f l i g h t e n g i n e e r s . 3. C reate a new grade of s e n i o r f i r s t o f f i c e r f o r f l e x i b i l i t y i n d i r e c t i n g c o - p i l o t s t o p a r t i c u l a r a i r c r a f t types.. While the second a l t e r n a t i v e o f f e r e d some sa v i n g s , the t h i r d a l t e r n a t i v e was of marginal b e n e f i t . N e i t h e r a l t e r n a t i v e was taken. The s i m u l a t i o n makes no attempt t o eva l u a t e the union problems t h a t might be i n v o l v e d , but was co n s i d e r e d a u s e f u l p l a n n i n g t o o l and was kept updated. F u t u r e i n f o r m a t i o n s y s t e m s w i l l g i v e management stro n g e r c o n t r o l than i s p o s s i b l e today. There has been some attempt t o d e f i n e f u t u r e r e s e r v a t i o n s systems. Doubtless computers w i l l f e a t u r e i n c r e a s i n g l y i n a i r l i n e i n f o r m a t i o n systems. New approaches to system d e s i g n and development may have profound e f f e c t s i n the long run. Tucker's r a t i o 24 25 a n a l y s i s has been of i n t e r e s t to Quantas as a p o s s i b l e S. Tucker, S u c c e s s f u l M a n a g e r i a l C o n t r o l by R a t i o  A n a l y s i s , New York, McGraw Hi 11"^ 1 9 6 1 . 25 L.G. K l i n g e n , " C o n t r o l of M a t e r i a l s Costs by R a t i o A n a l y s i s , " AGIFORS Proceedings, 1 9 6 7 , p. 3 6 4 . system for materials c o n t r o l . Ratio analys i s may play a strong part i n model b u i l d i n g i n the future, at l ea s t i n the f i r s t stages of model formulat ion. 2 6 Plans such as A i r France's Tarage that br ing together various operations research s tudies , are used at present to pred ic t equipment needs twelve to twenty-four months i n the future. Some day the system may be used for rea l- t ime de-c i s i o n s . I t i s s t i l l too ear ly to evaluate f u l l y the MASSOP 27 integrated information system. This plan i s an attempt to handle a t o t a l a i r l i n e system by means of a s ing le com-prehensive cont ro l package. Whatever success the current and projected systems may enjoy, a i r l i n e operations are recognized as less than per fec t . An improvement of only two or three per cent would j u s t i f y m i l l i o n s of d o l l a r s invested i n cont ro l hardware and software, p a r t i c u l a r l y i n the large a i r l i n e s . One of the major problems current ly i s the inter face between a i r l i n e s for information t rans fer . These are reasons enough to expect continued development. J . Agard, "The A i r France Tarage P l a n , " AGIFORS Proceedings, 1968, p. 223. 2 7 J . F . Judge, "MASSOP—A New Cost Weapon for Management," A i r l i n e Management and Marketing, October 1970, p. 96. I I . SCHEDULING A i r l i n e scheduling i s the process by which a i r c r a f t and aircrew i t i n e r a r i e s are s p e c i f i e d . E f f e c t i v e scheduling requires consideration of revenue t r a f f i c demand, connecting f l i g h t s , regulatory and operating constraints and costs. While treated here mainly as a short-term planning function, scheduling i s associated with longer range decisions of f l e e t planning, the a c q u i s i t i o n of new a i r c r a f t , and the retirement of e x i s t i n g a i r c r a f t . Scheduling begins with a i r c r a f t r o t a t i o n . In the short run, f l e e t size and maintenance requirements are r i g i d constraints. Constraints omitted from the models discussed i n t h i s chapter include b i l a t e r a l agreements (on numbers of f l i g h t s or percentages of t o t a l t r a f f i c permitted). F l i g h t s may be limited to a s p e c i f i c number per week, or to a number related to the a c t i v i t y of another a i r l i n e . T r a f f i c l i m i t s i n terms of another a i r l i n e or i n terms of t o t a l t r a f f i c are bothersome, i n Canada and elsewhere. In addition to lay-over and hours of work conditions, cabin crews must have s p e c i f i c language c a p a b i l i t i e s . A t t r i t i o n i n cabin crews i s high, but owing to seasonal buildups and declines, a t t r i t i o n provides a painless means to reduce crew sizes i n o f f seasons. However, the costs of t r a i n i n g are substantial. Reserve crews pose problems of u t i l i z a t i o n . What percentage of reserves should be used? Should f l i g h t s ever be c a n c e l l e d due t o r e s e r v e s s h o r t a g e s — a n d i f so, how oft e n ? Real world s o l u t i o n s are u s u a l l y compromises. Were i t p r a c t i c a l , a Boeing 707 f l y i n g the U n i t e d S t a t e s c o a s t -t o - c o a s t w i t h one hundred per cent l o a d f a c t o r would earn 2 8 p r o f i t s exceeding:the c o s t of the a i r c r a f t i n one year. The p r e s s u r e of co m p e t i t i o n i s such t h a t load f a c t o r s remain c l o s e t o a breakeven l e v e l . A i r l i n e p r o f i t l e v e l s a c c e p t a b l e to the U. S. C i v i l A e r o n a u t i c s Board have not been f a r above a ten per cent r a t e of r e t u r n . — R e v i e w of Sc h e d u l i n g Models F i g u r e 2 attempts t o show the r e l a t i o n s h i p s between d a t a and s c h e d u l i n g models. Rectangular boxes h o l d de-t e r m i n i s t i c i n f o r m a t i o n . C i r c l e s c o n t a i n p r e d i c t i o n s s u b j e c t t o u n c e r t a i n t i e s . Only the schedule models r e p r e s e n t e d i n the lower c i r c l e w i l l be d i s c u s s e d here. L e v e l o f s e r v i c e feedback i s a p p l i c a b l e mainly i n the long run. For most a i r l i n e s the schedule i s s t a t i c over a p e r i o d . The c h i e f e x c e p t i o n among U.S. c a r r i e r s i s E a s t e r n A i r l i n e s ' S h u t t l e s e r v i c e . S c h e d u l i n g models can be g e n e r a l i z e d i n the form: F i n d a combination of valu e s X (the problem v a r i a b l e s ) t h a t 2 8 -K.M Ruppenthal', A i r L i n e Management, p u b l i s h e d i n d r a f t form by the Graduate School of Bus i n e s s , S t a n f o r d U n i v e r s i t y , 1968. 1 income pofo/a-tn * ouri OpekATi CoA/STf?A firt are Scheofute • I i~\ per-form, an mainfen^an S-icL-fjOffS to^aat'ny SUMMARY Advert ise Promote ^ TRAFFIC FoKec/ts-ir {riff. if ?ouif.j-(/tflit, 1 market J si are 4 •fohtirtq / Q r\ r I -treqoertcy, t'rfiprf ops. a* J'/eet's.-, em arte 't/7\ ft, e t -L tin e -ttave/ a'tfeLr-f. CLrrtye feme, ce rep is e tt I i K T cy Cvmpett\tii/f Sen/. Le^e/s (f?e</enoe ft. COST r\e/a frerr 577 (f»s o p t i m i z e s an o b j e c t i v e f u n c t i o n R(X) and which s a t i s f i e s number o f c o n d i t i o n s or c o n s t r a i n t s , (X) = 0 . Some t y p i c a l o b j e c t i v e s are the f o l l o w i n g : Minimize f l e e t s i z e . Minimize o p e r a t i n g c o s t . Maximize (revenue minus cost) f o r the system. Maximize ( s o c i a l b e n e f i t minus cost) f o r the system and p u b l i c . Some t y p i c a l c o n s t r a i n t s t o s c h e d u l i n g models are l i s t e d as f o l l o w s : Number of a i r c r a f t i n the f l e e t . Route c o n s t r a i n t s i n d a i l y s e r v i c e , m u l t i - s t o p i t i n e r a r i e s . Type of a i r c r a f t i n the f l e e t . R e l a t i o n s h i p between demand and frequency of s e r v i c e T e r m i n a l gate r e s t r i c t i o n s . Minimum or maximum d a i l y f r e q u e n c i e s on r o u t e s . M u l t i p l e departure times f o r any s e r v i c e . Maximum d a i l y o p e r a t i o n s a t a s t a t i o n . S t a t i o n balance c o n s t r a i n t s . F l e e t a c q u i s i t i o n and d i s p o s a l c o n s t r a i n t s . S a h e d u l i n g m o d e 1 a l a s s i f i c a t i o n . The f i v e main types o f model d i s c u s s e d here are as f o l l o w s : 1. F l e e t Assignment Models. L i n e a r Programming, (LP) models a s s i g n a i r c r a f t types to s e t s of routes on the route map. 2. F l e e t P l a n n i n g Models. These are extensions of the f l e e t assignment of a i r c r a f t over s e v e r a l p l a n n i n g c y c l e s . 3. D i s p a t c h i n g Models. U s u a l l y f o r a s i n g l e r o u t e , d i s p a t c h i n g models determine o p t i m a l d i s p a t c h time p a t t e r n based on demand. 4. A i r c r a f t Routing Models. Given a schedule map, the r o u t i n g model determines an o p t i m a l r o u t i n e f o r the i n d i v i d u a l a i r c r a f t . 5. F l e e t Routing Models. Using network flow methods, f l e e t r o u t i n g models f i n d o p t i m a l f l e e t r o u t i n g s without i d e n t i f y i n g i n d i v i d u a l a i r c r a f t . F l e e t A s s i g n m e n t M o d e Is f o r s h o r t and medium range p l a n n i n g , i n LP format have grown from an o r i g i n a l model by 29 D a n t z i g and Ferguson i n 1954. F l e e t assignment models can be u s e f u l as f l e e t p l a n n i n g t o o l s because they can optimize type and numbers of a i r c r a f t f o r the a i r l i n e f l e e t . Assumptions i n these models u s u a l l y i n c l u d e : 1. A s o l u t i o n over a f i x e d time p e r i o d T. 2. Average t r a f f i c d u r i n g T i s estimated f o r each r o u t e . 3. A l o a d f a c t o r assumption i s made f o r each a i r c r a f t . E x t e n s i o n s of t h i s model can i n c l u d e c o n s i d e r a t i o n of c o m p e t i t i o n and can f i x market share as a f u n c t i o n of r e l a t i v e frequency. S i z e of the LP matrix f o r two hundred c i t y p a i r s , f i v e a i r c r a f t types twenty c i t i e s , and three b r e a k p o i n t s i n the .market share curves ( f o r l i n e a r approx-. im a t i o n of demand) ,. g i v e s 1,800 v a r i a b l e s and about seven hundred c o n s t r a i n t s . F l e e t assignment models have been used by a i r c r a f t manufacturers, and by a i r l i n e s f o r medium range p l a n n i n g , and by government r e g u l a t o r y departments. In a d d i t i o n , , s u b j e c t t o the c o n s t r a i n t s of e x i s t i n g f l e e t s i z e and type composition, the model i n d i c a t e s the op t i m a l d i s -p o s i t i o n of a i r c r a f t among the routes a v a i l a b l e . F l e e t . P l a n n i n g M o d e Is . . . are ext e n s i o n s of the assignment LP, and are used f o r p r o j e c t i n g f i v e t o ten years i n the f u t u r e . They p r o v i d e management i n f o r m a t i o n f o r long term p l a n n i n g and f i n a n c i n g . A i r c r a f t manufacturers have an i n t e r e s t i n f l e e t p l a n n i n g . To the extent t h a t they are able t o a n t i c i p a t e the needs of c i v i l a v i a t i o n , , they can d e s i g n and b u i l d a i r c r a f t w i t h the g r e a t e s t market success. I n d i v i d u a l a i r l i n e s make long run d e c i s i o n s on the type and number of a i r c r a f t needed, and s h o r t run d e c i s i o n s on how b e s t t o u t i l i z e the a i r c r a f t a v a i l a b l e . A i r l i n e G. B. D a n t z i g , L i n e a r Programming and E x t e n s i o n s , P r i n c e t o n : P r i n c e t o n U n i v e r s i t y P r e s s , 1963, p. 568. o b j e c t i v e s may be to maximize p r o f i t or r e t u r n on investment, or t o g i v e maximum s e r v i c e a t a giv e n cost., or to i n c r e a s e n a t i o n a l p r e s t i g e . A i r c r a f t manufacturers e v a l u a t e the o b j e c t i v e s of i n d i v i d u a l a i r l i n e s , summing t o o b t a i n a composite p i c t u r e of f u t u r e a i r c r a f t markets. E x e c u t i v e s of U n i t e d A i r L i n e s have been d i s a p p o i n t e d w i t h " c r o s s s e c t i o n a n a l y s e s " and " g r a v i t y models" t h a t t r y to r e l a t e passenger volume to socio-economic f a c t o r s such as p o p u l a t i o n , gross n a t i o n a l product, and d i s p o s a b l e p e r s o n a l 30 income. M u l t i p l e r e g r e s s i o n a n a l y s i s and l i n e a r programming have been s i m i l a r l y d i s a p p o i n t i n g as f o r e c a s t i n g techniques. The market i s the f i r s t c o n s i d e r a t i o n i n s c h e d u l i n g , but the r e are o t h e r s : Route a u t h o r i t y and r e s t r i c t i o n s imposed by law. Competition. A i r c r a f t c h a r a c t e r i s t i c s and s e r v i c e needs. A i r p o r t l i m i t a t i o n s and co n g e s t i o n . Passenger a v e r s i o n s , f o r example, changing pl a n e s . M a n u f a c t u r e r s ' M o d e I s . Three major a i r c r a f t manu-f a c t u r e r s , Lockheed, Douglas, and Boeing have developed f l e e t p l a n n i n g models mainly f o r examining the long range a i r -W. G. Wi l l i a m s o n , "Computer Programs f o r F l e e t and Schedule P l a n n i n g , " AGIFORS Proceeding, 1 9 6 7 , p. 1 1 . c r a f t market. The Lockheed model i s b u i l t around the " A i r -l i n e System S i m u l a t i o n Model," under development s i n c e 31 32 1959. ' Assumptions of the Lockheed model are p r i n c i p a l l y as f o l l o w s : 1. Demand i s u n i f o r m l y d i s t r i b u t e d over time. 2. F l i g h t s are u n i f o r m l y spaced.through the schedule p e r i o d . 3. Time of day. e f f e c t s of demand are i g n o r e d . 4. Time e f f e c t s of a i r c r a f t p o s i t i o n i n g are i g n o r e d . The model generates f l i g h t f r e q u e n c i e s by route and by equipment type, t o serve as i n p u t f o r the " A i r l i n e S c h e d u l i n g Program. 1 1 The major shortcomings of the Lockheed models have been p o i n t e d out as (1) i g n o r i n g time of day demand d i s t r i b u t i o n and (2) l a c k of i n t e r p l a y between f r e -33 quency and market share. The Lockheed model has been improved and expanded over the y e a r s . However, i n 1970 the a b i l i t y t o generate a good schedule was s t i l l i n development stages. Wm. A. Gunn, " A i r l i n e System S i m u l a t o r , " Operations  Research, V o l . 12, No. 2, 1964, pp. 206-229. 32 L.R. Howard, and D.O. Eberhardt, " A i r l i n e S i m u l a t i o n f o r A n a l y s i s of Commercial A i r p l a n e Markets," T r a n s p o r t a t i o n S c i e n c e , V o l . 1, No. 3, 1967, p. 131. Willxamson, op_; c i t . , p. 20. Douglas constructed an " A i r l i n e Operations and Planning Model" that included eight operat ional models. In 196 8 the composite Planning Model was s t i l l being improved and expanded. Douglas made no apology for " r e q u i r i n g the user to be both d i l i g e n t and i n t e l l i g e n t . Too often the analysts f ee l that the program i s an end i n i t s e l f , „34 • • • Boeing i n 1967 was i n the ear ly stages of developing a scheduling model that would r e f l e c t time-of-day d i s t r i b u t i o n of demand. I t i s apparent that the plane bui lders 1 problem i s not b a s i c a l l y a i r l i n e scheduling, although a l l three have worked on scheduling models. D i s p a t c h i n g M o d e Is are used for determining optimal departure times. The frequency pattern for the system i s an input . An i n i t i a l t imetable i s usua l ly made manually for each route without regard for network cons iderat ions . Time of day demand f luctuat ions should be known. Dynamic programming may be used. In Figure 3 the stage var iab le i s time and the state var iab le i s the number 35 of passengers wai t ing . Passengers begin queuing at time ,-J.D. Kings ley , " A i r l i n e Operations and Planning Model , " Douglas Paper 5058, May 1968. 35 R. W. Simpson, "A Review of Scheduling and Routing Models for A i r l i n e Schedul ing , " AGIFORS Proceedings, 1969. zero. T h i s i s re p r e s e n t e d by the "no d i s p a t c h a r c " (diagonal l i n e ) from time zero t o time 1. At time 1, (or stage 1), a d i s p a t c h a r c removes the queue and the process of queueing begins anew. Such a model has a p p l i c a t i o n i n E a s t e r n A i r l i n e s ' S h u t t l e s e r v i c e , or i n more c o n v e n t i o n a l networks f o r which the frequency p a t t e r n i s s e t . In the example of F i g u r e 3, the "no d i s p a t c h " arcs are p a r a l l e l s t r a i g h t l i n e s , but t h i s w i l l not be the case i n p r a c t i c e , p a r t i c u l a r l y i f a r r i v a l s from c o n n e c t i n g f l i g h t s are i n c l u d e d . A i r c r a f t R o u t i n g M o d e l s . Dynamic programming has been used s e q u e n t i a l l y i n a s i n g l e - v e h i c l e r o u t i n g model to 3 6 g i v e "good" but not o p t i m a l r o u t i n g f o r a s e t of v e h i c l e s . As the method i s i n e f f i c i e n t , i t w i l l not be d e s c r i b e d here. F l e e t R o u t i n g . M o d e l s have been c o n s t r u c t e d u s i n g the "Out of K i l t e r " a l g o r i t h m of network flow theory. The problem i s to f i n d the s e t of s e r v i c e s t h a t w i l l y i e l d maximum income, given a schedule of p o s s i b l e non-stop s e r v i c e s , and expected t r a f f i c f o r the l e v e l of s e r v i c e planned, ( i n c l u d i n g c o m p e t i t i v e s e r v i c e s ) . T h i s technique g i v e s an o p t i m a l s o l u t i o n f o r a given f l e e t s i z e , and e v a l u a t e s income f o r v a r y i n g f l e e t s i z e . C o n s t r a i n e d f l e e t r o u t i n g m o d e l s , u s i n g i n t e g e r LP, d e t e r m i n e t h e m i n i m a l f l e e t s i z e r e q u i r e d f o r a g i v e n s c h e d u l e o f s e r v i c e s t o be f l o w n by a f l e e t o f a i r c r a f t o f a s i n g l e t y p e , where d i s c r e t e d e p a r t u r e t i m e s a r e a s s i g n e d f o r e a c h s e r v i c e . M u l t i - f l e e t r o u t i n g m o d e ls d e t e r m i n e t h e m i n i m a l number o f a i r c r a f t r e q u i r e d and t h e number and r o u t i n g p a t t e r n f o r e a c h a i r c r a f t t y p e s u c h t h a t e v e r y s e r v i c e s p e c i f i e d i s f l o w n . Up t o 1970, f u l l s c a l e a i r l i n e p r o b l e m s had .not been t r i e d u s i n g t h i s t e c h n i q u e . S i m p l i f y i n g a s s u m p t i o n s t e n d t o remove a l l o f t h e s e m o d e ls f r o m r e a l i t y . Much o f t h e m a t e r i a l g i v e n i n t h e 37 b i b l i o g r a p h y was d e v e l o p e d a t t h e M a s s a c h u s e t s I n s t i t u t e o f T e c h n o l o g y b u t d o e s n o t a p p e a r t o have been w i d e l y known t o a i r l i n e o p e r a t i o n s d e p a r t m e n t s a t t h e t i m e Mr. Simpson's p a p e r was p r e s e n t e d . F l e e t S c h e d u l i n g a t A i r Canada A i r Canada d e v e l o p e d a t h r e e - p a r t p r o g r a m f o r f l o w -i n g p a s s e n g e r s o v e r r o u t e n e t w o r k s . The main v a r i a b l e i s t h e s c h e d u l e . T h i s i s i n p u t t e d t o t h e model and t h e o u t p u t i s a l i s t of passenger flows. The model i s not an opt imizer , but i t shows the ef fects of schedule changes and therefore indicates preferences among the schedules proposed. Figure 4 i l l u s t r a t e s the schematic r e l a t i o n s h i p of the three models used: 1. A t t r a c t i v e Path Generator. 2. T r a f f i c D i s t r i b u t i o n Est imator. 3. Passenger a l l o c a t i o n process. An a t t r a c t i v e path i s a f l i g h t or set of f l i g h t s having a f l y i n g time during which no a l t e rna t ive path can be traversed between the o r i g i n and de s t ina t ion . (Generally the most d i r e c t paths with shortest elapsed times are most a t t r a c t i v e ) . The a t t r a c t i o n of paths i s assumed to be a function of frequency and t r i p time. A t t r a c t i o n in terva l s are provided to cover the ent i re day, without overlap i n the period of a t t r a c t i o n of any two adjacent paths. Thus the a t t r a c t i v e path generator se lects from a l l proposed paths those that w i l l be most a t t r a c t i v e . An e f fec t ive a t t r a c t i v e path generator should include ex i s t ing schedules operated by competitors. A model of t h i s type, could be of in te re s t to regulatory author i t i e s for evaluat ion of route regulat ions and awards. G. Gagnon, "A Model for Flowing Passengers over A i r l i n e Networks," AGIFORS Proceedings, 1967, p. 29. The T r a f f i c D i s t r i b u t i o n E s t i m a t o r d e f i n e s p a s s e n g e r demand by day o f week and t i m e o f day b a s e d on e x p o n e n t i a l s m o o t h i n g o f h i s t o r i c a l d a t a . The r e s u l t a n t d i s t r i b u t i o n (two u n i m o d a l c u r v e s ) , was a p p r o x i m a t e d by means o f t h e B e t a 39 f u n c t i o n , s i m p l y by a d j u s t i n g p a r a m e t e r s . However, t h i s i s an a r e a where human judgement i s s t i l l much i n f o r c e . The m o d e l p r o v i d e s a n e a t q u a n t i f i c a t i o n method. The A l l o c a t i o n P r o c e s s c ombines t h e p a t h s f r o m t h e A t t r a c t i v e P a t h G e n e r a t o r w i t h t h e demand o f t h e T r a f f i c D i s t r i b u t i o n E s t i m a t o r t o p r e d i c t p a s s e n g e r f l o w s . I f . a p a s s e n g e r i s a l l o c a t e d t o a f l i g h t t h a t i s b o o k e d , t h e p a t h becomes " n o n - a t t r a c t i v e " and t h e p a s s e n g e r w i l l be r e a l l o c a t e d . T h i s means t h a t t h e a t t r a c t i o n p a t t e r n i s a f f e c t e d by t o t a l demand. However, i f t h e r e a r e a l t e r n a t i v e r o u t e s ( c o m p e t i -t i o n , o r o t h e r modes), t h e s e s h o u l d be c o n s i d e r e d . The model d e a l s w i t h l e g t r a v e l r a t h e r t h a n t r a v e l between u l t i m a t e o r i g i n a and d e s t i n a t i o n , and t h i s i s p e r h a p s i t s g r e a t e s t w e a k n e s s . A " s p u r i o u s " demand p i c t u r e f o r l e g t r a v e l i s i n s e n s i t i v e t o m a j o r f a c t o r s s u c h as c o n n e c t i n g f l i g h t s , where t h e u t i l i t i e s o f t h e d e p a r t u r e o r a r r i v a l t i m e s a r e s u b j e c t t o " a l l o r n o t h i n g " v a r i a t i o n s . P r o m o t i o n a l f a r e s m i g h t a l s o u p s e t t h e demand d i s t r i b u t i o n and s h o u l d be i n c l u d e d . N e v e r -t h e l e s s , t h e m odel i s c a p a b l e o f r e v e a l i n g b o t t l e n e c k s and s l a c k s i n a p r o p o s e d s c h e d u l e . 