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A dynamic vehicle-scheduling problem 1974

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A BYHABIC VFHICLE-SCBftULING PROBLEH by CABCLINE SZETC B . S c , S i n c n F r a s e r U n i v e r s i t y , 1971 A THESIS SUBMITTED IN PARTIAL FULFILMENT CF THE BEQUIBIMFNTS FCB TBE tIGBIE OF HASTER OF SCIENCE IN BUSINESS ADMINISTRATION i n the F a c u l t y of Commerce He accept t h i s t h e s i s as conforming to tbe r e q u i r e d standard THE UNIVERSITY OF BRITISH CCLUKBIA A p r i l , 197M In presenting 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 for an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that 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 reference and study. I f u r t h e r agree that permission f o r extensive 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 that 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 permission. ^ - Commerce Department of The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date A p r i l 28, 197k ABSTRACT This study applies Doll's formal decision rules to solve a dynamic vehicle-scheduling problem provided by ALLTRANS EXPK ESS LTD. { Vancouver ). Computer simulation i s used as the research tool. The computer simulated results are compared with ALLTRANS solutions based on the perfomance measures of mean t r a v e l time per customer, mean and standard deviation of time to serve a customer, and mean and standard deviation of delivery time per customer. Doll's decision rules contain two scheduling h e u r i s t i c s , i e , closest customer h e u r i s t i c and time saved h e u r i s t i c , and a set of three dispatching decision rules associated with parameters HE, MB and S. It i s found that Doll's decision r u l e methods do not improve the solutions i n terms of reducing t r a v e l time per customer but can produce higher service quality i n terms of reducing the time to s a t i s f y a customer requirement after i t s occurrence. The general performance of Doll's decision rules on th i s s p e c i f i c s i t u a t i o n indicates that: (1) The time saved h e u r i s t i c i s more preferable i n solving t h i s problem. (2) Both ME and MB can af f e c t the performance measures described above, and combinations of these two parameters can control the trade-off between the mean t r a v e l time per customer and mean time to s a t i s f y a i i customer request aft e r i t s occurrence. ( 3 ) Geographical r e s t r i c t i o n which depends b a s i c a l l y on the design of sectoring mechanism ( S ) can a f f e c t a l l f i v e performance measures. Further research should be done on testing the e f f e c t s of the within sector condition ( S ) of the dispatching decision rules, with emphasis on the design of a s p e c i f i c sectoring mechanism. Also, with a larger size problem, further sdudies should be performed on the use of combinations of the dispatching decision rules to control the trade-off between mean t r a v e l time per customer and mean times to s a t i s f y a customer request after i t s occurrence. i i i TABLE OF CONTENTS Page ABSTRACT .. i TABLE OF CONTENTS . . i i i LIST OF FIGURES •• . V LIST OF TABLES v i TABLE OF ABBREVIATIONS v i i i CHAPTER I INTRODUCTION . . . . 1 1.1 Objective of the Study .....2 1.2 Research Approach .....3 CHAPTER II REVIEW OF DOLL'S HORK .6 2.1 The Vehicle-scheduling Problem 6 2.2 Doll's Decision Rules 7 2.2.1 Scheduling Decision Rules .....7 2.2.1(1) Closest Customer Heuristic ........8 2.2.1(2) Travel Time SavedHeuristic ........9 2.2.2 Dispatching Decision Rules 12 2.3 Summary of Doll's Experiments and Results ....14 CHAPTER III METHOD OF ANALYSIS 18 3.1 Data Source 18 i v 3.2 Source Data Modification 21 3.3 Input Data .......23 3. 