@prefix vivo: . @prefix edm: . @prefix ns0: . @prefix dcterms: . @prefix skos: . vivo:departmentOrSchool "Business, Sauder School of"@en ; edm:dataProvider "DSpace"@en ; ns0:degreeCampus "UBCV"@en ; dcterms:creator "Alexander, Arthur"@en ; dcterms:issued "2011-04-14T21:51:25Z"@en, "1971"@en ; vivo:relatedDegree "Master of Science in Business - MScB"@en ; ns0:degreeGrantor "University of British Columbia"@en ; dcterms:description """The problem was to review and evaluate operations research techniques and models that had been applied in the airline industry and to discover problem areas where further research is needed. The method was to review management and operations research literature pertaining to airlines, and to formulate the thesis outline on the basis of literature consulted. More specialized literature was then sought under each of the main chapter headings: Marketing, Production, Airports, Finance. In Marketing, little was found that originated from airline companies, except in the area of forecasting. Advertising and pricing models studied were chiefly from manufacturing industries. Airline Production, the revenue-earning part of airline operation, has been extensively studied by operations researchers in the airline industry. Reservations systems, manpower planning, scheduling of aircraft and crews and passenger check-in and baggage handling were main topics of study. Airport models dealing with traffic congestion, Air Traffic Control, aircraft, maintenance, and inventory control have been successfully implemented. Financial models have been developed largely by airframe manufacturers as selling tools for new aircraft, and for market research by the plane builders. Cash flow models and models that aid financial control have been applied. General conclusions are that operations research has been investigated as a means to better airline management in most departments of airline operation. Much remains to be done to develop practical operations research competence in the following areas: 1. Advertising and Pricing. 2. Routing and Scheduling of aircraft and crews. 3. Financial Investment. The volume of the literature on operations research is growing rapidly. This thesis includes only a small sampling of the work done prior to 1971. For more intensive study, bibliographies of current and past work should be consulted. An excellent source of bibliographical data is the International Abstracts in Operations Research, by the International Federation of Operational Research Societies, (IFORS)."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/33652?expand=metadata"@en ; skos:note "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 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 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£ 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 • 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 \\. -• 0 d 0 r O tt. (x u i -4-•z. < V-- ( V 0 • c * e s_ l M i f 0 _ O r C ^, < / <•+• (A > rf\\ / O-d V u J • ^ < —v-j-y - j -< 2-< c E cr 0 C 1^ O 0 < f o C l £ -4^ C E ct #_^ 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 >_ i . 0 <4-0 0 0 — d V. _ 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 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. 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. The d e t a i l s of the mathematics, however, need not obscure the general solution approach nor the assumptions inherent i n the solution. Judgement i n making assumptions i s generally more relevant to model output, than model structure. Management s k i l l and compe-tent executive judgement have not been replaced by O/R, nor i s t h i s anticipated. Implementation of O/R programs often requires support from management who are aware of the objectives, the costs, and the r i s k s involved. BIBLIOGRAPHY A b b i n k , J . C . \" N o z z l e G u i d e V anes - A C a s e S t u d y . \" AGIFORS P r o c e e d i n g s . 1967, pp. 283-310. A b e r t , J.G., Kamrass, M., & N a v a r r o , J.A. \" E v a l u a t i n g A i r -c r a f t R e g ' t s i n t h e L i g h t o f V a r y i n g o r U n c e r t a i n M i s s i o n M i x e s . \" O p e r a t i o n s R e s e a r c h . V o l . 15, No. 4, 1967, p. 738. 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"@en ; edm:hasType "Thesis/Dissertation"@en ; edm:isShownAt "10.14288/1.0101741"@en ; dcterms:language "eng"@en ; ns0:degreeDiscipline "Business Administration"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "University of British Columbia"@en ; dcterms:rights "For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en ; ns0:scholarLevel "Graduate"@en ; dcterms:title "Application of operations research in the airline industry"@en ; dcterms:type "Text"@en ; ns0:identifierURI "http://hdl.handle.net/2429/33652"@en .