39 H.W. R e d d i c k , and F.H. M i l l e r , A d v a n c e d M a t h e m a t i c s  f o r E n g i n e e r s , New Y o r k : W i l e y , 1948, p. 216. A i r c r a f t R o t a t i o n A i r c r a f t r o t a t i o n i s the assignment of s p e c i f i c a i r c r a f t t o meet a given s e t of a r r i v a l s and d e p a r t u r e s . U n f o r t u n a t e l y , the term "schedule" may be used w i t h r e f e r e n c e to a i r c r a f t r o t a t i o n , or w i t h .reference to the s e t of a r r i v a l s and d e p a r t u r e s . Crewing c o n s i d e r a t i o n s are u s u a l l y secondary, and can a f f e c t the a i r c r a f t r o t a t i o n o n l y i n d i r e c t l y by i n d i c a t i n g p o s s i b l e economies t h a t may or may not be achieved by minor adjustments to the a i r c r a f t r o t a t i o n . W i t h i n an e x i s t i n g framework of a r r i v a l s and d e p a r t u r e s , r o t a t i o n might be o p t i m i z e d by f i n d i n g the minimum number of a i r c r a f t r e q u i r e d . A n i n t u i t i v e a p p r o a c h . An experimental approach by Helmut R i c h t e r proposed a simple h e u r i s t i c procedure f o r 4 0 m i n i m i z i n g i d l e times between f l i g h t segments. A"coupling matrix" shows the. i d l e times between a l l p o s s i b l e connecting segments. An i l l u s t r a t i o n o f the c o u p l i n g matrix and the schedule f o r which i t i s c o n s t r u c t e d i s shown i n F i g u r e 5. T h i s i s an assignment problem. By s h i f t i n g f l i g h t segments, i d l e times i n the matrix can be a l t e r e d . The s m a l l e s t sum of i d l e times corresponds w i t h the minimum a i r c r a f t requirement. The example given i s extremely simple compared wi t h a f u l l - s i z e d a i r l i n e problem. I t i s o n l y a one-day r o t a t i o n 4 0 H. R i c h t e r , "Optimal A i r c r a f t R o t a t i o n s Based on Optimal F l i g h t Timing," AGIFORS Proceedings, 1 9 6 8 , pp. 3 6 - 3 9 . whereas a weekly r o t a t i o n i s t y p i c a l of most a i r l i n e s . The e f f i c i e n c y of the method might prove d i s a p p o i n t i n g i n p r a c t i c e , and any s o l u t i o n s obtained would have to be reviewed w i t h r e s p e c t t o maintenance and .crew s c h e d u l i n g . An e x t e n s i o n of t h i s model t h a t overcomes some of these o b j e c t i o n s i s gi v e n below i n D. teWinkel's model f o r 41 a i r c r a f t s c h e d u l i n g i n a r a d i a l network. A i r c r a f t R o t a t i o n . w i t h s e v e r e c o n s t r a i n t s . A com-p l e t e l y d i f f e r e n t emphasis on r o t a t i o n was a p p l i e d by Quantas 42 Airways L i m i t e d . Due t o the c o n s t r a i n t s a s s o c i a t e d with a s m a l l a i r l i n e on long-haul r o u t e s , t h e r e i s l e s s freedom i n s c h e d u l i n g , and more complicated crew arrangements than on s h o r t h a u l r o u t e s . Because the movements are few, and because r e s t r i c t i o n s prevent e x t e n s i v e t i m i n g a l t e r a t i o n s , (high revenue p o r t s should be s e r v i c e d a t reasonable hours, and a i r p o r t curfews and cong e s t i o n peaks should be a v o i d e d ) , the schedules are prepared manually. The computer i s used i n t h i s case t o make a f e a s i b i l i t y check, p r i m a r i l y t o ensure t h a t the f l e e t can handle the schedule, with allowances f o r maintenance stops and route d e l a y s . D. teWinkel, "An A l g o r i t h m f o r A i r c r a f t S c heduling i n a R a d i a l Network," AGIFORS Proceedings, 1969. A.J. Walker-Powell, " A i r c r a f t S c h e d u l i n g by Computer," AGIFORS Proceedings, 1969. Route d e l a y s are not constant. There are wide v a r i -a t i o n s i n a r r i v a l times among the r o u t e s . "Time pads" f o r r o u t e - t o - r o u t e l i n k a g e s are designed to accommodate e i g h t y -f i v e per cent o f the d e l a y s , based on an assumed log-normal d i s t r i b u t i o n of d e l a y s . T h i s r o t a t i o n model was s t i l l i n t r i a l o p e r a t i o n a t the end of 1969, and at t h a t time was known to have some shortcomings, mainly i n connec t i o n w i t h allowances f o r minor maintenance. R o t a t i o n o f a i r c r a f t i n a_ r a d i a l n e t w o r k was d e s c r i b e d i n a paper by D. teWinkel, w i t h emphasis on the problems of ground crew and hangar u t i l i z a t i o n as w e l l as time a l l o c a t i o n s 43 f o r the maintenance of each a i r c r a f t . S o l u t i o n s t h a t y i e l d long unbroken' i n t e r v a l s of ground time a t home base are d e s i r a b l e . R i c h t e r ' s assignment matrix c o u p l i n g of F i g u r e 5 i s now made n x n f o r the f l i g h t combinations i n a week. A c o n f i g u r a t i o n matrix {-a^} s t o r e s the times r e q u i r e d t o convert from c o n f i g u r a t i o n "k" to c o n f i g u r a t i o n "1". A branch-and-bound a l g o r i t h m w i l l s o l v e the assignment problem t o minimize the p e n a l t y a s s o c i a t e d w i t h m i s - a l l o c a t i o n i n each row, but the n x n matrix leads t o a l a r g e number of s o l u t i o n s . A d j u s t i n g the a l g o r i t h m t o s k i p branches i n the D. teWinkel, op_. c i t . solution tree, the number of solutions generated i s greatly reduced. Computing time for a 57 x 57 matrix was about f i v e minutes, y i e l d i n g 440 useful solutions. The method i s applicable to other combinatorial problems, p a r t i c u l a r l y to crew scheduling. .Spare A i r c r a f t . A special case of a i r c r a f t rotation i s the use of spare a i r c r a f t , kept mainly to reduce schedule perturbations. D. Bindler-Gaspard reviewed the costs and expected benefits, taking into account the assumed binomial p r o b a b i l i t y d i s t r i b u t i o n of perturbations, and t h e i r costs, and comparing t o t a l expected perturbation costs with spare 44 a i r c r a f t costs. The conclusion reached (for Sabena) was that spare a i r c r a f t were not j u s t i f i e d . More f l e x i b l e scheduling of f l y i n g a i r c r a f t was suggested as a more suitable t a c t i c . This decision would not necessarily hold for every a i r l i n e . Sabena i n 1969 evidently had over-expanded i t s maintenance f a c i l i t y and was under heavy f i r e for having spent funds 45 from subsidies i n excess f a c i l i t i e s . ^D. Bindler-Gaspard, "Spare A i r c r a f t — A Necessity or a Superfluity?" AGIFORS Proceedings, 1969. Aviation Week and Space Technology, 7 A p r i l , 1969, p. 33. Scheduling of Personnel and Cargo S ta r t ing with manpower requirements by day and by time of day, .and. the union contract cons t ra in t s , an integer LP may be formed to determine the s t a r t ing times and the numbers of men required per s h i f t . I f th i s leads to a large program, the problem may be rewri t ten as an optim-46 i z a t i o n over a number of small i n t e g e r • L P ' s . The sub-problem i s to f ind the manpower necessary for each s h i f t . Where s h i f t s t a r t i n g times are f l e x i b l e , there are many poss ib le combinations of s h i f t s . To f ind the optimal s h i f t schedule, the problem i s formulated as a normal LP without integer cons t ra int s . The normal LP formulation may be used for non-union employees, where hours of work constra ints are less . s t r ingent . Implementation of such a program by TWA i n 19 69 was expected to save ha l f a m i l l i o n d o l l a r s annually i n labour 47 costs . However, there was s t i l l room for improvement. The so lu t ion method apparently d i d . n o t allow for schedule d i f ferences by day through the week, for s t a f f rota t ions s h i f t 48 to s h i f t , or for days o f f . 46 K . C . Khanna, and H. Takamori, "Optimal Staf f at A i r l i n e Terminal s , " AGIFORS Proceedings, 1969. 4 7 I b i d . 48 D. T h i b a u l t , Comments on Khana and Takamori, op. c i t . Crew S c h e d u l i n g i s normally formulated as an integer LP. One of the main d i f f i c u l t i e s with t h i s approach i s the matrix s i z e , with t y p i c a l l y hundreds of rows and tens of thousands of columns. Aer Lingus avoided th i s with an i n i t i a l matrix that was only 36 x 300,, but for large matrices , the methods of reduction are severa l , and i n 1970 were s t i l l 49 xn the experimental stages. A common object ive i s to minimize numbers of crews. Although some feas ib le solut ions were ava i lab le i n 1967, severa l approaches were under development by d i f f e r e n t a i r -l i n e s . They f e l l in to two main c lasses : 1. Integer LP formulations with appropriate algorithms, such as the Glenn T. Martin CEIR Inc. code or the House-Nelson RADO method. 2. Tree structures with combinatorial algorithms for exhaustive or inexhaustive enumerations of the so lu t ion space. Several branch and bound and p a r t i t i o n i n g techniques were being explored i n 1967. Some techniques were feas ib le but d e f i c i e n t i n the sense that they took 50 too much computer time or d i d not optimize. F. S te iger , " A c t i v i t y Report of the AGIFORS Study Group--Crew Schedul ing , " AGIFORS Proceedings, ,1967, p. 120. Deutsche L u f t h a n s a developed a three-phase model 51 f o r crew r o t a t i o n on a seven day c y c l e . S t a r t i n g with a gi v e n r o t a t i o n p l a n f o r the seven day c y c l e of f l i g h t number, departure s t a t i o n s and times, and crew requirements, (some f l i g h t s have no ca b i n crew), an i n t e g e r LP i s formed w i t h zero-one v a r i a b l e s a^_. f o r duty on l e g " i " and duty " j " . T h i s "duty matrix" has the o b j e c t i v e of m i n i m i z i n g the number of crews. Crew assignments are made im p e r s o n a l l y i n phase (1) s u b j e c t to maximum duty l e n g t h s , minimum r e s t between d u t i e s , and maximum c y c l e l e n g t h . Phase (1:) of the model was o p e r a t i o n a l and opt i m i z e d crews f o r given schedules. Phases (2) and (3) were t o a s s i g n crews i n d i v i d u a l l y and t o cover procedures f o r emergencies such as i l l n e s s . In s e p a r a t i n g a i r c r a f t r o t a t i o n from crew assignments, s u b o p t i m i z a t i o n of the whole system i s probable. However, the combined problem of a g e n e r a l o p t i m i z a t i o n of a i r c r a f t and crews i s l a r g e r than the a i r c r a f t r o t a t i o n problem or the crew schedule problem, e i t h e r of which can have thousands of v a r i a b l e s and c o n s t r a i n t s . R e s e r v e C r e w S e h e d u l i n g i s a s p e c i a l type of crewing. I n t u i t i v e l y , the heeds f o r r e s e r v e crews are f u n c t i o n s of weather, v a c a t i o n s , r e g u l a r crew workloads,.leaves of R. G r i e s s h a b e r , "A H e u r i s t i c Model f o r the Impersonal Phase of Crew Sche d u l i n g , " AGIFORS Proceedings, 1968, p. 535. absence, a i r t r a f f i c c o n t r o l (ATC) d e l a y s , t r a i n i n g r e q u i r e -ments, and the l i k e . P i n p o i n t i n g the r e l a t i o n s h i p between r e s e r v e requirements and any of these f a c t o r s had y e t to 52 be done in . 196 8. A i r l i n e s g e n e r a l l y use a b i d system f o r a i r c r e w s . L i s t s of scheduled and r e s e r v e r o u t i n e s are p u b l i s h e d and a l l a i r c r e w " b i d " on the p o s t i n g s . Assignments are made on the b a s i s o f p r e f e r e n c e s t a r t i n g w i t h the most s e n i o r and f i n i s h i n g w i t h the most j u n i o r crew members. At American A i r l i n e s i t was hypothesized t h a t : Reserve U t i l i z a t i o n =• K± + A ( U r e g ) + B (R) + C(T) + D (V) , where K^, A, B, C, and D, are co n s t a n t s , and Ureg = u t i l i z a t i o n of r e g u l a r crews i n man-hours R = r a t i o o f r e s e r v e s t o r e g u l a r s T = e q u i v a l e n t man-months of t r a i n i n g or r e t r a i n i n g V = e q u i v a l e n t man-months of v a c a t i o n . By r e g r e s s i o n a n a l y s i s , "A" was found t o be almost always p o s i t i v e , w h i l e "B" was c o n s i s t e n t l y n e g a t i v e . T h i s i m p l i e d t h a t r e s e r v e f l y i n g v a r i e d i n d i r e c t p r o p o r t i o n t o the number of f l y i n g hours scheduled, and t h a t average r e s e r v e D.R. Bornemann, "A L i n e a r Programming S o l u t i o n t o the Reserve Crew Sch e d u l i n g Problem," AGIFORS Proceedings, 1968, p. 455. u t i l i z a t i o n d e c l i n e d as more r e s e r v e b i d s were p u b l i s h e d . An LP f o r m u l a t i o n a r r i v e d a t the o p t i m a l s e t s o f b i d s , s u b j e c t t o d e s i r e d minimum r e s e r v e s on duty each day f o r one month. A r e s e r v e with only one day of duty remain-i n g , i s of l i m i t e d use. F i g u r e 6 shows how a v a i l a b i l i t y c o n s t r a i n t s ensure t h a t the number of r e s e r v e s w i t h three or more c o n s e c u t i v e duty days remaining, i s maintained above a s p e c i f i e d minimum f o r each day of the month. The problem may be w r i t t e n : Ax ^ b, minimize cx . where A = matrix of b i d parameters x = o p t i m a l s e t of b i d s b = d e s i r e d minimum number of r e s e r v e s on duty c = c o s t = 1 per b i d 1 i f h o l d e r of b i d j i s on duty a i j ^0 otherwise i = 1, 2, 3, • • • , 3 0 . (days of the month), but i a l s o has values 31, 32, •• , 60, corresponding t o days ( i - 30). For valu e s of i between 30 and 60, a.. has valu e s of 1., .5, .4, or zero, as f o l l o w s : a.. = 1.0 i f h o l d e r of j i s coming on duty on 1-' day ( i - 30) f o r three or more days a.. = .5 i f h o l d e r of b i d j i s on second duty ^ day and has three or more c o n s e c u t i v e days remaining A fi/ALY\StS dcJrafton oP X Trip jPvrcufio 0 or i Z 3 r D P ft* Set rob <L-t?r •a Cost: V/fi i z 3 3o V 3i 33 v t -So 2 5 /O / / / '*>£ ho 0 I I •s •4 t rom • A he •5 . - m i . y-WGfrtfes r^rocee C/^EvY 7 3 Z IS\ > 7 j Scf/&& clesi'red 'fft'rni/frrs duty or, each Ce/7-hi r trrt'rr O r ' m o r e Mys on reserves H^/i 3 t Corr&e c. resffa.irr < 7 4tz) a. . = .4 i f holder of b id j i s on his t h i r d i ~i J duty day and has three or more consecutive days remaining a . . = 0 otherwise. ID This system has been used success ful ly by American A i r l i n e s . Benefits r e s u l t i n g from.implementation were not s tated, but the model was aimed at d i r e c t d o l l a r savings i n reserve crew costs . Users of t h i s model should consider the assumption that the p r o b a b i l i t i e s of one, two or three day postings were assumed equal throughout the route system. This may not hold true for every a i r l i n e . C a r g o S c h e d u l i n g i s secondary to passenger flow i n a i r l i n e s with mixed f l i g h t s . The low p r i o r i t y for b e l l y cargo may be due to the low net r e turn . Ground handling costs were t y p i c a l l y 77 per cent of the 1968 revenue for haul ing a 53 thousand pounds three hundred mi les . A comparison between a l l - ca rgo and mixed passenger and cargo operations shows F l y i n g T i g e r ' s a l l - ca rgo produc t iv i ty as 409,000 ton km. per employee versus A i r Canada's mixed cargo produc t iv i ty of 54 66,000 ton km. per employee. A i r Canada appl ied an LP approach to cargo scheduling, maximizing revenue subject to de l ivery performance con-D.H. Maund, Comment on paper by Tennant and Batey, AGIFORS Proceedings, 1968, p. 16. A i r l i n e Management and Marketing, October 1970, p. 57. s t r a x n t s . The LP was used as a headquarters t o o l t o e s t i -mate a c t u a l loads i n the system fo r m e r l y a manual c a l c u l a t i o n . B e n e f i t s from the LP were m a i n l y . i n the r e d u c t i o n c a l c u l a t i o n s , and i n g i v i n g more e v a l u a t i o n s and more r a p i d assessment of a l t e r n a t i v e schedules at t w i c e - y e a r l y meetings w i t h cargo s e r v i c e managers. Much more development of s o l u t i o n techniques was needed t o a r r i v e a t o p e r a t i n g programs f o r weekly or d a i l y schedule response t o e x t e r n a l c o n d i t i o n s . I I I . CUSTOMER SERVICE In t h i s chapter, customer s e r v i c e i s a c t i v i t y t h a t r e q u i r e s p e r s o n a l c o n t a c t between a i r l i n e and customer, p a r t i c u l a r l y the l o a d i n g and u n l o a d i n g of passengers and baggage. As the a i r l i n e product i s g e n e r a l l y c o n s i d e r e d to be time, i t i s mainly i n time c o n s e r v a t i o n t h a t e f f o r t s toward b e t t e r s e r v i c e are d i r e c t e d , (always w i t h g r e a t e r e f f i c i e n c y and lower c o s t s i n mind). In 1969 Pan American planned to spend t h i r t e e n m i l l i o n d o l l a r s f o r a i r f r e i g h t t e r m i n a l s t o accommodate C.J. Tennant and A.T. Batey, "Schedule E v a l u a t i o n f o r A i r Cargo," AGIFORS Proceedings, 1968, p. 12. Boeing 747 t r a f f i c . ^ Spec ia l ground handling equipment expens.es for the Boeing 747 tended to of f set lower seat mile costs and reduce p r o f i t p o t e n t i a l . Passenger boarding on the 747 took from ten to f o r t y - f i v e minutes depending on 57 the load . Figure 7 i l l u s t r a t e s Pan American's ear ly experience loading the 747. A i r l i n e s sometimes agree to share f a c i l i t i e s for baggage handl ing , for example F i n n a i r and Bran i f f Internat ional at J . F . Kennedy A i r p o r t . United developed i t s own systems 5 8 at O'Hare a i r p o r t using Aerojet General high speed equipment. Eastern A i r Lines i n 1970 were studying "advance baggage" service expansion—sending baggage ahead on e a r l i e r f l i g h t s to improve service at d e s t i n a t i o n . This can be done i f 59 baggage i s checked i n ear ly enough. In 1968, passengers on average checked i n 1.3 bags. More than two hundred m i l l i o n pieces of baggage were handled. Ev ident ly more i n s t a l l a t i o n s for automatic baggage handling were needed. The Docutel system was designed for shock-proof carts t r a v e l l i n g f i f t e e n to twenty miles per hour b y , l i n e a r induct ion motor. In 1970 Pan American planned to be f i r s t to i n s t a l l t h i s system. The i n i t i a l i n s t a l l a t i o n , cos t ing more than three m i l l i o n 6 0 d o l l a r s was to be at Kennedy Internat ional A i r p o r t . 5 ^ A v i a t i o n Week and Space Technology, 31 March, 1969, p. 3 3 . 5 7 I b i d . , 29 June, 1970, p.25. 5 8 I b i d . , 31 March 59 p * 3 3 -I b i d . , 7 Sept. 1970, p . 33. 60 I b i d . , 6 J u l y , 1970, p. 30. 747 GROUND OPERATIONS "Ground operations on a New York to London departure take about three hours. Cargo loading, f u e l l i n g , systems checking and galley loading take place simultaneously, a l l within one and a half hours. Time sequence includes:" Taxi from hangar to terminal 10 to 15 Cargo loading 60 to 90 F u e l l i n g 30 to 45 Galley loading 30 to 43 Lounge boarding 60 Passenger boarding 45 Baggage loading 40 to 90 Taxi to runway 10 to 15 ATC delay (average i s 10 min.) 2 to 57 A r r i v a l at Kennedy: Deplaning 10 to 15 minutes Health and Immigration 10 to 20 II Baggage unload (biggest problem) 40 to 60 II Customs 20 t o 30 ti Figure 7 I n i t i a l Pan American 747 Experience. (From Aviation Week and Space Technology, 2 February 1970, p. 32) Although Braniff attempted to r e l i e v e congestion with a monorail at Love F i e l d , Dallas, conveying passengers from the parking l o t to the a i r c r a f t , ground transportation and congestion i s a problem area that . a i r l i n e s have seldom addressed i n the past, perhaps because road systems and surface transportation are outside t h e i r control. In the 1970's cargo may assume a more important r o l e , e s p e c i a l l y i n the jumbo f l e e t s . Cargo volume may increase as a r e s u l t ofXlower costs, including pickup and delivery, or through adoption of m i l i t a r y a i r l i f t systems innovations, standardized containers and handling f a c i l i t i e s and through 61 reduction of paperwork and documentation. While passenger t r a f f i c has increased, and w i l l continue to increase, f r e i g h t t r a f f i c growth has been more rapid. In 1953, cargo represented t h i r t y - f o u r per cent of a i r transport services. In 196 8 cargo represented forty-two per cent of a i r transport 62 service. Improvement of customer service i s often a problem of queueing. Three important ways of using queueing models are: (1) for planning new f a c i l i t i e s , (2) for seeking best use of e x i s t i n g f a c i l i t i e s , and (3) for comparison of B.A. Schriever, and W.W. S e i f e r t , A i r Transpor-t a t i o n 1975 and Beyond: A Systems Approach, Report of the Transportation Workshop, 1967, MIT Press, pp. 69-83. George R. Besse, "Some International Aspects of the Demand for A i r Transport," . A i r T r a n s p o r t a t i o n — a forward  look, Karl M. Ruppenthal (ed.), and Brian E. S u l l i v a n , Graduate School of Business, Stanford University, 1970, p. 18. a l t e r n a t i v e s . Queueing theory provides quant i ta t ive assessments of s p e c i f i c s i tua t ions rather than optimal dec i s ions . Present theory accommodates only the simplest queueing s i tua t ions and these are not the usual r e a l world s i t u a t i o n s . Simulations provide good answers but are c o s t l y . (How good an answer i s needed?) Simulations can be used to develop general rules of thumb. A l t e r n a t i v e l y , more t rac tab le so lu t ions , a l b e i t less accurate, may be found from s i m p l i f i e d models of r e a l s i t u a t i o n s . A t h i r d approach i s the Poisson Chain technique or imbedded Markov 64 chain technique. This method can handle Erlang s e r i e s , var i ab le a r r i v a l rates and var iab le service ra tes , and i t i s e a s i l y computerized. C h e c k - i n S e r v i c e . Aer Lingus examined manpower needs at i t s check-in counters. Service standards were set pre-v ious ly by management dec i s ion from tabulat ions of poss ible l eve l s of s e r v i c e : ^ 6 3 A . M . Lee, Appl ied Queueing Theory, London, Mac-M i l l a n , 1966. 