4 Computer Simulation Model 25 3.5 Experimental Design 28 3.6 Output Data ..39 CHAPTER IV RESULTS AMD ANALYSIS .41 4 .1 S t a t i s t i c s of Data Subplied by ALLTRANS ......41 4.2 Comparison of Actual and Simulated Data 43 4.3 Performance of Doll's Decision Rules i n the Problem ...50 4.3.1 Effects of Scheduling Heuristics and Dispatching Decision Rule Parameters M E and MB 51 4.3.2 Sectoring E f f e c t 54 4.3.3 E f f e c t on Combination of Decision Rule Conditions .58 4.4 Other Experiments ...............61 CHAPTER V CONCLUSIONS ....64 BIBLIOGRAPHY . . .67 APPENDIX I ....69 APPENDIX II 103 L I S T OF FIGURES Page FIGURE I I I . I A L L T R A N S ' SECTORING OF C I T Y VANCOUVER AND LOCATION OF CUSTOMERS ON RECORDS 20 FIGURE I I I . 2 MACRO FLOW CHART OF THE SIMULATION MODEL 29 FIGURE I I I . 3 SECTORING OF THE SIMULATED AREA BY SECTORING MECHANISM S(2 ) 34 FIGURE I I I . 4 SECTORING OF THE SIMULATED AREA BY SECTORING MECHANISM S(3 ) . . 35 FIGURE I I I . 5 SECTORING OF THE SIMULATED AREA BY SECTORING MECHANISM S(4 ) . . 36 v i L I S T OF TABLES Page TABLE I I I . 1 ANALYTICAL RESULTS OF DATA SUPPLIED BY ALLTRANS 24 TABLE I I I . 2 RANGE OF PARAMETER VALUES IN THE EXPERIMENTS DESIGNED . . 26 TABLE I I I . 3 L I S T I N G OF EXPERIMENTS IN SET A 31 TABLE I I I . 4 L I S T I N G OF EXPERIMENTS IN SET B 32 TABLE I I I . 5 L I S T I N G OF EXPERIMENTS IN SET C 37 TABLE I V . 1 STATISTICS OF DATA SUPPLIED BY ALLTRANS . 43 TABLE I V . 2 RESULTS OF EXPERIMENTS WITH A P P L I C A T I O N OF CLOSEST CUSTOMER HEURISTIC 44. TABLE I V . 3 RESULTS OF EXPERIMENTS WITH A P P L I C A T I O N OF TIME SAVED HEURISTIC 45 TABLE I V . 4 RESULTS OF DIFFERENT SECTORING MECHANISM WITH A P P L I C A T I O N OF CLOSEST CUSTOMER HEURISTIC . . 46 TABLE I V . 5 ' RESULTS OF DIFFERENT SECTORING MECHANISM WITH A P P L I C A T I O N OF TIME SAVED HEURISTIC 47 TABLE I V . 6 RESULTS OF MISCELLANEOUS EXPERIMENTS IN SET D 48 TABLE I V . 7. SUMMARY OF DIFFERENCES IN PERFORMANCE MEASURES DUE TO THE SCHEDULING HEURISTICS USED IN THE EXPERIMENTS 52 TABLE I V . 8. SUMMARY OF RESULTS OF EXPERIMENTS USING SECTORING MECHANISM S ( 3 ) 55 v i i Page TABLE I V . 9 COMPARISON ON RESULTS OF EXPERIMENTS USING SECTORING MECHANISM S ( l ) AND S(4 ) RESPECTIVELY 57 TABLE I V . 10 TRADE-OFF BETWEEN LOW MEAN TRAVEL TIME AND LOW DELIVERY TIME BY MEANS OF COMBINATION OF CONDITIONS OF DISPATCHING DECISION RULES . 60 v i i i TABLE OF ABBREVIATIONS C.C.H. THE CLOSEST CUSTOMER SCHEDULING HEURISTIC T .S .H. THE TIME SAVED SCHEDULING HEURISTIC ME THE MAXIMUM EFFICIENCY INDEX MB THE MINIMUM BACKLOG S THE NUMBER OF SECTORS ix ACKNOWLEDGEMENTS I wish to thank Dr. C.L. D o l l , my committee chairman, for his guidance and time during a l l stages of my thesis work. I wish to thank my committee members: Drs. J . Sidney and C. Swoveland for t h e i r comments to improve the quality of t h i s t h e s i s . I g r a t e f u l l y acknowledge the generous coorperation from ALLTRAHS EXPRESS LTD. ( Vancouver ) which provided me with the data used i n thi s research. 1 CHAPTER I INTRODUCTION A vehicle-scheduling problem involves developing schedules to serve customer demands at various locations with vehicles which travel to these locations. If the set of relevant factors such as the location of customers, customer requirements, number of vehicles and siz e of vehicles does not change as time progresses, the problem i s c l a s s i f i e d as s t a t i c vehicle- scheduling. On the other hand, i f some of these factors do change as time progresses, then the problem i s c l a s s i f i e d as dynamic vehicle-scheduling. As pointed out by D o l l 1 0 , the vehicle-scheduling problem has received only l i m i t e d benefit from the application of the set of techniques and theories c a l l e d management science, in spit e of the fact that i t must be solved every day by many people in business and government. This lack i s due to r e l a t i v e l y l i t t l e attention by researchers and managers, rather than the inappropriateness of management science. In his research, Doll developed a set of formal decision rules to solve a dynamic vehicle-scheduling problem and tested the general performance of these decision rules on a hypothetical problem by means of computer simulation. To supplement Doll's study, the present thesis compares formal decision r u l e solutions with the solutions implemented in an actual s i t u a t i o n . This actual business s i t u a t i o n i s 2 simulated. In the simulation, schedules are developed according to Doll's formal decision rules and vehicles are dispatched to follow these schedules. Results from the computer simulation experiments are analyzed and compared with the actual implemented solutions. This enables an assessment of the factors for deriving fast delivery and high e f f i c i e n c y i n customer services. 