64 A . . D e l l e r , "The Use of Poisson Chain Techniques i n the Solut ion of P r a c t i c a l Queueing Problems," AGIFORS Pro-ceedings , 1968, p. 483. ^ S . O ' B r o i n , "Manpower Planning for A i r p o r t Operat ions , " AGIFORS Proceedings, 196 8, p. 245. Standard A Mean Wait i n g Time B Prob. of wait _> 10 Min. C Prob. 5% of w a i t i n g 1. 1.5 min. 5% 10 min. 2. 2.0 " 10% 15 " 3. 4.0 11 20% 25 " In the t a b l e above, columns A, B, and C are a l t e r n a t e methods of s e t t i n g standards. They do not n e c e s s a r i l y apply s i m u l t a n e o u s l y , but Aer Lingus decided t o i n v e s t i g a t e A and B. Data r e q u i r e d i n c l u d e d a i r c r a f t schedules, expected passenger l o a d s , a r r i v a l p a t t e r n by f l i g h t , average group s i z e , s e r v i c e time by passenger group and s e r v i c e time d i s -t r i b u t i o n . For baggage r e g i s t r a t i o n the day i s d i v i d e d i n t o f i v e - m i n u t e i n t e r v a l s , " i " . The d i s t r i b u t i o n f o r a r r i v a l p a t t e r n i s g i v e n as P ( t - i ) , the p r o p o r t i o n of a r r i v a l s d u r i n g i n t e r v a l " i " f o r departure a t time " t " . Of those t h a t c a t c h the f l i g h t , i t was assumed t h a t P ( j ) i s zero where j = 36. (Nobody a r r i v e s more than three hours e a r l y ) . S e r v i c e time d i s t r i b u t i o n was found by o b s e r v a t i o n . I t was w e l l approximated by an E r l a n g d i s t r i b u t i o n . S i m i l a r analyses were made of the t i c k e t desk, and departure gate. V a l i d a t i o n was i n t u i t i v e on the b a s i s of informed judgement. Having thus s p e c i f i e d s t a f f requirements through the day f o r s p e c i f i e d l e v e l s of s e r v i c e , the next step was s h i f t s c h e d u l i n g i n compliance w i t h the union agreement. F i g u r e 8 shows.the s t a f f i n g p r o c e s s . Some r e - a l l o -c a t i o n of s u r p l u s may be p o s s i b l e i n order t h a t s u r p l u s e s be more u n i f o r m l y d i s t r i b u t e d a c r o s s the s h i f t . The second phase of s t a f f i n g was to make weekly c y c l e s f o r days o f f . 7 n j = l i = l where N = s t a f f r e q u i r e d i = s h i f t number j = day of week. KL.. i s the number of s t a f f on s h i f t " i " , day " j " , N, l a r g e r than ^, i n c l u d e s allowance f o r working f i v e days out. of seven. In the N x 7 s t a f f i n g a r r a y , each column r e p r e s e n t s a day of the week, and each row r e p r e s e n t s one s t a f f member. To o b t a i n .a l e g a l c o n f i g u r a t i o n , one or two s t a f f members may be added. The method need not be d e s c r i b e d i n more d e t a i l here. The experienced judgement of o p e r a t i n g s t a f f was the main v a l i d a t i o n of the a n a l y s i s , and the a n a l y s i s was c o n s i d e r e d adequate. The same problem was s t u d i e d by KLM a t Schiphol. A i r p o r t , where queues were m u l t i - s e r v i c e , f i r s t - c o m e - f i r s t -6 6 served, w i t h observed E r l a n g 8 s e r v i c e c h a r a c t e r i s t i c s . 6 6 W. Jensema, "Passenger Handling Model," AGIFORS Proceedings,. 1967, p. 52. INDEX START TIME REQUIRED R l OF NO. R SHIFT R2 R3 SURPLUS NUMBER o r S REPORT -S 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 S t a r t T i m e s t l t 2 0800 3 0 0 0 0 0900 7 4 -2 -2 2 1000 7 4 -2 -2 2 1100 9 6 0 0 0 1200 8 5 -1 -1 1 1300 7 4 -2 -2 2 1400 5 2 -4 -4 4 1500 3 0 -6 -6 6 1600 2 2 -4 -8 8 1700 3 3 3 r l 1 1800 4 4 4 0 0 1900 3 3 3 -1 1 2000 3 3 3 -1 1 2100 2 2 2 -2 2 2200 2 2 2 -2 2 2300 1 1 1 -3 3 2400 0 0 0 0 0 3 6 F i n i s h T i m e s R ( i ) max f o r t ^ < i < t 2 , i . e . l < i < 2 , i s 3. N-^  = 3. F o r t i < i < T ] _ , s u b t r a c t 3 f r o m R ( i ) t o g e t column R l . R l ( i ) max. f o r t 2 < i < t 3 , i . e . 2<i<5, i s 6. N2 = 6. F o r t 2 £ i < T 2 / s u b t r a c t 6 f r o m R l ( i ) t o g e t column R2. The max. v a l u e o f R2 ( i ) f o r t3<i<t£, i . e . 5<i<9, i s -1 , w h i c h i s l e s s t h a n z e r o . T h e r e f o r e N3 i s z e r o . R 2 ( i ) max. f o r t4<i<17, i . e . 9<i<17. os 4. N 4 = 4. F o r t 4 < i < 1 7 , s u b t r a c t 4 f r o m R 2 ( i ) t o g e t column R3. A l l e l e m e n t s i n column R3 a r e l e s s t h a n o r e q u a l t o z e r o , so s t a f f i n g i s c o m p l e t e . R 3 ( i ) i s t h e n e g a t i v e o f t h e s u r p l u s a t t i m e i . F i g u r e 8 Sample S h i f t S c h e d u l i n g P r o g r a m . (From t h e AGIFORS P r o c e e d i n g s , 1968, p. 257. Determination of the i n t e r - a r r i v a l time d i s t r i b u t i o n was the key t o the s o l u t i o n , and the development was more t h e o r e t i c a l than the approach taken by Aer Lin g u s , but the t h e o r e t i c a l development was based on the assumption t h a t i n t e r - a r r i v a l times were n e g a t i v e e x p o n e n t i a l . The KLM study was made p r i o r t o the Aer Lingus study, but M.A. F o l e y of Aer Lingus p o i n t e d out t h a t the assumption of n e g a t i v e e x p o n e n t i a l i n t e r - a r r i v a l time d i s t r i b u t i o n was c o n t r a r y t o Aer Lingus e x p e r i e n c e . While t h i s d i d not i n v a l i d a t e - t h e KLM model, Mr. F o l e y made the p o i n t t h a t l i t t l e i s gained by s o p h i s t i c a t i o n of a model i f a simpler approach g i v e s a c c u r a c i e s i n the order of ten per cent. He s t a t e d t h a t , " . . . f a s t simple s o l u t i o n s are q u i t e adequate i n p r a c t i c e even i f they may not be t e c h n i c a l l y r e s p e c t a b l e . " ^ , B a g g a g e C l a i m . A simple model f o r e s t i m a t i o n of maximum numbers of passengers w a i t i n g f o r baggage and maximum baggage a w a i t i n g passengers has been d e s c r i b e d f o r t y p i c a l a i r l i n e t e r m i n a l s . Given the a r r i v a l r a t e of passengers, a r r i v a l r a t e of baggage, and the number of passengers, e x i s t -i n g f a c i l i t i e s can be assessed i n terms of a new need--say t r a f f i c growth or the a r r i v a l of jumbo j e t s or the e f f e c t s of c u t t i n g - r o f f s e r v i c e a t baggage c l a i m f o r maintenance, or f o r o ther reasons. I b i d . , p. 57. This analysis resulted i n simple expressions for the inventories of baggage and passengers and respective maxima. The assumptions were based on observations of actual conditions at Kennedy International Airport: 1. Passengers and baggage a r r i v a l s are random at uniform rate. 2. Bags and passengers leave immediately there i s a matched set. If a delay of time t i s assumed, then the maximum queues are increased by the delay time mult i p l i e d by the a r r i v a l r a t e . 6 8 Telephone Trunks were studied by A i r Canada to evaluate the network c a p a b i l i t y i n terms of service l e v e l . A model was developed to analyze any proposed network but not to optimize the system* Estimates of the number of 69 rejected c a l l s were made for networks proposed. Inputs to the model included measured leg-flows and survey samples of c a l l s from any source to i t s set of destinations. From these inputs, the origins-destination patterns of t r a f f i c were obtained for the entire network. Estimation J . J . Browne, J.J. K e l l y , and P. leBourgeois, "Maximum Inventories In Baggage Claim: A Doubled-Ended Queue-ing System," Transportation Science, Vol. 4, No. 1, February 1970, p. 64. 69 A.T. Batey, "Some aspects of Telephone Network Design," AGIFORS Proceedings, 1967, p. 311. of l o s s , ( f r u s t r a t e d c a l l s ) , was developed from P o i s s o n and E r l a n g B models and v a l i d a t e d by means of r e c o r d i n g meters on one of the network p o i n t s , r e c o r d i n g c a l l a r r i v a l s , t e r m i n a t i o n s , and r e j e c t e d c a l l s . Observed hold-time d i s t r i b u t i o n s were s i g n i f i c a n t l y d i f f e r e n t from the t h e o r e t i c a l . Perhaps the reason f o r the d i f f e r e n c e was t h a t the models were f o r steady s t a t e , w h i l e the system was a c t u a l l y s u b j e c t to t r a f f i c f l u c t u a t i o n s through the day. The model used only one r a t i o . o f source to d e s t i n a t i o n and t h i s too may have v a r i e d through the day. While a d m i t t e d l y simple, work sampling s t u d i e s might provide a good measurement of r e a l c o n d i t i o n s i n the system. C a l l s c o u l d be o r i g i n a t e d from any p o i n t to any p o i n t at random through s e v e r a l weeks, p r o v i d i n g a s t a t i s t i c a l b a s i s f o r e s t i m a t i o n of r e j e c t e d c a l l s i n the system. C o n c l u s i o n s — A i r l i n e P r o d u c t i o n Models A i r l i n e i n f o r m a t i o n systems d e a l w i t h tremendous volumes of data, p a r t i c u l a r l y i n c o n n e c t i o n w i t h r e s e r v a t i o n s systems... without computers i t i s d o u b t f u l t h a t l a r g e a i r -l i n e s c o u l d have grown as r a p i d l y as they d i d i n the years 1945 to 1970. Some of the l a r g e s t commercial computer systems i n the world i n 1971 were operated by a i r l i n e s . But computers alone do not make a good system. Real world c o m p l i c a t i o n s may prevent adoption of t e c h n i c a l l y a t t r a c t i v e i n f o r m a t i o n systems. The U n i t e d A i r L i n e s o n - l i n e c h e c k - i n proposals p r o v i d e d such an example. E f f o r t s should be made to know a l l the requirements of a system b e f o r e spending h e a v i l y on i t s development. System d e s i g n c o n s i d e r a t i o n s must precede hardware. Operations r e s e a r c h models of computer systems can be used f o r e x p l o r a t i o n of system o p e r a t i n g c h a r a c t e r i s t i c s and f o r c o s t - b e n e f i t . a n a l y s e s . I n d i r e c t b e n e f i t s accrue from the abundance and t i m e l i n e s s of accurate computer output. Operations r e s e a r c h can take advantage of r e s e r v a t i o n s data t o opt i m i z e booking procedures and revenues while m a i n t a i n i n g p r e s c r i b e d s t a n -dards of customer s e r v i c e . O perations r e s e a r c h analyses f o r manpower and f a c i l i t i e s p l a n n i n g are used by s e v e r a l a i r l i n e s , but much remains t o be done. Future i n f o r m a t i o n systems should s i m p l i f y and speed up the r e s e r v a t i o n process, p a r t i c u l a r l y where i n f o r m a t i o n . i s t r a n s f e r r e d among d i f f e r e n t a i r l i n e s . I n t e g r a t e d i n f o r m a t i o n systems, p r o v i d i n g u n i t c o n t r o l packages i n 1971 were s t i l l i n co n c e p t u a l stages. The schedule i s the h e a r t of the a i r l i n e , but i t i s the source o f d i f f i c u l t management problems. Assignment problems, t r a v e l l i n g salesmen problems and t r u c k d i s p a t c h problems are f a m i l i a r to those engaged i n o p e r a t i o n s research, yet i n .real applications, solutions seem mainly in the future. Scheduling by manual methods i s "cut and try" u n t i l the deadline for implementation i s reached. The best f e a s i b l e solution discerned at deadline i s implemented. Small a i r l i n e s can and do schedule manually. Certain man-datory departure times, f l e e t s i z e , route configuration, and connections impose binding constraints such that scheduling freedom i s l i m i t e d . General computer solutions begin with a l i s t of a l l p o s s i b l e solutions and' an objective. Reasons for poor success i n scheduling by computer have been suggested as one or more of the fo l l o w i n g : 7 ^ 1. The model contains too many variables. The l i s t of a l l possible solutions should be reduced. The method suggested: use common sense. 2. The solution method may be too elaborate. Enumeration, integer LP, dynamic programming, branch and bound, Balas 1 algorithm—are a l l elegant and adequate for small scale problems, but impractical for larger problems, such as a i r l i n e schedules involving two thousand variables and one thousand .constraints. Spitzer suggests using heuris-t i c s or approximation methods, or removing zero-one con-s t r a i n t s — a t least i n i t i a l l y . 70 M. Spitzer, "The Computer Art of Schedule Making," Datamation, Vol. 15, No. 4, A p r i l 1969, p. 84. 3. S o l u t i o n s are i n f l e x i b l e . Any change of parameters r e q u i r e s a complete reworking of the problem. To reduce the i n f l e x i b i l i t y of a s o l u t i o n , p a r t i t i o n the problem by s e n s i b l e geographic s p l i t of customers. Changes i n one area may not a f f e c t the r e s t . In 1971, schedule b u i l d i n g was s t i l l mainly a manual ta s k . Many a p p l i e d models used f o r s c h e d u l i n g were check-i n g r o u t i n e s f o r comparison of a l t e r n a t i v e s , or f e a s i b i l i t y checks w i t h respect; to.maintenance and the l i k e . Customer s e r v i c e a t ch e c k - i n and a t baggage c l a i m has been the o b j e c t o f a p p a r e n t l y s u c c e s s f u l queue a n a l y s e s . S i m p l i c i t y and t e c h n i c a l i m p e r f e c t i o n s i n the models take p r e f e r e n c e over s o p h i s t i c a t i o n and r i g o r . T h i s was o f t e n because p r e c i s e f o r m u l a t i o n has l e d to s o l u t i o n s t h a t i n the past were too expensive, p a r t i c u l a r l y when s i m u l a t i o n models were employed. As computer and software c a p a b i l i t i e s improve the c o s t o b j e c t i o n s may be swept a s i d e . CHAPTER IV AIRPORT OPERATIONS Airp o r t a c t i v i t i e s include servicing of a r r i v a l s and departures of surface vehicles, passengers, baggage, f r e i g h t , and a i r c r a f t . The air p o r t i s a modal interface or a buffer between modes and between connecting f l i g h t s , . providing temporary storage or waiting areas i n the interv a l s between a r r i v a l s and departures. Some of the storage i s i n the a i r space i n the v i c i n i t y of the port, used to "stack" a r r i v i n g a i r c r a f t u n t i l landing clearance can be given. A i r p o r t operations related to passenger, cargo and baggage services are discussed i n Chapter I I I . In this chapter, the main topics are ai r p o r t design, a i r t r a f f i c c o n trol, and a i r c r a f t maintenance. Although a l l three topics are important to a i r l i n e operators, generally only maintenance i s d i r e c t l y under t h e i r control. The Federal Aviation Administration, (FAA), i n the United States, and the Department of Transport, (DOT), i n Canada, are respon-s i b l e for enactment and implementation of regulations on safety, ground and a i r crew c e r t i f i c a t i o n , navigation f a c i l -i t i e s , c ertain a i r p o r t standards, a i r t r a f f i c c o ntrol, a i r p o r t funds for improvements, and .sponsorship of research i n these areas. A i r p o r t L o c a t i o n A d e t a i l e d c o s t - b e n e f i t study should precede implemen-t a t i o n of a g r e a t p r o j e c t such as a new a i r p o r t . Research s h o u l d , i n c l u d e c o n s i d e r a t i o n of the importance of a v i a t i o n to the economy of the r e g i o n , the economic e f f e c t s of a new a i r p o r t , e f f e c t s of the a i r p o r t on r e a l e s t a t e v a l u e s , f u t u r e passenger and cargo plane movements and g e n e r a l a v i a t i o n t r a f f i c , a i r s p a c e and p o r t c a p a c i t y , a i r p o r t d e s i g n , land use and ground t r a n s p o r t a t i o n , t r a f f i c as a f u n c t i o n of a c c e s s i b i l i t y , c l i m a t e , e t c . 1 The proposed Stans t e d s i t e f o r the t h i r d London a i r -2 p o r t was found u n d e s i r a b l e f o r s i x main reasons: 1. Inadequate road and r a i l access f o r s h o r t h a u l t r a f f i c . 2. Poor s i t u a t i o n with r e s p e c t to passenger and cargo sources and w i t h r e s p e c t to p r i n c i p a l a i r r o u t e s . 3. A i r t r a f f i c c o n t r o l disadvantages e x p e c i a l l y with r e s p e c t to SST r o u t i n g s t o the West. 4. Climate and v i s i b i l i t y c o n d i t i o n s . 5. A i r l i n e o p e r a t i n g economy. 6. C o n f l i c t w i t h other a i r p o r t s . ^ S t u d i e s of the S i t e f o r a T h i r d London Airport,, sponsored by NortE~West Essex and E a s t H e r t s . P r e s e r v a t i o n A s s o c i a t i o n , 19 66. A l a n S t r a t f o r d & Associates,. A i r T r a n s p o r t C o n s u l t a n t s N i c h o l s o n house, High S t r e e t , Maiden-head, Berks. 2 I b i d . Information required for analys i s of proposed a i r -ports s i te s i s l a rge ly of a demographic nature and i s dependent upon routes and t r a f f i c both i n the a i r and on the ground. Technica l aspects of des ign, s o i l condit ions and weather involve spec i a l i zed engineering and meteorology. Airspace and port capac i t ie s involve some forms of queuing models as we l l as i n d u s t r i a l engineering for passenger and f re ight handling methods and f a c i l i t i e s . In protes t ing the proposed Stansted s i t e for London's t h i r d a i rpor t the aim was not to specify the best a l t e rna t ive but merely to show that Stansted was n o t the best s i t e . The fact that t h i s study cost about ^ 2 5 , 0 0 0 i n England p r i o r to 19 66 i s an i n d i c a t i o n of the high costs of researching for major a i rpor t development. The s o c i a l and economic conse-quences of s i t e s e l ec t ion are enormous. I t i s s i g n i f i c a n t that the Stansted study was financed e n t i r e l y by voluntary contr ibut ions from residents and businesses i n the area of the proposed s i t e . F a c i l i t i e s Design Considerations Some i n t e r e s t i n g models and p r a c t i c a l d i scuss ion of t y p i c a l a i r p o r t design considerat ions are found i n Lee 's 3 book on Appl ied Queueing Theory. Such queueing s i tua t ions 3 A.M. Lee, Appl ied Queueing Theory, London: Mac-m i l l a n , 1966. as' t a x i w a y t r a f f i c , t e r m i n a l t r a f f i c , p a s s e n g e r movements, bus t r a f f i c , a i r c r a f t t u r n - r o u n d (minimum s e r v i c e i n t e r v a l between l a n d i n g and n e x t t a k e - o f f ) , a r e i n c l u d e d . P e r h a p s t h e most i m p o r t a n t message i n L e e ' s book i s t h a t queue models a r e r a r e l y a p p l i c a b l e i n t e x t - b o o k f a s h i o n b e c a u s e most r e a l s i t u a t i o n s a r e t o o complex f o r c o n v e n i e n t m a t h e m a t i c a l s o l u t i o n . S i m u l a t i o n s a r e u s e f u l f o r c o m p a r i n g a l t e r n a t i v e s where a n a l y t i c a l models do n o t e x i s t . S i m u l a t i o n may be t h e o n l y p r a c t i c a l way t o model complex p r o b l e m s . The g r e a t e r t h e p e n a l t y f o r e r r o r , t h e more v a l u a b l e s i m u l a t i o n becomes. B u t s i m u l a t i o n c a n s u f f e r f r o m b i a s o r f r o m p o o r d e f i n i t i o n c a u s e d by o v e r s i m p l i f i c a t i o n o f t h e m o d e l . A n o t h e r f r e q u e n t o b j e c t i o n t o s i m u l a t i o n i s c o s t . A l l component v a r i a b l e s must be c a r e f u l l y e x a m i n e d . D i s t r i b u t i o n s o f a r r i v a l and s e r v i c e t i m e s must be d e r i v e d . I f t h e s e c o r r e s p o n d w i t h known d i s t r i b u t i o n s s u c h as P o i s s o n , l o g n o r m a l , o r E r l a n g , so much t h e b e t t e r . T h ey c a n be g e n e r a t e d by h i g h - l e v e l s i m u l a t i o n l a n g u a g e s as p a r t o f a s t a n d a r d r o u t i n e . I f n o t , Monte C a r l o t e c h n i q u e s a r e u s e d t o g e n e r a t e e v e n t s i n t h e s i m u l a t i o n . The h i g h c o s t o f s i m u l a t i o n a r i s e s f r o m t h e f a c t t h a t e a c h r u n g i v e s a n s wers f o r a s i n g l e s e t o f c o n d i t i o n s . I n o r d e r t o e x p l o r e t h e s o l u t i o n s p a c e , many r u n s a r e n e c e s s a r y , e a c h r u n b e i n g made u n d e r d i f f e r e n t c h o s e n c o n d i t i o n s . H a v i n g made s e v e r a l r u n s f o r v a r i o u s c h o s e n c o n d i t i o n s , t h e a n a l y s t t r i e s t o g e n e r a l -i z e t h e s i m u l a t i o n r e s u l t s by means o f e m p i r i c a l ( a n a l y t i c ) r e l a t i o n s h i p s t h a t w i l l y i e l d a p p r o x i m a t e l y t h e same s o l u -t i o n s . T h i s p r o c e d u r e i s d e m o n s t r a t e d i n C h a p t e r 15 o f 4 L e e ' s book. A p p r o x i m a t i o n s may be n e c e s s a r y t o keep t h e c o s t s o f s o l u t i o n r e a s o n a b l e , o r j u s t t o make a s o l u t i o n p o s s i b l e . T h r e e a p p r o a c h e s a r e a v a i l a b l e 1. Use o v e r s i m p l i f i e d m o d e l s . T h e s e a r e i m p e r f e c t b u t s i m p l e and p r a c t i c a l where g r e a t a c c u r a c y i s n o t r e q u i r e d . 2. Use a l i m i t e d number o f f a i r l y e l a b o r a t e s i m u l a t i o n s . F i n d e m p i r i c a l r e l a t i o n s h i p s between v a r i o u s f a c t o r s , f o r u s e i n g e n e r a l s o l u t i o n s . 3. S u b s t i t u t e an i n i t i a l s e t o f v a l u e s i n a complex f o r m u l a and i t e r a t e t o o b t a i n s o l u t i o n s . Unmanageable f u n c t i o n s sometimes may be expanded by power s e r i e s , i g n o r i n g l e s s i m p o r t a n t t e r m s o f h i g h e r o r d e r . A v o i d i n g C o n g e s t i o n . T h e n e ed f o r s o l u t i o n s t o a i r p o r t c o n g e s t i o n became g e n e r a l l y a p p a r e n t i n t h e 1960's. A t t h e l a r g e a i r p o r t s , l a r g e queues o f sometimes as many as t w e n t y -I b i d . , p. 185. 5 I b i d . , p. 89. f i v e planes waited on runways t o t a k e - o f f w h i l e other planes c i r c l e d sometimes f o r hours, w a i t i n g t o l a n d . Passengers walked a c o n s i d e r a b l e d i s t a n c e , perhaps three q u a r t e r s of a m i l e , from the p a r k i n g l o t to the t e r m i n a l , and then hun-dreds of yards t o the g a t e i A i r p o r t expansion t o r e l i e v e e x i s t i n g problems i s l i m i t e d by c o n s i d e r a t i o n s of f i n a n c e , h i g h land c o s t s , and s o c i a l r e s i s t a n c e t o n o i s e and a i r p o l l u t i o n . L o c a l , r e g i o n a l , and F e d e r a l governments s u f f e r from i n e r t i a and from the pres s u r e s o f lobby groups. Ground co n g e s t i o n can be reduced by l i m i t i n g the number of v e h i c l e s p e r m i t t e d , and perhaps through r e d u c t i o n of a i r p o r t s t a f f . At l a r g e a i r p o r t s there are more than 30,000 employees. Congestion c o u l d be reduced by e l i m i n a t i n g v i s i t o r s and s i g h t s e e r s , r e d u c i n g t r a f f i c peaks, improving a c c e s s , the use of more p u b l i c and l e s s p r i v a t e t r a n s p o r t a t i o n . . Another approach t o the problems of c o n g e s t i o n , i s v i a a i r p o r t d e s i g n . F i g u r e 1 i l l u s t r a t e s a t y p i c a l e v o l u t i o n of a i r cargo t e r m i n a l s . In t h i s e v o l u t i o n , an a i r l i n e faces two major d e c i s i o n s : 6 1. To separate a i r cargo o p e r a t i o n s from the passenger t e r m i n a l . 2 . To e s t a b l i s h one or more o f f - a i r p o r t c o n s o l i d a t i o n t e r m i n a l s . g S c h r i e v e r and S e i f e r t , A i r T r a n s p o r t a t i o n 1975 and Beyond: A Systems Approach, Cambridge Mass., MIT P r e s s , 1968, pp. 376,~377. INTEGRATED PAS S ENGER/CARGO TERMINAL SEPARATE CARGO FUNCTION AT PAX TERMINAL MULTIPLE AIRLINE J " SHARED CARGO TERMINAL INDIVIDUAL AIRLINE CARGO TERMINAL ON-AIRPORT SITE OFF-AIRPORT CONSOLIDATION TERMINAL SEPARATE CARGO AIRPORT SEPARATE CARGO AIRPORT WITH OFF-AIRPORT CONSOLIDATION TERMINAL SYSTEM F i g u r e 4.1 Cargo A i r p o r t E v o l u t i o n , (from S c h r i e v e r and S e i f e r t , A i r T r a n s p o r t a t i o n  1975 and Beyond, A Systems Approach, p. 375.) amount o f c o n g e s t i o n m i g h t be a v o i d e d . P r e f e r e n t i a l f a r e s r e d u c e t r a f f i c p e a k s , b u t many, i f n o t most t r a v e l l e r s a r e on b u s i n e s s t r i p s and a r e l e s s l i k e l y t o be i n f l u e n c e d by 7 o f f peak f a r e r e d u c t i o n s . L a r g e r a i r c r a f t r e d u c e t h e number o f movements a t a i r p o r t s . I n t h e New Y o r k a r e a , p a s s e n g e r t r a f f i c i n c r e a s e d 1 4 4 p e r c e n t between 1 9 5 8 and 1 9 6 7 . I n t h e same p e r i o d , a i r c r a f t movements i n c r e a s e d by 5 2 % and t h e s c h e d u l e day i n c r e a s e d on a v e r a g e by more t h a n two h o u r s by g o p e r a t i n g e a r l i e r and l a t e r . R e s c h e d u l i n g t o a v o i d p e a k s i s o f t e n v e r y d i f f i c u l t . Crew l a y o v e r s and f l i g h t c o n n e c t i o n s may i n t e r f e r e . A t y p i c a l example was an A m e r i c a n A i r l i n e s f l i g h t l e a v i n g New Y o r k a t 5:45 f o r D a l l a s , m aking c o n n e c t i o n s 9 w i t h 6 3 o t h e r f l i g h t s i n t h e two c i t i e s . G e n e r a l a i r t r a f f i c , ( s m a l l p r i v a t e and b u s i n e s s a i r c r a f t ) , c o u l d be d i s c o u r a g e d f r o m u s i n g b u s y a i r p o r t s a t peak h o u r s i f l a n d i n g f e e s were c h a r g e d i n p r o p o r t i o n t o demand. 1 1" 1 W h i l e t h i s w o u l d e a s e a i r t r a f f i c p e a k i n g , i t i s n o t a c u r e f o r t h e l o n g - t e r m c a p a c i t y p r o b l e m o f c o n t i n u e d r a p i d t r a f f i c g r o w t h . Between 1 9 6 8 and 1 9 7 5 p a s s e n g e r . 7 M e l v i n A. B r e n n e r , " P u b l i c Demand and A i r l i n e S c h e d u l i n g , " A i r T r a n s p o r t A s s o c i a t i o n P a p e r , . 1 9 6 8 , p. 9. 8 9 M.A. B r e n n e r , op. c i t . , p . 6 . I b i d . , p. 3 1 . 1(^W.D. Grampp, "An E c o n o m i c Remedy f o r A i r p o r t Conges-t i o n , " B u s i n e s s H o r i z o n s , V o l . 1 1 , No. 5, O c t o b e r 1 9 6 8 , pp. 2 1 - 3 0 . t r a f f i c was e x p e c t e d t o grow f r o m 1 5 0 m i l l i o n t o 300 m i l l i o n p a s s e n g e r s c a r r i e d a n n u a l l y , and by 19 80 t h e f i g u r e was e s t i m a t e d t o be 450 m i l l i o n . 1 1 Living With Congestion. Runway u s e c a n be m o d i f i e d by means o f p r i o r i t y r u l e s aimed a t c h o s e n o b j e c t i v e s . A q u e u e i n g m o d e l f o r runway w a i t i n g t i m e has been d e v e l o p e d t o i n c l u d e c o n s i d e r a t i o n o f w a i t i n g t i m e f o r d i f f e r e n t c l a s s e s 12 o f u s e r s . F o r example, p r i o r i t y r u l e s m i g h t be v a r i a t i o n s o f t h e f o l l o w i n g : 1. F i r s t come f i r s t s e r v e d . 2. L a n d i n g s have p r i o r i t y o v e r d e p a r t u r e s , b u t f i r s t come f i r s t s e r v e d i n b o t h g r o u p s . 3. P r i o r i t y by a i r c r a f t t y p e t o m i n i m i z e a v e r a g e d e l a y . 4. P r i o r i t y t o m i n i m i z e a v e r a g e d e l a y c o s t . A v e r a g e d e l a y i s n o t v e r y s e n s i t i v e t o t h e s e r u l e s , b u t t o t a l d e l a y c o s t c a n be a f f e c t e d . A t a b u s y p e r i o d , s m a l l a i r c r a f t w o u l d have t o w a i t u n t i l a l l t h e l a r g e r a i r -c r a f t h ad been s e r v i c e d . P r e s u m a b l y t h e l e a s t c o s t i s a d e s i r a b l e s o c i a l o b j e c t i v e . A d i s c i p l i n e o t h e r t h a n f i r s t 1 1 S . G . T i p t o n , " A i r l i n e C h a l l e n g e s o f t h e F u t u r e , " D a t a m a t i o n , V o l . 1 5 , No. 3, M a r c h 1 9 6 9 , p. 2 2 . 12 G. P e s t a l o z z i , " P r i o r i t y R u l e s f o r Runway Use," O p e r a t i o n s R e s e a r c h , V o l . 1 2 , No. 6, 1 9 6 4 , pp. 9 4 1 - 9 5 0 . come, f i r s t served would be r e q u i r e d . Complicated s e r v i c e r u l e s would r e q u i r e computer a s s i s t a n c e , p a r t i c u l a r l y i f queues became l a r g e . S i m u l a t i o n models f o r a i r p o r t s embrace the main a i r p o r t o p e r a t i o n s , many of which are queueing s i t u a t i o n s . A i r c r a f t Flow Approach & Land T a x i To Gate " Terminal P r o c e s s i n g Baggage Flow Passenger Flow ~~ Connections^ Maintenance T a x i Out' Take o f f ' or enter Hangar F i g u r e 2 Schematic t r a f f i c flows The d i f f i c u l t y w i t h an o v e r a l l s i m u l a t i o n i s the s i z e 13 of program and the computer f a c i l i t i e s r e q u i r e d . T h i s type o f model i s p r a c t i c a l f o r a s i n g l e a i r l i n e o p e r a t i o n at a l a r g e a i r p o r t , but not n e c e s s a r i l y f o r t o t a l a i r p o r t opera-t i o n . S i m u l a t i o n s are used t o approximate many o p e r a t i n g f e a t u r e s such as: K. Mountjoy, A i r p o r t S i m u l a t i o n Models, AGIFORS Proceedings, 1969. per cent of f l i g h t s w a i t i n g over ten minutes a t gate, baggage d e l i v e r y , average minutes, per cent of f l i g h t s m i s s i n g connections, c a p a c i t y of runways. - e f f e c t s of p o r t c o n f i g u r a t i o n on t a x i times. e f f e c t s of p o l i c i e s , p r i o r i t i e s , on w a i t i n g time and s e r v i c e . e f f e c t s of i n c r e a s i n g t r a f f i c volumes. I n d i v i d u a l s i m u l a t i o n s have been designed to e v a l u a t e proposed t e r m i n a l s and t r a c t o r a l l o c a t i o n s . A model f o r O'Hare a i r p o r t was made to estimate the number of a i r c r a f t w a i t i n g i n h o l d i n g areas, frequency d i s t r i b u t i o n of times taken to reach t e r m i n a l gates, and frequency d i s t r i b u t i o n s 14 of ramp times f o r d e p a r t i n g f l i g h t s . Models can be b u i l t on outputs of other models. Given time of f l i g h t a r r i v a l , number of passengers d e p l a n i n g , time of f i r s t bag a r r i v a l i n c l a i m area e t c e t e r a , secondary models can r e p r e s e n t say,.space requirements f o r s p e c i f i e d s e r v i c e l e v e l s i n baggage c l a i m , baggage c h e c k - i n , t i c k e t counters and the l i k e . A danger i n the p r o f u s i o n of models from a number of o r i g i n a l assumptions i s t h a t the models may grow f u r t h e r from r e a l i t y a t each stage. However, model o u t p u t s , i f c o n s i s t e n t , w h e t h e r h i g h o r low, c a n p r o v i d e a means f o r o r d e r i n g a l t e r n a t i v e s . I f t h e model i s v a l i d a t e d i n t e r m s o f e x i s t i n g o p e r a t i o n s , t h e n d i f f e r e n c e s between t h e model o u t p u t and r e a l i t y c a n be t a k e n i n t o c o n s i d e r a t i o n i n a s s e s s m e n t o f o u t p u t s f o r a l t e r n a t i v e s . A j r T r a f f i c C o n t r o l A l t h o u g h o p e r a t e d by gov e r n m e n t , a i r t r a f f i c c o n t r o l , ( A T C ) , i s v i t a l t o t h e a i r l i n e c o m p a n i e s . ATC p l a y s a r o l e t h a t a f f e c t s t h e s a f e t y o f t h e a i r t r a v e l l e r . S a f e t y i s sometimes g i v e n as a r e a s o n f o r n o t f l y i n g , d e s p i t e s t a t i s t i c s t h a t show f l y i n g t o be l e s s r i s k y t h a n h ighway t r a v e l . B ooks, 15 s u c h as A i r p o r t , m a g a z i n e a r t i c l e s a b o u t f l y i n g s a f e t y and c e l e b r i t i e s who r e f u s e t o f l y , a l l t e n d t o keep t h e p u b l i c aware o f t h e " r i s k " t h e y t a k e when t h e y b o a r d a p l a n e . T h e r e a r e r i s k s i n f l y i n g , as t h e r e c o r d s show. I n 1 9 5 9 , t h e r e were 5 , 0 0 0 a v i a t i o n a c c i d e n t s t h a t r e s u l t e d i n t h e d e a t h s o f 4 , 0 0 0 p i l o t s and 3 , 0 0 0 p a s s e n g e r s . O b v i o u s l y , t h e s e a c c i d e n t s i n v o l v e d few a i r l i n e i n c i d e n t s , and t h e c a u s e s o f t h e a c c i d e n t s were c e r t a i n l y n o t m a i n l y due t o ATC d e f i c i e n c i e s . N e v e r t h e l e s s , i n 1 9 6 1 , t h e U.S. T a s k F o r c e on A i r T r a f f i c C o n t r o l p o i n t e d o u t d e f i c i e n c i e s i n t h e ATC A. H a i l e y , A i r p o r t , New Y o r k , D o u b l e d a y , 1 9 6 8 . of t h a t day, due to s e p a r a t i o n standards (not on radar c o n t r o l ) mixtures of instrument and v i s u a l f l i g h t r u l e s , (IFR and VFR), s e p a r a t i o n not c o n t r o l l e d f o r VFR a i r c r a f t , outmoded radar a t t e r m i n a l s , and complex h o l d i n g , r e p o r t i n g and c l e a r a n c e 16 r o u t i n e s . Government a c t i o n t o improve ATC i s l i m i t e d by t e c h n i c a l o b s t a c l e s , such as the need f o r i n t e r n a t i o n a l standards f o r equipment and procedures and e v o l u t i o n a r y con-v e r s i o n standards f o r equipment and procedures. Noise abatement l i m i t a t i o n s on a i r p o r t i n g r e s s and eg r e s s , human l i m i t a t i o n s o f c o n t r o l l e r s , and f l i g h t crews, weather con-d i t i o n s , snow removal, e t c . , a l l add to the d i f f i c u l t i e s . S a t e l l i t e weather o b s e r v a t i o n has l e d t o improved f o r e c a s t i n g , but improvements are needed i n the a b i l i t y t o d e t e c t and ' 17 r e a c t t o t u r b u l e n c e , i c i n g and poor v i s i b i l i t y . Many of the needs f o r improved ATC appear t o be methods and equipment o r i e n t e d , y e t the continued use of human con-t r o l l e r s p r o v i d e s some f r u i t f u l areas f o r o p e r a t i o n s r e s e a r c h . The need f o r ATC can be f o r e c a s t i n much the same way t h a t t o t a l a i r t r a f f i c i s f o r e c a s t . As f o r e c a s t i n g models have been d i s c u s s e d i n Chapter I I , they s h a l l not be d i s c u s s e d Report of the Task Force on A i r T r a f f i c C o n t r o l , B.A. -Schriever, W.W. S e i f e r t , op_. c i t . , p. 281. here. Other models have been made to r e p r e s e n t c o l l i s i o n 18 r i s k s f o r a i r c r a f t and s h i p s . These are not p r o p e r l y a i r l i n e models because they d e a l w i t h problems t h a t are the r e s p o n s i b i l i t i e s o f government. Below, two models t h a t d e a l w i t h c o n t r o l l e r c a p a c i t y are b r i e f l y d e s c r i b e d . . 19 A . I . C . W o r k l o a d T i m e M o d e I ( E n r o u t e ) . C o n t r o l l e r s d u t i e s may be c o n s i d e r e d as r o u t i n e and c o n f l i c t workloads. The r o u t i n e workload i n c l u d e s acceptance from and handoff to other en route c o n t r o l l e r s , r o u t i n e communication w i t h a i r c r a f t and r e l a t e d c l e r i c a l f u n c t i o n s . The c o n f l i c t work-loa d a r i s e s from i n t e r a c t i o n between a i r c r a f t i n f l i g h t . For a g i v e n c o n t r o l l e r , r o u t i n e workload time may be expressed as: K, N where = average time spent per a i r c r a f t f o r r o u t i n e c o n t r o l N = number of a i r c r a f t under c o n t r o l at any time T = average time t h a t an a i r c r a f t i s under c o n t r o l 18 L. Stachtchenko,"An I n v e s t i g a t i o n of C o l l i s i o n R isks Over the North A t l a n t i c , " Canadian O p e r a t i o n a l  Research J o u r n a l , V o l . 3, No. 2, 1965. 19 M. Rosenshine, "O/R i n the S o l u t i o n of ATC Problems," J o u r n a l of I n d u s t r i a l E n g i n e e r i n g , V o l . XIX, No. 3 March 1968, p.~T2T. C o n f l i c t c a n o c c u r among a l l p o s s i b l e a i r c r a f t p a i r s , 2 N ( N - l ) / 2 , o r , more a p p r o x i m a t e l y , as a f u n c t i o n o f N . T h i s f u n c t i o n c o u l d be e x p r e s s e s a s : C T = K 2 a N 2 where , a a r e c o n s t a n t s . T hen o v e r a l l w o r k l o a d t i m e w o u l d be: K N 2 L T = ± + K 2 a N z . S i n c e N v a r i e s w i t h t i m e a more a p p r o p r i a t e e x p r e s s i o n w o u l d be: E(L„) = — [E (N) ] + K „ a [ E ( N 2 ) ] T Z where E(N) = e x p e c t e d v a l u e o f (N). U s i n g i n d u s t r i a l e n g i n e e r i n g measurements t o e s t a b l i s h t h e c o n s t a n t s , and c o n s i d e r i n g t h e v a r i a n c e o f t h e e x p r e s s i o n ( i n t h i s c a s e on assumed n o r m a l d i s t r i b u t i o n s ) , t h e components o f w o r k l o a d were combined t o y i e l d t h e r e q u i r e d number o f c o n t r o l l e r s . The e x p e c t e d w o r k l o a d i s g i v e n by: L T = 3~0 + * ^ a N ^ ( m i n u t e s / m i n u t e ) , and . 0 0 0 8 < a < . 0 0 2 5 , depending on the route a i r s p a c e s t r u c t u r e . 2 Because of the N term, the c o n f l i c t component becomes more s i g n i f i c a n t w i t h t r a f f i c b u i l d - u p . T h i s model measured the workload and i n d i c a t e d the number of c o n t r o l l e r s r e q u i r e d under gi v e n t r a f f i c c o n d i t i o n s . 2 0 A. T.C.. Communication Mode I (Terminal) . At the t e r m i n a l , a i r c r a f t a r r i v e and l a n d , or t a x i and tak o f f . The c o n t r o l l e r c l e a r s a w a i t i n g a i r c r a f t t o l a n d , and n o t i f i e s other w a i t i n g a i r c r a f t i n ascending a l t i t u d e sequence to descend by one l e v e l . S e r v i c e times (between r e l e a s e of s u c c e s s i v e a i r c r a f t from the s e c t o r ) i s e v i d e n t l y a f u n c t i o n of the number of a i r c r a f t i n the s e c t o r . I f a i r c r a f t a r r i v a l s are Poisson and the r e l e a s e of a i r c r a f t i s s t o c h a s t i c , depending on the number of a i r c r a f t i n the s e c t o r the s e c t o r can be r e p r e s e n t e d as an imbedded 2 1 Markov c h a i n . Change of s t a t e p r o b a b i l i t i e s are represented mathematically i n r a t h e r complicated f a s h i o n , a r r i v i n g at a queue model f o r the c o n t r o l l e r . For such a model a queue limit can be c a l c u l a t e d , such t h a t the p r o b a b i l i t y of empty-i n g the queue i s kept c l o s e to u n i t y , (say > • 9 0 ) . 2 0 I b i d . , p. 1 2 6 . 2 1 F.S. H i l l i e r and G.J. Lieberman, I n t r o d u c t i o n to  Operations Research, San F r a n c i s c o , Holden Day, 1 9 6 7 , p. 4 3 8 . T h i s m odel has been v a l i d a t e d by t r i a l s b a s e d on o b s e r v e d t r a f f i c i n t e n s i t y i n a c t u a l s e c t o r s . E f f e c t s o f tandem queues and e x t r a c o n t r o l l e r s have a l s o b e en s t u d i e d . F l e e t M a i n t e n a n c e M a i n t e n a n c e p l a n n i n g i s an i m p o r t a n t p h a s e o f a i r l i n e management. O p e r a t i o n s R e s e a r c h has been a p p l i e d t o i n v e n t o r y c o n t r o l , w o r k l o a d f o r e c a s t i n g , s c h e d u l i n g and shop methods. As a p l a n n i n g t o o l , s i m u l a t i o n has been a p p l i e d by s e v e r a l a i r l i n e s . The d e v e l o p m e n t o f computer s y s t e m s f o r m a i n t e n a n c e a p p l i c a t i o n s was d i s c u s s e d as an O/R p r o b l e m i n a p a p e r by 22 F.P. W a l l a c e . T y p i c a l d e v e l o p m e n t i s h a p h a z a r d i n t h e e a r l y s t a g e s o f computer a p p l i c a t i o n . " P e t " p r o j e c t s and i n d i v i d u a l s y s t e m s p r o l i f e r a t e w i t h o u t r e g a r d t o d u p l i c a t i o n o r g e n e r a l s y s t e m s t r u c t u r e . S p e c i f i c a t i o n s f o r i n t e g r a t e d s y s t e m s may r e q u i r e d e t a i l e d k n owledge b e y o n d t h e c a p a b i l i t y o f any i n d i v i d u a l . A c o m m i t t e e may be r e q u i r e d b u t t h e d a n g e r i n a c o m m i t t e e i s t h a t e a c h member w i l l i n s i s t upon m a i n t a i n i n g h i s own p r o g r a m i n e v e r y p a r t i c u l a r . One a i m o f i n t e g r a t i o n s h o u l d be t o r e d u c e . i n p u t by m a k i n g e f f i c i e n t u s e o f d a t a banks i n t h e F.P. W a l l a c e , An O/R A p p r o a c h t o t h e D e f i n i t i o n o f Computer S y s t e m R e q u i r e m e n t s i n A i r l i n e M a i n t e n a n c e , AGIFORS  P r o c e e d i n g s , 1969. s y s t e m . O/R p e o p l e w i t h e x p e r t i s e i n n e t w o r k t h e o r y s h o u l d be c o m p e t e n t t o c o o r d i n a t e s y s t e m s d e v e l o p m e n t . U s i n g C P M / r e s o u r c e A l l o c a t i o n , W a l l a c e s t a t e s t h a t an i n t e g r a t e d s y s t e m d e s i g n r e q u i r e s t h e f o l l o w i n g i n p u t s : 1. Segments o r i m p l e m e n t a b l e p a c k a g e s . 2. A c t i v i t i e s m a k i n g up e a c h segment. 3. Manpower r e s o u r c e s t o make up e a c h segment. 4. E l a p s e d t i m e e s t i m a t e f o r e a c h a c t i v i t y . 5. S e q uence r e l a t i o n s h i p s between s e g m e n t s . I n s t r u c t i o n s b a s e d on t h e above w o u l d be s u b j e c t . t o e r r o r s o f judgement b e c a u s e t h e y d e a l w i t h unknowns t h a t c a n be o v e r o r u n d e r - r a t e d . The a t t e m p t t o t a k e a b r o a d o v e r v i e w i s n e v e r t h e l e s s w o r t h w h i l e . I t i s more c h a r a c t e r -i s t i c o f o r g a n i z a t i o n s e x p e r i e n c e d i n computer s y s t e m s work, t h a t d e v e l o p m e n t o f s y s t e m s i s p l a n n e d . F o r t h e b e g i n n e r , who has a c o m p l e t e l y c l e a r s l a t e , some i n i t i a l e x p e r i m e n -t a t i o n w i t h " p e t " p r o j e c t s i s i n e v i t a b l e . S h o p P l a n n i n g . . A m e r i c a n A i r l i n e s d e v e l o p e d a s i m u -l a t i o n m o d e l t o p r e d i c t w o r k f o r c e o v e r t i m e , i n v e n t o r y l e v e l s and b a c k l o g u n d e r v a r i o u s p r o p o s e d o p e r a t i n g r u l e s . S i m u l a -t i o n c a n e v a l u a t e t h e e f f e c t s o f new f a c i l i t i e s , c h a n g e s i n 23 t h e w o r k f o r c e o r i n t h e work l o a d . S i m u l a t i o n i s u s e r 23 F.P. W a l l a c e , An O/R A p p r o a c h t o t h e D e f i n i t i o n o f Computer S y s t e m R e q u i r e m e n t s i n A i r l i n e M a i n t e n a n c e . AGIFORS  P r o c e e d i n g s , 1969. o r i e n t e d . The u s e r may p r o p o s e p o l i c i e s t h a t a r e r e a s o n a b l e i n t h e l i g h t o f e x p e r i e n c e . By v a r y i n g t h e p o l i c i e s and o b s e r v i n g t h e s i m u l a t e d e f f e c t s , t h e u s e r has t h e o p p o r t u n i t y t o a r r i v e a t good r u l e s o f o p e r a t i o n w i t h o u t t h e c o s t and d e l a y o f t r i a l and e r r o r i n t h e s h o p . W h i l e s i m u l a t i o n c a n p r o v i d e good e v a l u a t i o n s o f a l t e r n a t e p o l i c i e s , i t i s u s u a l l y e x p e n s i v e and c o m p l i c a t e d . U p d a t i n g f o r changes i n f l e e t s i z e o r c o m p o s i t i o n , shop p r o c e d u r e s , c o l l e c t i v e a g r e e m e n t s , shop f a c i l i t i e s , c a n be c o s t l y . D e s p i t e i t s t e n d e n c y t o have a l i m i t e d l i f e , s i m u l a t i o n i s u s e d by s e v e r a l a i r l i n e s f o r m a i n t e n a n c e shop p l a n n i n g . S i m u l a t i o n was u s e d by A i r F r a n c e t o f i n d t h e r e l a t i o n -s h i p between t e c h n i c a l manpower and r e g u l a r i t y o f f l i g h t s as 24 w e l l as t o t e s t a l t e r n a t i v e o v e r h a u l s t r u c t u r e s . S y n t h e t i c o u t p u t s o f o p e r a t i o n s i n d i c a t e r e g u l a r i t y o f o p e r a t i o n s , p e r c e n t c a n c e l l a t i o n s and d e l a y e d d e p a r t u r e s , o v e r h a u l d u r a t i o n , m a i n t e n a n c e crew u t i l i z a t i o n , h a n g a r s p a c e u t i l i z -a t i o n , and numbers o f a i r c r a f t w a i t i n g f o r h a n g a r s p a c e . A s i m u l a t i o n m odel f o r m a i n t e n a n c e management i n f o r -m a t i o n was d e v e l o p e d i n 1969 by KLM R o y a l D u t c h A i r l i n e s t o e c o n o m i z e m a i n t e n a n c e manpower. U s i n g manual s o l u t i o n J . V a u t i e r , R e p o r t on t h e C a r a v e l l e S i m u l a t i o n , AGIFORS P r o c e e d i n g s , 1968, p. 426. methods, e a c h c a l c u l a t i o n t o o k a b o u t two weeks. T h i s was s h o r t e n e d t o a few m i n u t e s on t h e c o m p u t e r . Manpower a l l o -c a t i o n s were made f r o m a tremendous r a n g e o f p o s s i b l e a l l o -c a t i o n s by means o f an a l g o r i t h m t h a t s e t l o w e r u p p e r bounds f o r h o u r s worked, on t h e b a s i s o f l e a s t sums o f s q u a r e s o f 25 h o u r s a l l o c a t e d . T h i s m o d e l , i n a d d i t i o n t o a l l o c a t i n g m a i n t e n a n c e man h o u r s c o u l d be u s e d t o s u g g e s t a l t e r n a t e f l i g h t s c h e d u l e s . M a n u a l methods were t o o s l o w f o r a f e e d b a c k t o t h e f l i g h t s c h e d u l i n g p r o c e s s b u t t h e s p e e d o f t h e computer a s s e s s m e n t s t r e n g t h e n e d t h e a b i l i t y o f t h e m a i n t e n a n c e g r o u p t o i n f l u e n c e f l i g h t s c h e d u l i n g f o r o v e r a l l company b e n e f i t . Maintenance Workload Forecast. M a i n t e n a n c e f o r e -c a s t i n g i s e a s y f o r s c h e d u l e d s e r v i c e o p e r a t i o n s . The i n t e r v a l s b etween m a j o r o v e r h a u l s and c h e c k s a r e l a i d down i n terms o f f l y i n g h o u r s . G i v e n t h e a i r c r a f t s c h e d u l e i t i s a r o u t i n e p r o c e d u r e t o . l i s t t h e s e m a i n t e n a n c e a c t i v i t i e s . Non s c h e d u l e d m a i n t e n a n c e i s more d i f f i c u l t t o f o r e c a s t . On new a i r c r a f t and e n g i n e s r e l i a b i l i t y i s n o t known. As e x p e r i e n c e i s g a i n e d , r e l i a b i l i t y d a t a a r e a c c u m u l a t e d . B . J . Verdoes,"Manpower L e v e l i n g f o r Medium and L o n g Term P l a n n i n g P u r p o s e s , AGIFORS P r o c e e d i n g s , 1969. R e l i a b i l i t y t e n d s t o i m p r o v e w i t h a c c u m u l a t e d s e r v i c e e x p e r i e n c e . M o d i f i c a t i o n s i n d e s i g n a r e t h e t y p i c a l e n g i n e e r -i n g r e s p o n s e t o r e p e t i t i v e component f a i l u r e , and p r e - f a i l u r e d e t e c t i o n o f t r o u b l e c a n sometimes p r e v e n t t h e ne e d f o r e x t e n s i v e m a i n t e n a n c e . I n 19 67 E a s t e r n A i r L i n e s i n c o o p e r a t i o n w i t h IBM were t r y i n g t o d e v e l o p a p r a c t i c a l s y s t e m f o r r e c o r d i n g p e r f o r m 2 g a n c e d a t a on a i r c r a f t i n s e r v i c e . A B o e i n g 707 was s u i t a b l y w i r e d , a r e c o r d i n g s y s t e m was i n s t a l l e d t o t r a c k 120 e n g i n e p a r a m e t e r s . A p r o g r a m was d e v e l o p e d t o c o n v e r t t h e r e c o r d e d d a t a t o e n g i n e e r i n g d a t a f o r v a l i d i t y c h e c k s , and t r e n d a n a l y s i s . T h i s p r o g r a m e n c o u n t e r e d d i f f i c u l t i e s w i t h t h e r e c o r d i n g h a r d w a r e . C o s t i n f o r m a t i o n f o r i m p l e m e n t a t i o n and f o r r u n n i n g t h e s y s t e m was n o t g i v e n b u t i t a p p e a r s t o be r e l a t i v e l y e x p e n s i v e . U n i t e d A i r L i n e s a t t e m p t e d o r i g i n a l l y t o f o r e c a s t , 2 e n g i n e r e p a i r and m a i n t e n a n c e w o r k l o a d by means o f s i m u l a t i o n . T h i s a p p r o a c h was r e j e c t e d f o r s e v e r a l r e a s o n s . L o n g r u n -t i m e s f o r r e p e a t e d s i m u l a t i o n s , t h e need f o r l a r g e c o m p u t e r s , e x t e n s i v e r e p r o g r a m m i n g f o r m a i n t e n a n c e p o l i c y c h a n g e s , and t e d i o u s i n p u t p r e p a r a t i o n — a l l t e n d e d t o make s i m u l a t i o n V.D. M a c k l e , " A i r b o r n e I n t e g r a t e d D a t a S y s t e m ( A I D S ) , " AGIFORS P r o c e e d i n g s , 1967, p. 320. 27 F.S. Nowlan,"Some T o p i c s P e r t a i n i n g t o E n g i n e Management, AGIFORS P r o c e e d i n g s , 1 1 1 9 6 7 , p. 171. u n a t t r a c t i v e f o r e n g i n e w o r k l o a d f o r e c a s t i n g . A m a t h e m a t i c a l programming a p p r o a c h was t a k e n i n s t e a d . I n t e r v a l s between o v e r h a u l s i n c r e a s e d as e x p e r i e n c e was g a i n e d w i t h an e n g i n e t y p e . U n i t e d A i r L i n e s ' T u r b i n e E n g i n e R e l i a b i l i t y P r o gram, (TERP), s e l e c t e d sample e n g i n e s f r o m among t h e o l d e s t e n g i n e s i n s e r v i c e . The sample e n g i n e s were c l o s e l y i n s p e c t e d and r e p a i r e d as n e c e s s a r y . The aim was t o e x t e n d t h e i n t e r v a l between o v e r h a u l s as l o n g as r e l i a b i l i t y i n d i c a t i o n s c o n t i n u e d f a v o r a b l e . TERP samples were t a k e n a t a s p e c i f i e d a n n u a l r a t e t h a t a l l o w e d f l u c t u a t i o n i n t h e number o f e n g i n e s s e l e c t e d month by month. T h e r e was no h a r d o v e r h a u l t i m e l i m i t ; s a m p l e s c o u l d be c h o s e n f r o m e n g i n e s t h a t were w i t h i n 2 0 0 h o u r s o f t h e o l d e s t . Some p r e -m a t u r e l y removed e n g i n e s were t h u s a l l o w e d as TERP s a m p l e s . E n g i n e r e m o v a l f r e q u e n c y g r a d u a l l y d e c l i n e d as r e -l i a b i l i t y d a t a a c c u m u l a t e d f r o m TERP s a m p l i n g . Reasons f o r r e m o v a l were g r o u p e d . By p r o j e c t i n g t h e e n g i n e age d i s t r i -b u t i o n f o r f u t u r e t w e n t y - e i g h t ' d a y p e r i o d s , . t h e number o f r e m o v a l s were f o r e c a s t as a f u n c t i o n o f e n g i n e l i f e i n s e r v i c e . F o r e c a s t s f o r 1 9 6 7 t h r o u g h 1 9 8 0 f o r t w e n t y - o n e f l e e t s and t w e n t y - e i g h t day i n t e r v a l s r a n t w e n t y - s i x m i n u t e s on t h e c o m p u t e r . U n i t e d A i r l i n e s ' a p p r o a c h was i n s t a l l e d b e c a u s e i t w orked. I t was n o t a s o p h i s t i c a t e d d e v e l o p m e n t , b u t i t a p p e a r e d t o do t h e j o b r e a s o n a b l y w e l l . The o v e r h a u l i n t e r v a l was g r a d u a l l y e x t e n d e d , and t h e o v e r h a u l w o r k l o a d was smoothed because of the f l e x i b i l i t y o f the TERP program. A d i f f e r e n t approach i s seen i n A i r Canada's mainten-2 8 ance s i m u l a t i o n . The aims of the s i m u l a t i o n were t o f o r e c a s t m a t e r i a l usage and to e v a l u a t e maintenance p o l i c y i n terms of m a t e r i a l usage. The model simulated i n h e r e n t performance c h a r a c t e r -i s t i c s of 1 1 8 assemblies and 6 , 0 0 0 i n d i v i d u a l components. F i v e - y e a r runs r e p l i c a t e d ten times ran three to f i v e hours on an IBM 1 4 1 0 computer. R e s u l t s i n c l u d e d : . average number of components accepted and r e p a i r e d , number of components scrapped and reasons f o r same,, number of r e p l a c e d components, and engine events summarized by month. T h i s s i m u l a t i o n presumably s u f f e r e d from the inadequacies mentioned above i n the d i s c u s s i o n of U n i t e d A i r L i n e s ' engine workload, f o r e c a s t i n g . I t appears t h a t very l i t t l e i s constant i n engine r e l i a b i l i t y e x p e c t a t i o n s , (except t h a t t h e r e tends to be a long run improvement). Informed o p i n i o n i s d i v i d e d on the s u i t a b i l i t y of s i m u l a t i o n as a maintenance f o r e c a s t i n g method. Unless the o b j e c t i o n s have been c o n s i d e r e d , a d e c i s i o n t o s i m u l a t e c o u l d l e a d to disappointment. A. Bodnarchuk, J e a n n i o t , P.J.,"A Maintenance S i m u l a t i o n f o r Complex Assemblies 1, 1 AGIFORS Proceedings, 1 9 6 8 , p. 3 7 3 . M a i n t e n a n c e Shop S c h e d u l i n g R e p a i r work may be d i v i d e d i n t o p r i o r i t y c l a s s e s a c c o r d i n g t o t h e n e e d f o r t h e i t e m b e i n g r e p a i r e d . I f t h e r e p a i r i s h o l d i n g up a h i g h e r a s s e m b l y , ( f o r example an a i r -c r a f t i s w a i t i n g f o r an e n g i n e ) , t h e r e p a i r w o u l d be a s s i g n e d a h i g h e r p r i o r i t y t h a n r e p a i r s g o i n g t o s t o r e s i n v e n t o r i e s . Queue d i s c i p l i n e a f f e c t s t h e l e n g t h o f t h e w a i t i n g l i n e . T h r e e e x amples o f queue d i s c i p l i n e a r e as f o l l o w s : 1. J o b s a r e s e q u e n c e d a c c o r d i n g t o p r o c e s s t i m e , s h o r t e s t f i r s t ( S P T ) . 2 . J o b s a r e s e q u e n c e d i n o r d e r o f a r r i v a l ( F I F O ) . 3. J o b s a r e s e q u e n c e d w i t h L o n g e s t p r o c e s s t i m e s f i r s t ( L P T ) . SPT l e a d s t o t h e s h o r t e s t queues and t h e s h o r t e s t a v e r a g e w a i t i n g t i m e . LPT l e a d s t o t h e l o n g e s t queue and t h e l o n g e s t a v e r a g e w a i t i n g t i m e . The SPT r u l e h as a l a r g e v a r i a n c e i n w a i t i n g t i m e t h a t w i l l be u n a c c e p t a b l e i n some c a s e s b e c a u s e o f d u e . d a t e s . P r o v i d i n g t h a t due d a t e s c o n -s t r a i n t s a r e b i n d i n g i n . a small p r o p o r t i o n o f c a s e s , two p r i o r i t y c l a s s e s w i l l s e r v e t o meet t h e due d a t e s w i t h o u t c a u s i n g l a r g e i n c r e a s e s i n mean w a i t i n g t i m e s . ' To m i n i m i z e t h e d o l l a r i n v e s t m e n t i n t h e queue, t h e j o b s s h o u l d be s c h e d u l e d i n i n c r e a s i n g o r d e r o f t h e i n d e x P^ p r o c e s s i n g t i m e p e r d o l l a r v a l u e o f i t e m . Queues a t i n d i v i d u a l work s t a t i o n s may be s t u d i e d independently i f they have P o i s s o n i n p u t s . The in p u t s t o a p a r t i c u l a r work s t a t i o n are the cumulative outputs of other work s t a t i o n s , and f o r p r a c t i c a l purposes the assumption 29 t h a t the cumulative outputs are Poisson i s o f t e n j u s t i f i e d . S i m u l a t i o n s t u d i e s have been used t o eva l u a t e s c h e d u l i n g r u l e s w i t h r e s p e c t t o per cent of l a t e jobs, l a t e n e s s v a r i a n c e , mean l a t e n e s s , and mean shop time. S c h e d u l i n g t o due dates, the o b j e c t i v e i s t o minimize the overdue t o t a l . . An example of such a r u l e i s the SLPO, (s l a c k per o p e r a t i o n ) , g i v e n by: SLPO D i " T - k l c P i , k g. - G + 1 ^ i where = due date, job i T = presen t date. g^ = t o t a l number of o p e r a t i o n s i n job p^ .^ = process time f o r o p e r a t i o n k G = number of presen t o p e r a t i o n ( i n p r o c e s s ) . T h i s r u l e minimizes the o p e r a t i n g r i s k by s c h e d u l i n g jobs a c c o r d i n g t o due dates. A comparison between SPT and a 50/50 combination of the two are shown i n the f o l l o w i n g t a b l e : 29 J.A. vanHamel, B.J. Verdoes, "Maintenance As A C y b e r n e t i c System and A p p l i c a t i o n t o Shop Sche d u l i n g , " AGIFORS Proceedings, 196 8, p. 281. % of Lateness Mean Mean Late Variance Lateness Shop Jobs Time SPT 5.0 2878 44.9 34.0 SLPO 3.7 226/ 12.8 66.1 SPT/SLPO 1.5 232 14.0 57.6 Improved performance to due date i s at the expense of increased shop time with SLPO r u l e . Doubt i s cast on the whole table because of the re su l t s given for the SPT/SLPO. The object ive of SLPO i s to minimize the percentage of la te jobs. I t has been pointed out that the combined r u l e , SPT/ SLPO, can not provide better operating r i s k than the pure SLPO rule because the object ive of the SPT ru le i s not to reduce operating r i s k , but to minimize investment i n the queue. However, i f more than one job i s l a t e , then i t i s conceivable that an SPT schedule for la te jobs would reduce the number of l a te jobs just as i t reduces the number wait ing i n any queue. The SLPO ru le minimizes r i s k i n a sense, but i t does not weigh jobs according to importance. Assume there are two la te jobs, A and B. Loss per day associated with delay of B i s greater than for job A. I t may be better to l e t job A f i n i s h l a t e r i f th i s allows job B to be completed e a r l i e r , even though job A has a p r i o r due date. 30 M. Etschmaier, Comments on the paper "Maintenance as a Cybernetic System and A p p l i c a t i o n to Shop Schedul ing, " AGIFORS Proceedings, 1968, p. 368. B e c a u s e j o b a r r i v a l s and j o b d u r a t i o n s a r e p r o b a b i l -i s t i c , s i m u l a t i o n a p p e a r s t o be t h e most p r a c t i c a l method f o r c h e c k i n g o u t a p r o p o s e d shop s c h e d u l i n g p o l i c y . Many o b j e c t i v e s a r e d e s i r a b l e i n j o b shop s c h e d u l i n g . 31 P . M e l l o r l i s t s t w e n t y - s e v e n . No one has a t t e m p t e d t o s o l v e a p r o b l e m t h a t c o n t a i n s a l l t h e s e o b j e c t i v e s . E v e n t h e p r i o r i t y o f o b j e c t i v e s v a r i e s w i t h c i r c u m s t a n c e . Most o f t h e r e a l - l i f e c o m p l e x i t i e s a r e e x c l u d e d f r o m e x i s t i n g m o d e l s . B l i n d a d h e r e n c e t o a s c h e d u l i n g r u l e i s t h e r e f o r e i m p r a c t i c a l . P r o d u c t i o n s m o o t h i n g i s one o b j e c t i v e t h a t seems o u t o f p l a c e f o r an a i r l i n e m a i n t e n a n c e shop a l t h o u g h U n i t e d A i r L i n e s ' TERP p r o g r a m i s a s t e p i n t h e d i r e c t i o n o f more u n i f o r m shop l o a d i n g . T r a f f i c v a r i e s by f a c t o r s o f a b o u t 3 t o 1, between b u s y months and o f f - s e a s o n months. D u r i n g t h e b u s y summer p e r i o d t h e a i r c r a f t a r e a l l i n s e r v i c e . M a i n t e n a n c e i s m i n i m a l . M o s t . m a i n t e n a n c e and r e p a i r work i s done i n t h e o f f s e a s o n . B e c a u s e a t o t a l s y s t e m s a p p r o a c h i s b eyond t h e c a p a b i l i t y o f • p r e s e n t day c o m p u t e r s , a i r l i n e s y s t e m s a r e b u i l t a r o u n d t h e f o c a l p o i n t o f o p e r a t i o n s — t h e f l i g h t s c h e d u l e . O t h e r p l a n n i n g i s p e r i p h e r a l t o t h e f l i g h t s c h e d u l e . An a s s e s s m e n t o f , f l i g h t s c h e d u l e r e q u i r e m e n t s i s made by t h e 32 f o l l o w i n g f o r m u l a f o r e n g i n e m a i n t e n a n c e . 31 P. M e l l o r , "A Review o f J o b S c h e d u l i n g , " O p e r a t i o n a l  R e s e a r c h , V o l . 17, 1966, p. 161. 32 F.S. Nowlan, op. c i t . . , p. 184. IN • EI where IN index number SS = the.number of s e r v i c e a b l e spare engines IP = the number of engines (of a type) i n process EI = engines of one type/average shop c y c l e time f o r t h a t type A h i g h index number s i g n i f i e s a s t r o n g i n v e n t o r y p o s i t i o n . A low number corresponds to a need f o r replenishment. Each day, by c a l c u l a t i n g the index number f o r each engine a w a i t i n g o v e r h a u l , the schedule sequence i s found. T h i s r u l e i s s impler than the SLPO sequence mentioned above, i n t h a t i t s e l e c t s an i n p u t t i n g sequence, but i s not dependent upon d e t a i l e d knowledge of every engine i n the shop. E m p i r i c a l l y , i t has been found t h a t the average index number i n d i c a t e s the o v e r a l l c a p a b i l i t y of the maintenance f a c i l i t y . A g i v e n number of spare engines w i l l r e s u l t i n a c e r t a i n average index number. I f the number of spares i s i n c r e a s e d then the average index number i s i n c r e a s e d . The d e s i r e d average index number was found by experience. At 33 U n i t e d , i t was about 3. 3.3. I b i d . Application of the index number can.be p a r t i c u l a r l y b e n e f i c i a l during a conversion program—as for, example,' i n the introduction of a new engine, or for some general modifica-t i o n to a large number of engines. By reducing the index number to a safe minimum, on a l l other types of engine, a maximum e f f o r t can be applied to the conversion program, with-out disrupting necessary service elsewhere. Engine. Provisioning should minimize the sum of the following costs: - stockouts or u n f i l l e d demand costs - system management costs - spare engine ownership costs. To b u i l d a provisioning model, an evaluation of annual volume of overhauls, costs and flow times i s e s s e n t i a l : - the number of scheduled and non-scheduled engine removals - the time required to prepare, ship, repair and return engines sent, for maintenance - shop capacity constraints - (men or f a c i l i t i e s ) - costs of owning spares - costs of u n f i l l e d demand, - costs of overtime work costs of expediting i n shop, or i n t r a n s i t . A dynamic programming approach was developed by U n i t e d A i r L i n e s f o r maintenance of engines f o r i t s f l e e t of 34 Boexng 727 a i r c r a f t . The dynamic programming method i s 35 w e l l d e s c r i b e d i n the book by H i l l i e r and Lieberman. The engine l o g i s t i c s c y c l e a t U n i t e d i s represented by F i g u r e 3. Stages were numbered i n r e v e r s e order. (The l a s t stage of maintenance i s Number 1). Stage 1 i s d e f i n e d by optimal a l l o c a t i o n of: s e r v i c e a b l e engines f o r any number (between zero and twenty-one) of such engines and the c o s t of u n f i l l e d demand a s s o c i a t e d w i t h each number of s e r v i c e a b l e spares (between zero and twenty-one). Zero and twenty-one were c o n s i d e r e d t o be the l i k e l y l i m i t s of numbers of s e r v i c e a b l e spares. Stage 2 does not a f f e c t c o s t s and i s r e s o l v e d s u b j e c t to c r i t e r i a other than c o s t s . Stage 3 weighs the c o s t s of overtime a g a i n s t the b e n e f i t s of more s e r v i c e a b l e engines, and reduced u n f i l l e d demand. As the stock of s e r v i c e a b l e engines i n c r e a s e s , the p r o b a b i l i t y of u n f i l l e d demands decreases. Stage 4 decides which type of engine goes next i n t o the r e p a i r shop. T h i s d e c i s i o n i s based on the index,number 3 6 d i s c u s s e d above. 34 F.S. Nowlan, " A p p l i c a t i o n of Dynamic Programming Techniques t o the Management of the Engine L o g i s t i c s C y c l e and to the Determination of Spare Engine Reguirements',' AGIFORS  Proceedings, 1969. 35 F.S. H i l l i e r and Lieberman, G.J. I n t r o d u c t i o n t o O/R, San F r a n c i s c o , Holden Day Inc., 1967, pp. 243-244. 3 6 F . S . Nowlan, AGIFORS Proceedings, 1967, op. c i t . *4) tu Nat to f H i f 3 1 i i V 1 I-l-0--I I I--1-4 —£!» r-— Ui -4 - J Si ^4 <0 I 1 "XT -1 to. Tl" UJ ft .0 .0 a rt -I -tt-i ^ JC>_ I _U1_ ur o •5 ->s-t •ft J o . • f t -0-0 I* -UJ I Stage 5 and Stage 6 weigh c o s t s a g a i n s t b e n e f i t s of e x p e d i t i n g engines to the maintenance base. C a l c u l a t e d t o t a l c o s t s (of ownership and shortage) i n c r e a s e d about,3 per c e n t . i f the a c t u a l number of spares was 7 per cent over or under the optimum. T h i s programme was i n t r o d u c e d by UAL i n 1969. The approach was a p r a c t i c a l i l l u s t r a t i o n of dynamic programming i n a day t o day schedule o p e r a t i o n . An approach s i m i l a r to the index number f o r engine sequencing was a p p l i e d t o Lufthansa's e l e c t r i c a l shop s c h e d u l i n g . The o b j e c t i v e was to minimize the r i s k of a 37 s t o c k o u t . A v a r i e t y of two-bin r e o r d e r i n g was used such t h a t when the r e o r d e r p o i n t was reached, a p r i o r i t y tag was generated f o r each item withdrawn from s t o c k . The tags were attac h e d t o the most advanced spares i n process i n the r e p a i r shop so t h a t these were completed w i t h h i g h p r i o r i t y and p l a c e d i n s t o c k as s e r v i c e a b l e spares. Q/R In Shop Methods Not many examples are a v a i l a b l e to i l l u s t r a t e the use of O/R i n shop methods. S t a t i s t i c a l q u a l i t y c o n t r o l and programs such as TERP f o r e v a l u a t i o n of engine c o n d i t i o n s 37 M. Etschmaier, "Optimal Scheduling of Rotables Through the E l e c t r o n i c s Workshop," AGIFORS Proceedings, 1968, pp. 516-533. were, o f . course , shop uses of O/R, but these d id not d i r e c t l y a f fect shop methods. In some assemblies such as turbine blade sets there may be combinatorial problems created by s t r i c t design s p e c i f i c a t i o n s . Nozzle guide vanes d i r e c t engine exhaust through the turbine'. A set of vanes may be worth $8,000, (or $100 per vane). Depending upon cer ta in measurements, vanes have a "value" that i s subject to f ive condit ions i n an assembled set . 1. average set value must be within spec i f i ed l i m i t s 2. maximum and minimum values per vane are spec i f i ed 3. number of vanes per set i s e x p l i c i t 4. d i f ference i n adjacent vane values must be less than a spec i f i ed maximum. 5. va r i a t ions i n a set should be uniformly d i s t r i b u t e d around the c i r c l e . O/R inves t i ga t ion of t h i s problem was i n v i t e d by the materials planning department because of a growing inventory 3 8 of vanes. Despite large stocks of vanes, new vanes had to be supplied to match sets being assembled. To sa t i s fy the f ive assembly, condit ions the eas iest method was to choose J . C . Abbinck, "Nozzle Guide Vanes - a case study," AGIFORS Proceedings, 1967, p. 283. v a n e s w i t h v a l u e s c l o s e t o t h e a v e r a g e r e q u i r e d f o r t h e s e t . D e t a i l s o f t h e method n e e d n o t be d i s c u s s e d h e r e . A com p u t e r p r o g r a m was d e v i s e d t o compose t h e s t o c k o f v a n e s i n t o s e t s t h a t met a l l r e q u i r e m e n t s . T h e r e was a t i m e i n t e r v a l b etween s t o c k t a k i n g and computer o u t p u t . The shop e x c h a n g e d good v a n e s i n o r d e r - t o b u i l d s e t s as d i c t a t e d by t h e computer. T h i s c a u s e d e x t r a work b e c a u s e e a c h vane had t o be wrapped and boxed s e p a r a t e l y . The s o l u t i o n was t o s t o p r e g a r d i n g v a n e s as r o t a b l e s . I n s t e a d , c o m p l e t e s e t s were r o t a t e d and t h e s e t s were matched as a s t o r e s f u n c t i o n . The shop t u r n e d i n a s e t w i t h a p p r o v e d and r e j e c t e d v a n e s and t h e s t o r e p r o v i d e d a matched s e t c o m p l e t e l y r e a d y f o r a s s e m b l y . The s t o r e was r e s p o n s i b l e t o have one matched s e t a v a i l a b l e a t any t i m e . "O/R i s t h e a r t o f g i v i n g b a d answers t o p r o b l e m s t o 39 w h i c h o t h e r w i s e w orse answers a r e g i v e n . " The dynamic i n v e n t o r y p r o b l e m . h e r e was s o l v e d by a s t a t i c s o l u t i o n . From t h e s t o c k p o s i t i o n a t any moment, a number o f p o s s i b l e s e t c o m b i n a t i o n s were c a l c u l a t e d . O n l y one s e t was made up. Whenever c h a n g e s o c c u r r e d i n t h e s t o c k , t h e c a l c u l a t i o n s were r e p e a t e d . One s e t was r e l e a s e d and one more s e t was matched up f o r a s s e m b l y . Inventory C o n t r o l A p p l i c a t i o n s of O/R Inventory .control i s aimed at the l e a s t t o t a l c o s t of procurement, h o l d i n g , and stockout. The procurement i n t e r v a l or l e a d time, (the time el a p s e d between o r d e r i n g , and r e c e i p t of order from the s u p p l i e r ) , i s not known w i t h pre-c i s i o n , and i s g e n e r a l l y v a r i a b l e . "Lead time usage" i s the q u a n t i t y r e q u i r e d d u r i n g the l e a d time. In p r a c t i c e , l e a d time usage i s known only approximately. O r d e r i n g c o s t s may be c a l c u l a t e d , but the stockout c o s t s are g e n e r a l l y l e s s w e l l known. An i n v e s t i g a t i o n of i n v e n t o r i e s of expendable p a r t s a t S w i s s a i r r e v e a l e d t h a t f i f t y per cent of the 61,000 items 40 i n stock had not moved i n the pre c e d i n g three y e a r s . Con-sumption of many items was low and e r r a t i c . The n a t u r a l q u e s t i o n was whether or not r u l e s c o u l d be found to reduce the t o t a l c o s t . I f s e r v i c e c o u l d be improved without r a i s i n g investment i n i n v e n t o r y , or i f the investment c o u l d be reduced without i m p a i r i n g s e r v i c e , an o v e r a l l improvement would be a t t a i n e d . Lead time usage may be d i s t r i b u t e d i n almost any f a s h i o n . V a r i a n c e of l e a d time usage i s l i k e w i s e o f wide l a t i t u d e . T a r g e t stockout frequency can be d e f i n e d i n terms W. Grassman, "The C a l c u l a t i o n of the Reorder L e v e l of Expendable P a r t s , " AGIFORS Proceedings, 1968, p. 500. of a s p e c i f i c time p e r i o d , say, one stockout i n ten y e a r s , o r . i n terms of le a d time, or order c y c l e . Computer systems, such as IBM IMPACT a u t o m a t i c a l l y r e c a l c u l a t e mean and v a r i a n c e of l e a d time consumption and aim at a percentage of demand met without d e l a y , r a t h e r than a s p e c i f i e d i n t e r v a l between s t o c k o u t s . At S w i s s a i r , a s i m u l a t i o n was used t o t e s t proposed o r d e r i n g r u l e s . Consumption d u r i n g a one-year p e r i o d served as i n p u t and the s i m u l a t i o n t e s t e d the proposed r u l e s . R e s u l t s i n d i c a t e d t h a t the proposed r u l e s would l e a d to a. r e d u c t i o n of i n v e n t o r y while p r o v i d i n g a very high s e r v i c e l e v e l . . Long engine overhaul c y c l e s o f 5,000 hours or more, i i n d i c a t e t h a t a one-year h i s t o r y i s too s h o r t a v a l i d a t i o n p e r i o d . A s i n g l e o r d e r i n g r u l e , based o n , d o l l a r value of items used, i s probably u n s u i t a b l e f o r some items i n a com-p l e t e range of stock.. The consequences of stockout vary from t r i v i a l t o d i s a s t r o u s , and other c o n s i d e r a t i o n s such as f l e e t and schedule changes may a f f e c t the o r d e r i n g r u l e . I f such r e a l f a c t o r s are kept i n mind, th e r e i s l e s s danger of p l a c i n g too much conf i d e n c e i n the s p e c i f i c output of the i n v e n t o r y model s i m u l a t i o n . I n i t i a l Provisioning. I n i t i a l p r o v i s i o n i n g f o r a new a i r c r a f t type i s more d i f f i c u l t than i n v e n t o r y maintenance f o r a f l e e t w i t h a reasonable s e r v i c e h i s t o r y . For each p a r t , the manufacturer should specify p r i c e , d e l i v e r y , usage ra te , she l f l i f e , mode of usage (during overhaul , during maintenance, e t c . ) , end usage ("goes i n t o " ) . The customer or user , i n t h i s case the a i r l i n e , should estimate or speci fy f l e e t s ize over time, scheduled f l y i n g hours, abnormal overhaul rates during ear ly months of operat ion, and locat ions of spares . . 41 inventor ie s . O v e r a l l f l e e t requirements may be broken down for spares a l loca t ions between the overhaul base and the f i e l d s t a t ions . A two-echelon model was used by American A i r l i n e s for rotable spares. (Rotables are normally recondit ioned and re-used) . This model, was ana ly t i c and was predicated 42 upon a v a i l a b i l i t y c r i t e r i a set by a i r l i n e p o l i c y . S e n s i t i v i t y analyses of the models indicated that minimum stocks could be reduced without serious penalty to a v a i l a b i l i t y standards. Introduction of the new i n i t i a l p rov i s ion ing sys tem, .ca l led .RACE, was expected to reduce i n i t i a l investment by 22 per cent on rotables and by 7 to 13 per cent on consumables (consumables are replaced, not repaired) while saving 30,000 man hours by means of automatic performance of previous ly manual f u n c t i o n s . 4 3 41 H . E . Norwood, "An I n i t i a l Prov i s ioning System and i t s Decis ion Models ," AGIFORS Proceedings, 1969. 4 2 I b i d . 4 3 I b i d . These f o r e c a s t s were made p r i o r t o o p e r a t i n g experience w i t h the program. The assumptions made by the manufacturer and by the a i r l i n e were fundamental to the pre-d i c t i o n of s a v i n g s , y e t these assumptions, of n e c e s s i t y , had t o be made without o p e r a t i n g experience. T h i s c o u l d i n v a l i d a t e the s e n s i t i v i t y a n a l y s i s . About a l l t h a t can be s a i d here i s t h a t judgement e r r o r s should be documented as they become apparent, so t h a t e r r o r s can be reduced i n f u t u r e programs. Stocks may be d i v i d e d between maintenance base and f i e l d s t a t i o n s . Two-echelon i n v e n t o r y models d i s t r i b u t e stock among s t o r e s w i t h the o b j e c t i v e of mi n i m i z i n g t o t a l c o s t s 44 o f : (1) ownership and (2) delays due t o shortages. The two-echelon mode 1 can be used t o r e d i s t r i b u t e e x i s t i n g stock to achieve maximum item s e r v i c e l e v e l . Item s e r v i c e l e v e l and ownership l e v e l can be r e l a t e d f o r v a r i o u s t r a n s i t times (between s t o r e s ) and f o r v a r i o u s mean shop ove r h a u l times. The two-echelon model optim i z e s item s e r v i c e l e v e l by seeking the b e s t a l l o c a t i o n of i n v e n t o r y among the v a r i o u s s t o r e s at the overhaul base and at the f i e l d s t a t i o n s . The s o l u t i o n 45 was found by means of d i s c r e t e o p t i m i z a t i o n techniques. NN. Amin, K.C. Khanna, " S e n s i t i v i t y A n a l y s i s of Optimal A l l o c a t i o n of Rotable Spares," AGIFORS Proceedings-, 1969 . 45 B. F o x , " D i s c r e t e O p t i m i z a t i o n v i a M a r g i n a l A n a l y s i s , Management S c i e n c e , V o l . 13, No. 13, pp. 210-216. "Item s e r v i c e l e v e l s " ( o r I t e m a v a i l a b i l i t i e s ) v a r y a c c o r d i n g t o (a) t h e t o t a l i n v e n t o r y l e v e l and (b) t h e i n v e n -t o r y a t t h e c e n t r a l ( o v e r h a u l ) b a s e . TWA c o s t s o f o v e r h a u l , t r a n s p o r t a t i o n and d e l a y s due t o p a r t s s h o r t a g e s were n o t a v a i l a b l e . The p r o b l e m t h e n was t o s o l v e f o r t h e most e c o n o m i c way t o i n c r e a s e i t e m s e r v i c e l e v e l . The a l t e r n a t i v e s a v a i l a b l e were (a) i n c r e a s e s t o c k s , and (b) r e d u c e r e p l e n i s h m e n t t i m e . The c o s t o f i n c r e a s i n g s t o c k s by one u n i t was e a s i l y e s t i m a t e d . The t w o - e c h e l o n model c o u l d p r e d i c t s e r v i c e l e v e l improvement r e s u l t i n g f r o m s u c h an i n c r e a s e . The model c o u l d a l s o p r e d i c t t h e r e d u c t i o n i n r e p l e n i s h m e n t t i m e f o r t h e same i n c r e a s e i n s e r v i c e l e v e l . I t i s a m a t t e r o f judgement w h e t h e r o r n o t t h e r e d u c e d r e p l e n i s h m e n t t i m e s c o u l d be a c h i e v e d a t l e s s c o s t t h a n i n c r e a s i n g i n v e n t o r y , b u t f o r e x p e n s i v e i t e m s , w i t h 46 l o n g o v e r h a u l t i m e s , t h i s judgement s h o u l d be made. Insurance Spares a r e a i r c r a f t s u r f a c e , components s t o r e d as a s a f e g u a r d a g a i n s t damage t o a i r w o r t h i n e s s . S m a l l a i r l i n e s o p e r a t i n g l i m i t e d f l e e t s c a n n o t a f f o r d t o keep f u l l s e t s o f i n s u r a n c e s p a r e s . I n s t e a d t h e y c a n buy a c c e s s t o s p a r e s . A r r a n g e m e n t s v a r y , b u t s p a r e s may be a v a i l a b l e f r o m t h e m a n u f a c t u r e r , f r o m o t h e r a i r l i n e s , o r f r o m an a i r l i n e p o o l . N.N. Amin, K.C. Khanna, op. c i t . The p r o p a b i l i t y of damage requ i r ing insurance spares has been found to f i t the Poisson d i s t r i b u t i o n : A x -A P(x) • e x! where A = average rate of damage occurrences x = ( 0 , 1 , 2 , 3 , . . . . ) , the number of occurrences. Occurrence of damage has been h i s t o r i c a l l y confirmed as a regress ion of the form: where the K's are constants F = hours flown L = number of landings. Conceptual ly, two p o l i c i e s can be compared: Strategy (1), to buy a f u l l set of spares or , strategy (2), to buy access to spares. . Let A and B.be f ixed costs associated with the s trategies r e spec t ive ly . I f the expected average rate of damage i s less than the breakeven rate of damage, \i, then strategy (2) i s the more economical. x K o 47 J . Byrne," A B747 Insurance Spares Strategy? AGIFORS Proceedings, 1969. F i g u r e 4 Insurance S t r a t e g i e s The problem i s t o assess c o s t s r e l a t i v e t o the s t r a t e g i e s . F a c t o r s t h a t a f f e c t t h i s assessment are f l e e t s i z e and u t i l i z a t i o n , maintenance p o l i c y , route s t r u c t u r e and f r e q u e n c i e s , l o c a t i o n of maintenance base. A f a c t o r f a v o r i n g non-ownership i s t h a t damage may occur away from the mainten-ance base, i n which case the spares might have t o t r a v e l t o the a i r c r a f t . In such a case, the advantage of ownership b o i l s down to marginal c o s t of t r a n s i t d e l a y s (between s t o r e s and r e p a i r s i t e s ) . H i s t o r i c a l i n f o r m a t i o n on types and causes of damage and geographic occurrence of damage would h e l p t o q u a n t i f y expected c o s t s and b e n e f i t s of a l t e r n a t i v e s t r a t e g i e s . A s i m u l a t i o n i s c o n c e i v a b l e as a s o l u t i o n approach. I n t u i t i v e l y a p o o l i n g arrangement wi t h spares c o n v e n i e n t l y a l l o c a t e d to main p o r t s of c a l l should p r o v i d e p a r t i c i p a t i n g a i r l i n e s w i t h more insurance than they c o u l d p r o v i d e i n d i v i d u a l l y . The problem then becomes a d e c i s i o n r u l e f o r the s h a r i n g o f p o o l c o s t s . Keeping such r u l e s p e r f e c t l y i m p a r t i a l would be d i f f i c u l t i f routes and schedules were s u b j e c t to change. However, as long as i n d i v i d u a l a i r l i n e s gained from p o o l member-» s h i p , the arrangement c o u l d be s a t i s f a c t o r y . Expendable Inventories p r e s e n t a somewhat d i f f e r e n t problem. Overhaul times do not a f f e c t the s i z e of i n v e n t o r y r e q u i r e d . The items are s u p p l i e d by o t h e r s . Economic order 48 q u a n t i t i e s can be found by means of the Wilson formula, but the o b j e c t i v e was to f i n d the s a f e t y stock t h a t maximized the s e r v i c e l e v e l over a l l items s u b j e c t t o : - s p e c i f i e d minimum s e r v i c e l e v e l f o r each item - g i v e n t o t a l s a f e t y stock investment. The d u a l . o f t h i s problem i s to minimize the t o t a l s a f e t y stock investment s u b j e c t t o : - a g i v e n system s e r v i c e l e v e l - a gi v e n minimum item s e r v i c e l e v e l . 48 K.C. Khanna, A.V. B h a t i a , Optimal D e c i s i o n Rules f o r an Expendable Inventory System, AGIFORS Proceedings, 1967, P- 215. The l a t t e r problem may be s t a t e d s y m b o l i c a l l y as N Min, ( t o t a l s a f e t y stock investment) i = l s u b j e c t t o : ^ * ^ i ^ R i ' ^ i ^ — S S L (system s e r v i c e l e v e l ) R. > 0 1 — f.(R., Q.) > M (minimum item s e r v i c e l e v e l ) i i ' l — o where R^ = d o l l a r v alue of s a f e t y stock - item i CK = Economic Order Quantity - item i Care should be taken to observe the nature of the f u n c t i o n f . . I f f. i s a n o n - l i n e a r f u n c t i o n then the "dual" x i above i s not a d u a l , but a r e l a t e d problem. S e r v i c e l e v e l can be expressed i n s e v e r a l ways, f o r example: A. Item: per cent of p e r i o d i c item demand t h a t i s s u p p l i e d without d e l a y . System: per cent of p e r i o d i c system demand s u p p l i e d without d e l a y . B. Item: -as f o r A. above. j System: an average of the item s e r v i c e l e v e l s i n the e n t i r e system. C. Item: p r o b a b i l i t y o f item demand s a t i s f i e d d u r i n g l e a d time c y c l e . System: average of item s e r v i c e l e v e l s i n the e n t i r e system. S a f e t y stocks e x i s t to cover v a r i a t i o n s of requirements d u r i n g the l e a d time i n t e r v a l , caused by hig h usage or longer than average l e a d times. U n l i k e economic order q u a n t i t i e s t h a t o p t i m i z e g r a d u a l l y from both d i r e c t i o n s , the l o s s f u n c t i o n a s s o c i a t e d w i t h too s m a l l a s a f e t y stock i s s u b j e c t t o an abrupt i n c r e a s e a t the occurrence of a sto c k o u t . The advantages of s o p h i s t i c a t e d i n v e n t o r y c o n t r o l systems may not be e v i d e n t i n the r e c o r d of any s i n g l e item. Over thousands of items i n stoc k , however, good r u l e s r e s u l t i n h i g h performance per d o l l a r i n v e s t e d . The e f f e c t i v e n e s s of r u l e s depends upon the extent t o which usage p a t t e r n s are known. Because the f u t u r e i s u n c e r t a i n , t h e r e i s a tendency to under-rate advanced i n v e n t o r y c o n t r o l methods. L i k e the s l o t machines a t a gambling c l u b , i n d i v i d u a l winnings are im p o s s i b l e to f o r e t e l l . The long run laws of chance on the other hand, are known wit h p r e c i s i o n . AIRLINE FINANCE The Current F i n a n c i a l P ic ture Adverse f i n a n c i a l trends for a i r l i n e s began i n 1966. Revenue Passenger M i l e s , (RPM), increas ing annually at a rate of 22.2 per cent i n the second quarter of 1966, were s t i l l increa s ing , but at only 13.6 per cent per annum by the f i r s t quarter of 1969. The dec l ine i n the rate of increase i n t r a f f i c was steady through t h i s per iod . In 1969, i t was expected to remain at about 11.1 per cent per year i n the years 1969 - 1973. 1 During the same per iod , ava i lab le seat miles increased at an annual rate of 19.0 per cent i n i t i a l l y , and grew to a rate of 2 4.6 per cent per annum i n the f i r s t quarter of 19 69. Earnings peaked at $412 m i l l i o n i n 1967, then f e l l . Earnings 2 i n 1969 were $219 m i l l i o n . Figure 1 i l l u s t r a t e s how capacity grew faster than revenues. At the end of 1970, a i r l i n e costs were cl imbing annually at an estimated 8.6 per cent on average. About 8,0 00 ''"Major U.S . A i r l i n e s Economic Review and F i n a n c i a l Outlook 1969 - 1 9 73, A i r Transport Assoc ia t ion of America, June, 1969. 2 I b i d . "6 3 i t K f3 -vn-R 4 V s: c o Hi SI V V 4 employees were l a i d of f from scheduled U.S . a i r l i n e payro l l s i n 19 70 and there were 658 fewer f l i g h t s i n December 1970 than there were twelve months e a r l i e r . The A i r Transportat ion as soc ia t ion of America forecast $192 m i l l i o n loss for the 3 twelve major U.S . c a r r i e r s i n 1971. "In re t rospect , i t i s d i f f i c u l t to understand why the manufacturers bel ieved the a i r l i n e s could absorb hundreds of expensive new a i r c r a f t 4 wi th in a r e l a t i v e l y short p e r i o d . " How d id the 1970 losses come about? Hardship seems p a r t i c u l a r l y unnecessary i n an indus t ry . tha t has prospered only r ecent ly , and that has enjoyed continued growth. Relat ive to the economy as a whole, the growth p ic ture for a i r l i n e s appears good for an unl imited future. Did the 1970 a i r l i n e s i t u a t i o n have p a r a l l e l s i n railways or i n water transport? Evident ly i t d i d . In the 1800's r a i l r o a d expansion i n the United States was rapid and sometimes murderously competit ive. Government intervent ion was necessary i n the publ ic in te re s t because of "gouging" where r a i l roads held monopolies.^ In shipping world tonnage grew from 79 m i l l i o n i n 1939 to 147 m i l l i o n i n I960, 6 and i n the process, American shipping lo s t most of i t s dry. cargo 3 A v i a t i o n Week and Space Technology, V o l . 94, No. 2, 11 January 1971, p . 4Dan Gordtz, "The Withering A i r c r a f t Industry , " Fortune, V o l . LXXXII, No. 3, September 1970, p. 117. 5 A . S . Boyd, "Government's Role i n Transpor ta t ion , " Perspectives i n Transporta t ion , K.M. Ruppenthal, (ed. ) , Stanford, C a l i f o r n i a , Stanford Univer s i ty Graduate School of Business, 1963, pp. 44-54. t r a d e to f o r e i g n competitors w i t h lower c o s t s . Strong c o m p e t i t i o n . i n f a s t growing c a p i t a l i n t e n s i v e i n d u s t r i e s leads to some' m i s a l l o c a t i o n of r e s o u r c e s . The a i r l i n e s p r o v i d e an example of growth i n d u s t r y c o m p e t i t i o n s u b j e c t to government r e s t r i c t i o n s . Three main i n t e r e s t s are i n v o l v e d : the a i r l i n e s i n c o m p e t i t i o n w i t h one another, the government on b e h a l f of the p u b l i c served by a i r t r a n s -p o r t , and the f i n a n c i a l i n t e r e s t s s u p p o r t i n g development of the i n d u s t r y . The f i n a n c i a l i n t e r e s t s are probably the most n e u t r a l . I f t h e i r c o n d i t i o n s are met, they can g e n e r a l l y be counted upon to lend support. Banks look upon a i r l i n e s w i t h c o n s i d e r a b l y more k i n d l i n e s s f o r short-term borrowings. One reason i s t h a t many of the l a r g e r banks have s u b s t a n t i a l loans out t o the a i r f r a m e manufacturers, and the h e a l t h of the l a t t e r i s c l o s e l y dependent upon t h a t of t h e i r customers. 7 Government, p a r t i c u l a r l y i n the u n i t e d S t a t e s appears more a f r a i d of monopoly and excess p r o f i t s or bureaucracy ( i n p r i v a t e e n t e r p r i s e ) than i t i s a f r a i d of excess c o m p e t i t i o n and c o n t i n g e n t i n d u s t r i a l r e c e s s i o n s . A i r l i n e s , S.B. Turman, "The Challenge to the-American Merchant Marine," Challenge to T r a n s p o r t a t i o n , K.M. Ruppenthal, (ed.) S t a n f o r d C a l i f o r n i a , S t a n f o r d U n i v e r s i t y Graduate School of Business, 1961, pp. 161-169. Tom Alexander, "Is there A n y Way t o Run an A i r l i n e ? " Fortune, V o l . LXXXII, No. 3, September 1970, p. 211. r e a l i z i n g t h a t the market i s growing, are concerned w i t h t h e i r long-run share of the market, and are i n c l i n e d t o f i g h t a hard b a t t l e i n order t h a t they w i l l u l t i m a t e l y s u r v i v e . Whether the e x i s t i n g arrangement i s s a t i s f a c t o r y i s a q u e s t i o n t h a t i n v o l v e s tremendous study. No attempt w i l l be made t o answer t h i s q u e s t i o n here. F a c t o r s A f f e c t i n g Money Supply t o A i r l i n e s In the U n i t e d S t a t e s , f e d e r a l c o n t r o l s of a i r t r a n s -p o r t cover e n t r y , p r o f i t l e v e l , i s s u e to s e c u r i t i e s , r a t e s and f a r e s , f r e i g h t c l a s s i f i c a t i o n s , mergers, c o n t r o l s and d i r e c t o r a t e i n t e r l o c k s , s e r v i c e a u t h o r i z a t i o n and o b l i g a t i o n s , (use i t or l o s e . i t ) , s u b s i d i e s , equipment d e s i g n , safety,. g working ru las and other more t e c h n i c a l matters. An example of the C i v i l A e r o n a u t i c s Board's p e r v a s i v e c o n t r o l was order ER-586, t h a t c a l l e d f o r c o l l e c t i o n of t r a f f i c and c a p a c i t y data on a f l i g h t stage b a s i s and t r a n s m i t t a l on magnetic tape or punched cards f o r use by the Board. A i r p o r t expansion has been c o n s t r a i n e d by l i m i t e d and undefined sources of f i n a n c i n g , by r i s i n g land c o s t s and s o c i a l r e v u l s i o n f o r a i r p o r t s i n metro areas. Bureau-c r a c y , weak l o c a l governments and . l o c a l r e g i o n a l c o n f l i c t s , lobby groups versus the " g e n e r a l good" and i n e r t i a — a l l tended K.M. Ruppenthal, Issues i n T r a n s p o r t a t i o n Economics, Columbus, Ohio, C h a r l e s E. MerrilT~Books Inc., 1965, p. T~. to impede development. The new a i rpor t and Airway Develop-ment Act was expected to improve t h i s s i t u a t i o n i n the United States by spending $840 m i l l i o n on a i r p o r t improvements during 1971-1973. Forty f ive m i l l i o n d o l l a r s were s la ted 12 for the planning e f f o r t . Ownership of the a i r l i n e s was not p rec i s e ly known. Holders of 5 per cent or more stock i n major a i r l i n e s were l i s t e d , but holder were often owners' representat ives . Speculative swings i n a i r l i n e stocks i n the 1960's, contributed to the d i f f i c u l t y i n a t t r a c t i n g equity cap i t a l . 1 ' ' " On two po int s , any company must guard against f i n a n c i a l v u l n e r a b i l i t y . F i r s t l y , excess investments i n f ixed assets w i l l reduce current assets to the danger point—where i t i s d i f f i c u l t to meet current ob l i ga t ions . Secondly, the debt-to-equity r a t i o should not be allowed to grow beyond a safe l i m i t . Credi tors must be pa id , but propr ietors are e n t i t l e d only to p r o f i t s earned. In bad times, high debt c a p i t a l means v u l n e r a b i l i t y . L i q u i d i t y was not considered a near-term c r i s i s for U. S. a i r l i n e s i n 1970, but signs of p o t e n t i a l c a p i t a l problems were looming unless earnings were to improve. The long term a i r l i n e debt i n comparison with net worth grew 9 B.A. Schr iever , W.W. S e i f e r t , A i r Transportat ion  1975 and Beyond: A Systems Approach, Report of the Trans-por ta t ion Workshop, 1967, pp~. 337 , 355 . " ^ J . E . Skinner, " A i r p o r t Development Money i s Here , " A i r L i n e Management and Marketing, August 1970, p. 14. 1 "'"Airline Management and Marketing, June 1970 , p. 32. for U. S. a i r l i n e s over the 1960's, and prospects for improved 12 earnings i n 1971 were not encouraging. Investment Decisions Before f inancing an a i r l i n e se rv ice , or making f inan-c i a l contr ibut ion toward the improvement of ex i s t ing serv ices , there should be some assessment of expected market and expected costs . Marketing, i n response to management i n t u i t i o n or i n i t i a t i v e , locates and assesses the market s i z e . Cost estimates often come from experience. A i r l i n e accounts would be studied i f the project were to increase or improve an e x i s t i n g se rv ice . I f the service were to be s tarted from nothing, check- l i s t s of costs could be obtained from some . , . . 1 3 reference on a i r l i n e management. To te s t the projected cost estimate, comparison can be made with a i r l i n e cost models. A paper by Eads, Nerlove 14 and Raduchel, demonstrates the extensive analys i s necessary for a genera l i za t ion of a i r l i n e costs . A de sc r ip t ion of the model formulation i s too long for presentat ion here. An ana ly t i c model i s developed i n d e t a i l for l o c a l service a i r l i n e s , g iv ing equations for : fue l cost s , short-run 12 A. A l t s c h u l , " L i q u i d i t y , " A i r l i n e Management and  Marketing, October 1970, p. 37. 13 W.S. Barry, A i r l i n e Management, Geo. A l l e n and Unwin, London, 19 65, ppT 2~0"3, 204. 14 G. Eads, M. Nerlove, and W.. Raduchel, "A Long Run Cost Function for the Loca l Service A i r l i n e Industry: An Experiment i n Non-lenear Es t imat ion , " The Review of Economics and S t a t i s t i c s , V o l . L I , No. 3, August 1969, pp. 258-270. variable costs, a l l other long-run costs, long-run t o t a l costs and a production function. Cost analyses such as the study by Eads,.Nerlove and Raduchel demonstrate the gulf between the analytic and the p r a c t i c a l approach. While t h i s study was not tremendously d i f f i c u l t from a mathematical standpoint, i t nevertheless exceeds the grasp of many operating managers whose a b i l i t i e s grew from long experience i n the industry, and who generally might not have the time to acquire in-depth f a m i l i a r i t y with sophisticated mathematical models. I f therefore, the model output were at variance with the judgement of experience, i t becomes the analysts' task to reconcile the difference and to ensure that appropriate corrections are pointed out to the model builders or to the p r a c t i c a l managers as required. F l e e t P l a n n i n g 3 from the a i r l i n e point of view begins with a choice of a i r c r a f t a vailable. New a i r c r a f t types r e s u l t from a i r l i n e needs as seen by a i r c r a f t manufacturers. This i s a c i r c l e of i n t e r a c t i n g industry needs. The manufacturers are concerned with needs of the a i r l i n e industry as a whole, but each a i r l i n e i s faced with making decisions based on the needs of i t s own market and the l i m i t a t i o n s of i t s own f i n a n c i a l resources. Figure 2 i s a very schematic i l l u s t r a t i o n of the 15 Lockheed A i r l i n e System Simulator. The simulator " f l i e s " 15 Lockheed A i r l i n e System Simulation, Burbank, Lock-heed publication CTR 2007, 1970. each a i r c r a f t w i t h i n a gi v e n a i r l i n e f l e e t over each route a v a i l a b l e to the a i r l i n e , a s s i g n i n g the most p r o f i t a b l e a i r c r a f t / r o u t e combinations. New f l i g h t s are assign e d u n t i l s p e c i f i e d l e v e l s of o p e r a t i o n s are reached. The process normally continues beyond the p o i n t of maximum system e a r n i n g s , because s p e c i f i e d l e v e l s of o p e r a t i o n s are u s u a l l y f o r c e d by r e g u l a t i o n and by co m p e t i t i o n t o y i e l d no more than about a ten per cent r a t e of r e t u r n . Input data are as important as the model i t s e l f . These data i n c l u d e a i r c r a f t o p e r a t i n g c h a r a c t e r i s t i c s , maintenance c o s t s , c a p i t a l c o s t s , a i r l i n e ground r u l e s f o r maintenance, i n d i r e c t c o s t s such as l a n d i n g f e e s , meals and h a n d l i n g c o s t s , estimated wind c o n d i t i o n s , a l l f l y i n g c o s t s , t a x i times, revenues, t r a f f i c f o r e c a s t s , a l l o w a b l e l o a d f a c t o r s , and com p e t i t i o n f a c t o r s from other a i r l i n e s , automobiles, e t c . The a d d i t i o n or removal of routes must be co n s i d e r e d i n terms of rou t e i n t e r a c t i o n . A d d i t i o n a l r o utes p r o v i d e a d d i t i o n a l paths between o r i g i n s and d e s t i n a t i o n s . P r o f i t -a b i l i t y on a proposed new rou t e may r e s u l t i n p r o f i t l o s s e s elsewhere i n the system. On the other hand, the a d d i t i o n of u n p r o f i t a b l e segments may augment p r o f i t s on other segments, and e v a l u a t i o n should be made f o r the whole system r a t h e r than f o r i t s i n d i v i d u a l p a r t s . Competitive f a c t o r s w i l l a f f e c t market share and thr e e approaches t o market share a n a l y s i s are as f o l l o w s : 2. m a r k e t s h a r e f a c t o r s a r e v a r i a b l e f o r t h e a i r l i n e u n d e r s t u d y . 3. m a r k e t s h a r e f a c t o r s a r e v a r i a b l e f o r t h e a i r l i n e and f o r i t s c o m p e t i t o r s . The L o c k h e e d s i m u l a t i o n u s e s a s s u m p t i o n 2 and r e j e c t s 3 on t h e g r o u n d s t h a t 3 w o u l d r e s u l t i n h i g h e r a v e r a g e l o a d f a c t o r s and more u n s e r v e d demand i n peak p e r i o d s t h a n w o u l d be t h e c a s e u s i n g a s s u m p t i o n 2. T h i s i s p r o b a b l y c o r r e c t , b u t f r o m t h e p o i n t o f v i e w o f t h e a i r l i n e i n d u s t r y as a w h o l e , i t . c o u l d l e a d t o o v e r c a p a c i t y due t o assumed b e n e f i t s o f e x p a n s i o n by t h e i n d i v i d u a l a i r l i n e s . A l l c o m p e t i n g a i r l i n e s may t r y t o enhance t h e i r own m a r k e t s h a r e s by i m p r o v i n g f a c i l i t i e s and s e r v i c e . I f c o m p e t i t o r s ' a c t i o n s a r e i g n o r e d , t h e a i r l i n e u n d e r s t u d y may g e t an o v e r o p t i m i s t i c v i e w o f b e n e f i t s f r o m e x p a n s i o n . M o d e l o u t p u t s a r e shown i n F i g u r e 3. P u r c h a s e o f new a i r c r a f t t y p i c a l l y p r e c e d e s d e l i v e r y by two y e a r s . I f an a i r l i n e buys one l a r g e j e t t o o many, c a s h f l o w and,: o t h e r i n v e s t m e n t a c t i v i t i e s a r e i m p a i r e d . D o u g l a s A i r c r a f t Company s e l l s a i r c r a f t w i t h t h e h e l p o f an o p e r a t i o n s and p l a n n i n g m o d e l c o m p r i s i n g o f a number o f sub-m o d e l s d e a l i n g w i t h a i r c r a f t p e r f o r m a n c e , r o u t e p e r f o r m a n c e , a i r p o r t t a k e - o f f a n a l y s i s , s c h e d u l e p l a n n i n g and e v a l u a t i o n , a i r l i n e o p e r a t i n g c a s h f l o w , e c o n o m e t r i c f o r e c a s t i n g , e c o n o m i c s , V (V is < \- -c--uj-~C" Q) C Z d. • w c r _c_ 0» in d 0 V -e -»-> C 0 l -< J -n 0 ~tr o 4-* C CO u y V E Hi h V • —* V» O - 0 -o _1 (x-1J c > o o Q* CO u l l c-1 r u - - M - 0) * w p t ; < CO s \. <u 1 c OL \ > -• 0 d 0 r O tt. (x u i -4-•z. < V-- ( V 0 • c * e s_ l M i f 0 _<ac \. - d 0 tfl - ? * ^ - J > O r C </» O 0 - c r 6 i l LS. u E 0) -o-cr it O 0 _£> ^, < / <•+• (A > rf\ / O-d V u J • ^ < —v-j-y - j -< 2-< c E cr 0 C 1^ O 0 < f o C <u -E-0-CO 4-_E j Id 0 E . O V a- O 0. > l £ -4^ C E ct </) cn - -h in — i . ->#_^  V >-- < -_U-u < fl y < I •» CT » v. -0)-0-_c. .d 4-» C" - V -> 0 4-u Pv Ul •> c 1 "Z U) VA < l l c > > Ut X c 0 1 \ \n 3 VI -v - -< f *w In >_</»-0 CO CJ 4-r o \ • —> i . 0 <4-0 0 0 — d V. <U <3" u _2> _ a d d 0 4> —O-(L _ f l r? i / - \ 0 — c 0> —tfv-v> o • < O 6 0 0 PQ E " O '5 > < b 0- * »0 % (L <U Z. Hi CO —r^.f J — • — — — u 0 •0 t/C (ft _C -V ' Si. \l c CO > J — < < L 0 r 7°~ d M c • 0 — « c 0 i . o « J O" a) • * d 4* <-*-T - < -_ d •3: - $ C" a O 1 d • v u u f & tL *-4- -s-— o cr < X. <C 0 : and r e t u r n on investment."*"^ F l e e t p l a n n i n g i n v o l v e s a g r e a t d e a l more t h a n s e l e c t -i n g t y p e s and numbers o f a i r c r a f t t o s a t i s f y demand e c o n o m i c -a l l y . A i r l i n e s must g u a r d a g a i n s t b u y i n g what i s known as a " t r a n s i t i o n " a i r c r a f t t h a t has a t e m p o r a r y a d v a n t a g e when i n t r o d u c e d i n t o s e r v i c e . When more e f f i c i e n t a i r c r a f t a r e d e v e l o p e d , t h e t r a n s i t i o n a i r c r a f t i s n o t s u i t a b l e f o r down-g r a d i n g . I t s h o u l d be r e a l i z e d t h a t a i r c r a f t m a n u f a c t u r e r s ' s t r a t e g i e s a r e t o d e v e l o p d e s i g n s t h a t c a p t u r e a l a r g e p o r t i o n o f t h e m a r k e t , t r a p p i n g c o m p e t i t i v e a i r c r a f t i n t o t r a n s i t i o n c a t e g o r i e s . An a i r l i n e t h a t has p u r c h a s e d t r a n s -i t i o n a i r c r a f t i s g o i n g t o be f a c e d w i t h t h e n e e d t o r e p l a c e t h e ' t r a n s i t i o n f l e e t a t some p o i n t i n t h e r e l a t i v e l y n e a r f u t u r e , when t h e m a r k e t v a l u e o f t r a n s i t i o n a i r c r a f t i s low. An example o f t h i s was t h e DC-7. DC-7's were p h a s e d o u t w h i l e DC-6's ( t h a t had been r e p l a c e d by D C - 7 ' s ) , were down-17 g r a d e d and c o n t i n u e d i n s e r v i c e . A i r c r a f t p r o d u c t i v i t y c an sometimes be e n h a n c e d by m i x i n g a i r c r a f t t y p e s . T h i s i s p a r t i c u l a r l y e v i d e n t i n c a r g o o p e r a t i o n s o f a m i l i t a r y n a t u r e . I n an example g i v e n f o r a s t r a t e g i c f l e e t o f t r a n s p o r t a i r c r a f t c o n s i s t i n g o f v a r i o u s 16 J.D. K i n g s l e y , " A i r l i n e O p e r a t i o n s and P l a n n i n g M o d e l , " L o n g B e a c h , D o u g l a s A i r c r a f t Company p a p e r 5058, 1968. 17 M. G u r e l , and L.A. V a r g h a , " A i r l i n e F l e e t P l a n n i n g R e s t r i c t e d M o d e l s , " B o e i n g Company P a p e r , C o m m e r c i a l A i r p l a n e D i v i s i o n , 1968. proportions of C141 and C5A machines, p roduc t iv i ty of both types was improved when they were used together as a mixed 18 f l e e t . The optimum r a t i o or mix was dependent upon the type of cargo as wel l as upon the amount of cargo. As the p roduc t iv i ty was a function of mix, ordinary LP methods were ruled out. Piecewise l i n e a r approximations r e l a t i n g p roduc t iv i ty to a i r c r a f t mix led to ser ies of LP problems. Branch and bound methods were used to reduce the amount of 19 c a l c u l a t i o n for an optimal s o l u t i o n . The method appears to be unwieldy for an a i r l i n e s i t u a t i o n , t y p i c a l l y more complex than s t ra teg ic problems. The savings inherent i n the use of opt imal ly designed a i r c r a f t must be weighed against the investment i n mixed f l e e t s . Expensive l o g i s t i c s backups, ground equipment and 20 spares should be included i n the c a l c u l a t i o n . C a p a c i t y E x p a n s i o n . Several models of optimal capacity expansion have been developed. In the expansion problem the object ive i s to cont ro l the l e v e l of p r o d u c t i o n c a p a c i t y through a ser ies of time per iods , minimizing the 18 D. Gross , .and R.M. Soland, "A Branch and Bound Algorithm for A l l o c a t i o n Problems i n which constra int coeff ic-ients depend on Decis ion V a r i a b l e s . " Research Analys i s  Corportaion paper RAC-TP-327, 1968. 19 I b i d . , p. 10. 2 0 J . G . Abert , M. Kamrass, J . A . Navarro , "Evaluat ing A i r c r a f t Requirements i n the L ight of Varying or Uncertain Miss ion Mixes, Operations Research, V o l . 15, No. 4, 1967, p. 738. composite c o s t of investment and c a p a c i t y shortage. Owing to the complex manner i n which e x t r a c a p a c i t y a f f e c t s a i r l i n e p r o d u c t i v i t y , expansion of c a p a c i t y f o r a i r l i n e s i s not capable of simple f o r m u l a t i o n . The most p r a c t i c a l models f o r a i r l i n e expansion are probably those of the a i r c r a f t manufact-21 u r e r s . C a s h F l o w M o d e l s G i v e n a p r o p o s e d a d d i t i o n t o t h e f l e e t , r e t u r n on i n v e s t m e n t c a l c u l a t i o n s a r e o b t a i n a b l e f r o m t h e D o u g l a s m o d e l . I n p u t i n c l u d e s assumed o p e r a t i n g c o n d i t i o n s and c o s t s , s t a r t u p c o s t s , t a x c o n s i d e r a t i o n s , and p a r t i c u l a r s o f t h e f i n a n c i n g a g r e e m e n t . O u t p u t i t e m i z e s c u m u l a t i v e c a s h f l o w and p r o f i t s f o r e a c h y e a r o v e r t h e l i f e o f t h e i n v e s t m e n t , and r e t u r n on a v e r a g e i n v e s t m e n t o v e r t h e same p e r i o d . T h e r e i s n o t h i n g v e r y n o v e l i n t h i s m o d e l . I t u s e s s t a n d a r d p r e s e n t v a l u e c o n c e p t s . I n t h i s c a s e t h e r e l a t i o n s h i p o f t h e o u t p u t t o t h e i n p u t a s s u m p t i o n s i s t h e main p o i n t o f i n t e r e s t . B e c a u s e D o u g l a s s e t up t h e p r o g r a m w i t h c a t h o d e r a y t u b e d i s p l a y f a c i l i t i e s , i t was an e a s y m a t t e r t o p l u g i n r a n g e s o f a s s u m p t i o n s t o o b s e r v e t h e e f f e c t s on o u t p u t . M o d e l s 21 G.T. Howard, and G.L. Nemhauser, "Optimal C a p a c i t y Expansion," Naval Research L o g i s t i c s Q u a r t e r l y , V o l . 15, No. 4, December 1968^ p. 535. 22 B.J. Heap, "Return on Investment.Program," Long Beach, Douglas Paper, No. Cl-806-1316, 1968. o f t h i s t y p e a r e p a r t i c u l a r l y c o n v e n i e n t f o r a n s w e r i n g q u e s t i o n s o f t h e t y p e , "What i f . . . .?" T h i s m o d e l was e a s i l y s e t up on t h e u s e r s p r e m i s e s and d i d n o t r e q u i r e a l a r g e computer i n s t a l l a t i o n . C a s h f l o w i s s u b j e c t t o a number o f i n p u t p r o b a b i l i t y d i s t r i b u t i o n s . R e t u r n on i n v e s t m e n t models w i l l c a l c u l a t e c a s h f l o w s f o r s p e c i f i c i n p u t a s s u m p t i o n s , b u t t o know t h e d i s t r i b u t i o n o f c a s h f l o w p o s s i b i l i t i e s , a more g e n e r a l model 23 i s r e q u i r e d . The p r o j e c t e d c a s h f l o w model g e n e r a t e s o u t p u t p r o b a b i l i t y d i s t r i b u t i o n s r e s u l t i n g f r o m t h e i n p u t d i s t r i b u -t i o n s . I n p u t p r o b a b i l i t y d i s t r i b u t i o n s , u n f o r t u n a t e l y , must be o b t a i n e d f r o m a b a r r a g e o f q u e s t i o n s o f t h e t y p e shown b e l o w : Which do y o u p r e f e r ? 1. Win t h e 50/50 c h a n c e o f $100 on t h e t o s s o f a c o i n . 2. R e c e i v e $10 0 i f RPM g r o w t h e x c e e d s x p e r c e n t . When p r o b a b i l i t y d i s t r i b u t i o n s f o r a l l t h e i m p o r t a n t i n p u t p a r a m e t e r s a r e g e n e r a t e d i n t h i s f a s h i o n , random s e l e c t i o n s o f i n p u t s a r e made and s u b s t i t u t e d i n t h e c a s h , f l o w f o r m u l a e . The o u t p u t s a r e d i s t r i b u t e d i n some manner c h a r a c t e r i s t i c o f t h e i n p u t . P.T. G l a s c a l l , " P r o b a b i l i t y - An A p p l i c a t i o n t o P r o j e c t e d A i r l i n e C a s h F l o w , " D o u g l a s P a p e r 5052, 1968. The A i r l i n e O p e r a ting Cash Flow Model i s intended to p r o v i d e more accurate f i n a n c i a l and o p e r a t i n g data i n l e s s time than say, repeated use of the ROI model. I t enables managers t o c o n s i d e r only s p e c i f i c , i n p u t s t o the cash flow problem r a t h e r than the imponderable problem as a whole, and i t produces a statement of cash flow i n the form of a p r o b a b i l i t y d i s t r i b u t i o n c o v e r i n g the e n t i r e range of l i k e l y outcomes. I f r e t h i n k i n g leads to a change i n a s u b j e c t i v e i n p u t d i s t r i b u t i o n , i t i s p o s s i b l e t o weigh the e f f e c t s i n the r e v i s e d output d i s t r i b u t i o n . In 1967 the manufacturers' f l e e t p l a n n i n g models were c r i t i c i z e d f o r not i n c l u d i n g time of day e f f e c t s and not 25 r e f l e c t i n g market share as a f u n c t i o n of frequency. However, system s i m u l a t i o n s f o r many years to come w i l l operate on judgemental i n t e r p r e t a t i o n . F i n a n c i n g A l t e r n a t i v e s . . . should be c o n s i d e r e d b e f o r e an investment d e c i s i o n i s .taken. In p a r t i c u l a r , the l e a s e or l e a s e purchase arrangements may prove a t t r a c t i v e when tax c o n s i d e r a t i o n s are i n c l u d e d . T h i s d e c i s i o n i n v o l v e s no more than normal e v a l u a t i o n by d i s c o u n t e d cash flow methods. I f f o r e c a s t s of income and a c q u i s i t i o n s were c e r t a i n , 2 6 o p t i m a l f i n a n c i n g becomes an LP problem: 24 I b i d . , p. 1. 25 W.G. Williamson,."Computer Programs f o r F l e e t and Schedule P l a n n i n g , AGIFORS Proceedings, 1967, pp. 11-22. Present value 1 Min aft e r tax cos of purchases. Present value afte r tax cost of leases. r Investment tax credits, subject to V«T x m c . ( i B T . , P 1 / 8 , P 1 / 9 2,8 07 j + 3 E Y=j"7 3Y + z=8-j E z=l U where V = proportion of gross taxes eliminatable by tax credits T corporate tax rate INC. income as a function of IBT. and purchases 3 3 IBT.. income before i n t e r e s t , rent and depre-c i a t i o n of acquisitions i n the period covered by the analysis Pj^. purchases i n year j with depreciable l i f e of k years Tj purchases i n year j , tax cr e d i t s for which apply i n year y. (y= j-3 -> j+7) U. unused tax credits earned z years before jz the period of analysis, used i n year j . 26 J. Slade, " E f f i c i e n t Financing of Equipment Acquisi-tions," AGIFORS Proceedings, 1969. T h i s model as i t stands i s of l i t t l e g e n e r a l use, f i r s t l y because earnings and a c q u i s i t i o n s are n o t c e r t a i n , and secondly because the tax p i c t u r e depends upon l o c a t i o n of the f i r m . J u s t as a d e t e r m i n i s t i c p r e d i c t i o n of r e t u r n on investment or cash flow r e p r e s e n t s only o n e p o i n t i n the d i s t r i b u t i o n of p o s s i b l e outcomes, t h i s LP r e p r e s e n t s one p o i n t on the d i s t r i b u t i o n of optimal f i n a n c i a l s t r a t e g i e s . By t a k i n g the d i s t r i b u t i o n of p o s s i b l e p r o f i t s , t h i s LP c o u l d be run f o r v a r i o u s outcomes a s i f the outcome were c e r t a i n . P o i n t s t o watch are sudden or l a r g e changes i n f i n a n c i n g s t r a t e g y caused by v a r i a t i o n s i n c o r p o r a t e income. I f income v a r i a t i o n s are p r e s e n t , f i n a n c i a l d e c i s i o n s should be kept open f o r o p t i o n a l f l e x i b i l i t y u n t i l the f u t u r e becomes more c e r t a i n . Mathematical programming can be a p p l i e d to the problem of s e l e c t i n g an o p t i m a l combination of investments where the budgets are l i m i t e d i n a s e r i e s of time p e r i o d s . The L o r i e -Savage model f o r two p e r i o d s has been e l a b o r a t e d by Weingartner. The d u a l v a r i a b l e s i n t h i s f o r m u l a t i o n are "shadow p r i c e s , " t h a t i n d i c a t e the marginal r a t e of r e t u r n on each of the c o n s t r a i n t s of the p r i m a l problem. For example, a budget c o n s t r a i n t t h a t l i m i t s investment, might be i n c r e a s e d . The b e n e f i t of a u n i t i n c r e a s e i n the con-s t r a i n t i s g i v e n by the value of the corresponding d u a l v a r i a b l e . F o r a w a r e h o u s i n g o p e r a t i o n , t h e i n v e s t m e n t s may be d i v i s i b l e f r o m an a l l o c a t i o n p o i n t o f v i e w . I n t h e c a s e o f m a j o r c a p i t a l i n v e s t m e n t , t h e d e c i s i o n i s a l l - o r - n o t h i n g . W e i n g a r t n e r d e v e l o p e d . a n i n t e g e r p r o g r a m t o make t h e " e i t h e r -o r " d e c i s i o n s and t o t a k e a c c o u n t o f m u t u a l l y e x c l u s i v e p r o j e c t s . W e i n g a r t n e r 1 s m o d els have been e x t e n d e d by Q u i r i n t o h a n d l e o t h e r c o n s t r a i n t s s u c h as l a b o u r . The d i f f i c u l t y w i t h m a t h e m a t i c a l programming a p p r o a c h e s t o c a p i t a l b u d g e t i n g i s t h e a s s u m p t i o n t h a t f u t u r e i n v e s t m e n t o p p o r t u n i t i e s a r e known. Programming models a r e b a s e d on e x p e c t e d v a l u e s t h a t a r e t r e a t e d as c e r t a i n t i e s . R i s k may be programmed i n t o t h e model by means o f c h a n c e c o n s t r a i n t s 27 and q u a d r a t i c programming. M a t h e m a t i c a l programming h a s b e e n a p p l i e d t o t h e r a i s i n g o f e x t e r n a l c a p i t a l b u t t h e m o d els were c r u d e and 2 8 u n r e a l i s t i c . The methods a r e s y s t e m a t i c and c o m p r e h e n s i v e , and w i t h f u r t h e r s o p h i s t i c a t i o n may become more a p p l i c a b l e t o r e a l s i t u a t i o n s . 27 J . Van Ho.rne, F i n a n c i a l Management and P o l i c y , E n g l e w o o d C l i f f s , P r e n t i c e H a l l , 1968, p . BIT. F i n a n c i a l Contro l Accounting ra t io s are used conventional ly to i n d i -cate l i q u i d i t y or solvency, earning power and the operating condit ion of business i n general . Apart from conventional r a t io s used by accountants around the world, there are s p e c i f i c ra t io s that are pecu l i a r to spec i a l i zed needs of i n d i v i d u a l f i rms. Operations research i n finance could s t a r t with Tucker 's approach i n the search for r a t io s that do more 29 than ind ica te f i n a n c i a l s tatus . For day by day cont ro l of factors a f fec t ing f inance, r a t io s should be constructed as to suggest s p e c i f i c remedial actions that benef i t the f i rm. Aer Lingus proposed a f i n a n c i a l plan i n 196 8 to 3 a l loca te annual a i r c r a f t dependent costs and overhead costs . Figures of merit were devised to compare route p r o f i t a b i l -i t i e s , gross p r o f i t s and p r o f i t s of marginal s e rv ice . A i r -cra f t dependent costs are a l loca ted on the basis of a i r c r a f t block hours. Overhead costs are a l loca ted by judgemental weighting of t r a f f i c volume, revenue, e tc . P r o f i t a b i l i t y indices are functions of load factors on the various routes . As indicated by the Lockheed A i r l i n e System Simulat ion, p r o f i t a b i l i t y on a given route does not t e l l the whole story i f there i s route i n t e r a c t i o n . An "unprof i t -29 S. Tucker, Successful Managerial Contro l by Ratio  A n a l y s i s , New York, McGraw H i l l " 1961. 3 0 R . H . W . Johnston, "A Computerized Capacity Plan and Budget System," AGIFORS Proceedings, 1968, p. 77. a b l e " r o u t e may enhance p r o f i t s on o t h e r r o u t e s . A l l o c a t i o n o f o v e r h e a d s a p p e a r s t o o f f e r no c o n t r i b u t i o n t o t h e improvement o f o v e r h e a d management, and t h e same c a n be s a i d f o r a l l o c a t i o n o f a i r c r a f t d e p e n d e n t c o s t s . I t has become t r a d i t i o n a l t o " a b s o r b " c o s t s on a b a s i s o f h o u r s worked and t h e n t o compare " b u d g e t " v e r s u s " a c t u a l " c o s t s t o make y e a r - e n d c o r r e c t i o n s and l i s t s o f v a r i a n c e s f o r management r e v i e w . P e r h a p s a more f r u i t f u l a p p r o a c h w o u l d be t o r e v i e w t h e c o s t s t h e m s e l v e s i n t h e hope o f m a k i n g i m p r o v e m e n t s . E l i m i n a t i o n o f a l l o c a t i o n e f f o r t w o u l d r e p r e s e n t i n i t i a l s a v i n g s . A e r L i n g u s b e n e f i t s f r o m t h e s p e e d o f i t s c o m p u t e r i z e d f i n a n c i a l p l a n . U n t i l 1 9 6 8 t h e p r o c e d u r e had b e e n t o d e v e l o p a s c h e d u l e p l a n as t h e f i r s t s t e p i n e l a b o r a t i n g t h e f i n a n c i a l p r e d i c t i o n s . The f i n a n c i a l p l a n e v o l v e d by D r . J o h n s t o n was an i t e r a t i v e p r o c e d u r e t h a t s t a r t e d w i t h an o r i g i n a l s c h e d u l e p l a n and i n d i c a t e d a c t i o n s t h a t w o u l d l e a d t o im-p r o v e d p r o f i t a b i l i t y . U s i n g t h e f o r m e r manual p r o c e d u r e , t h e r e was n o t t i m e t o change t h e s c h e d u l e p l a n i n r e s p o n s e t o f i n a n c i a l a n a l y s i s . The A e r L i n g u s p l a n m i g h t p r o v e u n w i e l d y i n a l a r g e a i r l i n e s y s t e m where many i t e r a t i o n s w o u l d be r e q u i r e d . I t d i d n o t i n c l u d e a l l o w a n c e s f o r c o m p e t i t o r s 1 a c t i o n s t h a t w o u l d a f f e c t t o t a l s e r v i c e , and i t lumped t o g e t h e r f r e q u e n c y and a i r c r a f t c a p a c i t y i n an o v e r a l l measure o f c a p a c i t y . I n t h e l o n g r u n t h i s m i g h t l e a d t h e a i r l i n e t o w a r d l a r g e r a i r c r a f t and r e d u c e d f r e q u e n c y whereas f r e q u e n c y may be t h e m a i n d e t e r m i n a n t o f m a r k e t s h a r e . I n 1 9 6 8 , A i r F r a n c e was d e v e l o p i n g i t s TARAGE p l a n t h a t b r i n g s t o g e t h e r v a r i o u s O/R s t u d i e s . " T h e r e i s a b s o l u t e l y no q u e s t i o n o f f i n d i n g o p t i m a l s c h e d u l e s , t h e meaning o f 3 1 o p t i m a l i t y b e i n g d i f f i c u l t t o s p e c i f y . " B u t g i v e n a s c h e d u l e i t s h o u l d be p o s s i b l e t o c a l c u l a t e e x p e n d i t u r e a u t o m a t i c a l l y . Revenues a r e more d i f f i c u l t . . . s t i l l i n t h e f u t u r e . A i r F r a n c e ' s E c o n o m i c M o d e l was u s e d t o e v a l u a t e c o m b i n a t i o n s o f b o r r o w i n g , a m o r t i z a t i o n , f i n a n c i n g and c a p i t a l 32 i n v e s t m e n t s . I n p u t s were: i n i t i a l s t a t e o f f l e e t s , b a l a n c e s h e e t , e x p e n d i t u r e and c a s h f l o w and r a t i o s f r o m w h i c h simu-" l a t e d p o l i c y w o u l d be j u d g e d . The s i m u l a t i o n s u f f e r e d f r o m d i f f i c u l t i e s i n f i n d i n g laws o b e y e d by r e v e n u e and e x p e n d i t u r e o nce a p r o d u c t i o n s c h e d u l e was g i v e n . A c c u r a t e measurement o f p o l i c y i m p a c t i s l i m i t e d by t h e n e c e s s i t y f o r a g g r e g a t i o n and by a s s u m p t i o n s o f l i n e a r i t y i n r e v e n u e and e x p e n s e . Any m o d e l , manual o r c o m p u t e r , i s s u b j e c t t o e r r o r — b u t what a c c u r a c y i s r e q u i r e d ? A m e r i c a n A i r l i n e s and M c D o n n e l l D o u g l a s worked t o d e v e l o p a more J . A g a r d , "The A i r F r a n c e TARAGE P l a n , " AGIFORS P r o c e e d i n g s , 1 9 6 8 , p. 2 2 3 . 3 2 J . A g a r d , " A i r F r a n c e E c o n o m i c M o d e l , " AGIFORS P r o c e e d i n g s , 1 9 6 9 . comprehensive f i n a n c i a l model, but much w i l l be learned before human experience, judgement and i n t u i t i o n can be re-33 placed by dec i s ion rules and equations. I n t e r l i n e Samp l i n g schemes were introduced by European a i r l i n e s i n the. f i f t i e s to r e l i e v e the tremendous c l e r i c a l task of keeping track of i n t e r l i n e accounts. Each a i r l i n e s e l l s and receives payment for coupons that may be honoured by other a i r l i n e s . (Certain legs of the route are flown by two or more a i r l i n e s and the passenger t rave l s part of h i s journey on a i r l i n e s other than the one from which the t i c k e t was purchased). Complicating t h i s , the l o c a l fares i n most cases add up to more than the t o t a l fare from o r i g i n to de s t ina t ion , so a prorat ing system must be used to c a l c u l -34 ate amounts owing. F. Van Dam i l l u s t r a t e s how the estim-ators i n the o r i g i n a l fare sampling scheme were biased, and describes the development of unbiassed estimators. Swissair i n the la te 1960's received up to 13,000 b i l l i n g s per month per a i r l i n e , and even the 10% sampling 35 precedure was becoming a large c l e r i c a l problem. The J . E . Wells Jr.,"Comments on J . Agard's paper'; AGIFORS  Proceedings, 19 69. 3 4 F. Van Dam, " A p p l i c a t i o n of the Unbiassed.Ratio Estimator to the I n t e r l i n e Sampling Scheme," AGIFORS  Proceedings, 1969, 35 M.L . Siegwart, "Simulat ion to Evaluate Sampling Methods i n I n t e r l i n e Account ing , " AGIFORS Proceedings , : 1969. q u e s t i o n t h e r e f o r e , was, "Can the sample s i z e be reduced?" A c t u a l (used) punched cards, a l r e a d y prepared f o r p r o r a t e d coupons were c o l l e c t e d . Thus an exact d i s t r i b u t i o n was o b t a i n e d . The punched cards were s u p p l i e d by some of the p a r t i c i p a t i n g a i r l i n e s over a p e r i o d of s e v e r a l months. The s i m u l a t i o n v e r i f i e d t h a t the unbiassed e s t i m a t o r would r e s u l t i n more p r e c i s e a l l o c a t i o n s . For a g i v e n accuracy, the sample c o u l d be reduced, but the unbiassed e s t i m a t o r was not confirmed as a c o s t r e d u c t i o n because of i t s added c o m p l i c a t i o n . Assuming t h a t computer f a c i l i t i e s were a v a i l a b l e f o r accounting purposes, t h i s o b j e c t i o n appears r e l a t i v e l y t r i v i a l . F uture F i n a n c i n g Commercial a v i a t i o n i s only one mode of t r a n s p o r t . Other main a l t e r n a t i v e s are: highway, r a i l , barge and p i p e -l i n e t r a n s p o r t . Past developments has been piecemeal i n a i r t r a n s p o r t , w i t h many problems on the ground. The Trans-p o r t a t i o n Research Foundation ..proposed t h a t a study (to c o s t $900,000) be launched to determine f u t u r e trends i n r e q u i r e -3 6 ments and sources of funds up t o the year 1990. Such a study would attempt to e v a l u a t e f u t u r e develop-ments i n a l l areas of t r a n s p o r t , a d i f f i c u l t t ask even f o r 3 6 E.G. Plowman, " F e a s i b i l i t y Report of the Transpor-t a t i o n Research Foundation on the Proposed Study to E v a l u a t e T r a n s p o r t a t i o n C a p i t a l Requirements and Investment Sources," Washington, 196 8. a s t a t i c technology. Modal.development c o s t s and intermodal dependencies would have t o be estimated. Rates o f r e t u r n would a f f e c t the sources of funds, and perhaps non-government sources would prove inadequate. Where f a c i l i t i e s are used by many, f o r example net-works of p u b l i c roads or telephone c e n t r a l o f f i c e equipment, a " f a i r " system of charges i s i m p r a c t i c a l or i m p o s s i b l e . On l a r g e i n d i v i d u a l p r o j e c t s such as t u n n e l s , t u r n p i k e s , o r b r i d g e s , t o l l s may be charged, but the c o s t of t o l l c o l l e c t i o n and the minor d e l a y i n v o l v e d i n paying t o l l s — t e n d t o reduce the s o c i a l b e n e f i t s of the p r o j e c t s . On the other hand, some routes are so crowded t h a t those who are i n a.hurry are q u i t e prepared to pay f o r the e x c l u s i o n of those who are not i n a hur r y . Whether long-range n a t i o n wide s t u d i e s can be e f f e c -t i v e i s a moot.point. Studi e s can be made of i n d i v i d u a l developments, p o r t s or urban road systems e t c e t e r a , but whether or not funds are government s u p p l i e d , r i g h t of way o f t e n r e q u i r e s e x p r o p r i a t i o n , and t h i s w i l l remain a govern-ment p r e r o g a t i v e . E v a l u a t i o n of i n d i v i d u a l developments i n terms of c o s t b e n e f i t w i l l use the t o o l s of op e r a t i o n s r e s e a r c h . Government sources and a p p l i c a t i o n s o f funds however, f a l l more i n t o the f i e l d of economics. CHAPTER VI CONCLUSION By 1971 e x t e n s i v e a p p l i c a t i o n s of Operations Research had been made i n a i r l i n e management and o p e r a t i o n . In a d d i t i o n , f l e e t s i m u l a t i o n and p l a n n i n g models were developed by a i r f r a m e manufacturers. A i r l i n e s and a i r p o r t a u t h o r i t i e s have used O/R models to study a i r p o r t o p e r a t i n g c h a r a c t e r -i s t i c s under v a r i o u s c o n d i t i o n s of t r a f f i c . The l i t e r a t u r e a s s o c i a t e d w i t h these a p p l i c a t i o n s has grown tremendously s i n c e the e a r l y 19 50's. The chapters above r e f e r t o a fragment of the l i t e r a t u r e p u b l i s h e d p r i o r to 1971, and-g i v e only a g e n e r a l impression of problems and s o l u t i o n approaches developed to date. Any of the chapters on Marketing, P r o d u c t i o n , A i r p o r t s , or A i r l i n e Finance c o u l d be developed i n t o broad t h e s i s t o p i c s . S cheduling i t s e l f p r o v i d e s a wide range of problem s i t u a t i o n s and a c o n s i d e r a b l e v a r i e t y of models and s o l u t i o n methods. In r e s e a r c h i n g O/R a p p l i c a t i o n s i n any of these areas, e x c e l l e n t b i b l i o g r a p h i c data i s a v a i l a b l e i n the I n t e r n a t i o n a l A b s t r a c t s i n Operations Research, p u b l i s h e d by the I n t e r n a t i o n a l F e d e r a t i o n of O p e r a t i o n a l Research S o c i e t i e s , (IFORS). S u c c e s s f u l A p p l i c a t i o n s of O / R . To 1971, perhaps the most successful a i r l i n e applications of O/R were i n various queueing s i t u a t i o n s , for example, i n baggage handl-ing, and i n passenger service at t i c k e t counters, at check-in and at departure gates. Some examples were discussed under C u s t o m e r S e r v i c e i n Chapter I I I . Queueing models have also served well i n the analysis of runway u t i l i z a -t i o n , a i r p o r t design, and A i r T r a f f i c Control. O/R models have been used successfully i n evaluating a i r l i n e information systems, and i n the design of booking procedures consistent with required standards of customer service. Several maintenance shop scheduling models appear to have been e f f e c t i v e i n providing s p e c i f i e d supply r e l i a b i l i t y from r e l a t i v e l y small stocks of rotable spares. E n g i n e P r o v i s i o n i n g , i n Chapter IV i s a good example of p r a c t i c a l application of dynamic programming. Spares inventories pose s p e c i a l problems, p a r t i c u l a r l y for small a i r l i n e s operating new a i r c r a f t types. However, inventory models appear to have resulted i n good spares inventory management. O/R solutions to problems of a i r p o r t manpower planning have been implemented with evidently s a t i s f a c t o r y r e s u l t s . This i s not to say that further improvements w i l l stop. A r e a s f o r F u r t h e r D e v e l o p m e n t . Slow developments i n some problem areas may be partly due to a lack of analysis. Many problems of a i r p o r t access, (such as ground congestion and bottlenecks), appear soluble. In some cases.route authorizations, p a r t i c u l a r l y i n the United States, may have been i l l - c o n s i d e r e d . While o p t i m a l solutions to ground congestion and route authorizations are yet i n the future, e x i s t i n g O/R methods could y i e l d s i g n i f i c a n t improvements. In other areas, developments seem to be impeded by lack of technical knowledge.- Scheduling and crewing prob-lems were s t i l l i n experimental stages of solution i n 1971. While much work had been done on various mathematical programming approaches, schedule solutions by O/R were gen-e r a l l y p a r t i a l and not necessarily optimal. A i r c r a f t r o tation was s t i l l l a rgely a manual c a l c u l a t i o n . In the more subjective problems of marketing and f i n a n c i a l decisions, good O/R solutions appear.dependent upon-deeper understanding and knowledge of factors external to the a i r l i n e s . D o e s O/R P a y ? In objective problem s i t u a t i o n s , such as inventory control and manpower planning, where measure-ments of cost-benefits are e a s i l y made, O/R should generally y i e l d savings to the a i r l i n e . In other areas such as marketing, b e n e f i t s may be l e s s t a n g i b l e and d i f f i c u l t t o measure with p r e c i s i o n . T h i s might a l s o be the case i n r e p a i r shop s c h e d u l i n g where O/R leads to improved r e l i -a b i l i t y of supply. In passenger queues, b e n e f i t s may take the form of improved customer - s e r v i c e . In booking p o l i c y , O/R might l e a d to some combination of improved revenues to the a i r l i n e w h i l e g i v i n g improved s e r v i c e to the customers. O/R s t a f f s a t a i r l i n e s a r e " t y p i c a l l y fewer than te n . I f p r o j e c t s are s e l e c t e d to y i e l d short-term p a y o f f , then O/R groups ought to be s e l f - s u p p o r t i n g . I f d i f f i c u l t long-range p r o j e c t s are undertaken, the pa y o f f w i l l be f u r t h e r i n the f u t u r e . I n s t a l l a t i o n o f a N e w O / R G r o u p . Probably the group should s t a r t with a s m a l l number of engineers or mathe-m a t i c a l l y o r i e n t e d people w i t h s e v e r a l years of company-expe r i e n c e . An O/R l i b r a r y should be s t a r t e d a t the o u t s e t , and a l l O/R members encouraged to keep up to date w i t h the l i b r a r y m a t e r i a l s . A survey of the l i t e r a t u r e should be made to f i n d out what has been done, but there should be immediate problem assignments and t a r g e t dates from the s t a r t . Otherwise the group l o s e s coherence and sense of purpose. For quick r e s u l t s i n i t i a l l y , early projects should be simple copies of successful applications elsewhere (modified as necessary). Inventory control, maintenance shop scheduling, or passenger queue models might be s u i t -able choices. Gradually, after several simple problems are solved, more attention could be devoted to d i f f i c u l t and long-range projects. A_ F i n a l C o m m e n t . O/R departments tend to assume an esoteric nature because they deal with m a t h e m a t i c a l repre-sentations of the world. 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