1.1 Qbjective_of_the_Stud_ Most vehicle-scheduling problems attempt to minimize t o t a l t r a v e l l i n g time and to minimize the time required to s a t i s f y a customer's order under the conditions that t o t a l load a l l o t t e d to each vehicle does not vi o l a t e i t s capacity l i m i t and the vehicles can complete a l l schedules within a time l i m i t . Since customer requirements fluctuate during a working day according to changing location and varying amount of goods to be delivered, the scheduling problem i s often dynamic rather than s t a t i c . Dollio recently made a study of the dynamic vehicle- scheduling problem. He developed decision rules to solve such problem and performed computer simulation on a hypothetical case i n order to evaluate the performance of his decision rules. The present study makes use of Doll's decision rules to develop schedules and to dispatch available vehicles i n accordance with these schedules so as to generate solutions that s a t i s f y a set of customer order a c t u a l l y received by a transportation company. The generated solutions are then compared with the implemented 3 solutions which are derived from the experience of the company. The objectives of t h i s study are therefore as follows: (a) to t e s t the s u i t a b i l i t y of the application of Doll's decision rules on an actual business s i t u a t i o n ; (b) to detect the ef f e c t s of Doll's decision rules on an actual scheduling s i t u a t i o n , hence to discover factors for deriving fast delivery and high e f f i c i e n c y i n customer services. 1.2 R§sear_h_A££roach As i n Doll's research, computer simulation i s used as the research t o o l i n t h i s study. An actual business si t u a t i o n i s simulated, schedules are developed and vehicles are dispatched to follow these schedules according to formal decision r u l e s . The r e s u l t s of these simulation experiments are analyzed and compared to the summary s t a t i s t i c s of the actual schedules used in the business s i t u a t i o n . Before setting up the experiments, information about the actual business si t u a t i o n must be available. They are: (a) vehicle f l e e t information: t h i s includes simulation of the t o t a l number and size of vehicles available on each day; (b) information on certain l i m i t a t i o n s such as working 4 hours of each of the days being simulated, and some service time c o e f f i c i e n t s ; (c) information on the set of customers such as a r r i v a l time of each customer requirement, together with i t s location and quantity. A computer simulation model i s developed using the above information. Different sets of experiments are established to investigate d i f f e r e n t solution methods. These solution methods are generated by means of taking d i f f e r e n t scheduling h e u r i s t i c s with various parameter values for each of the dispatching decision rule parameters contained in Doll's scheduling decision rules and dispatching decision rules. Included also are di f f e r e n t ways of sectoring i n dispatching vehicles to follow the schedules developed. In each of the experiments , s t a t i s t i c s such as mean tr a v e l time per customer, mean and standard deviation of time to serve a customer and mean and standard deviation of delivery time per customer w i l l be collected and compared to the corresponding s t a t i s t i c s of the schedules ac t u a l l y implementd i n the business s i t u a t i o n . Here, the time to serve a customer includes the t r a v e l time and unloading time to serve t h i s customer, and the delivery time per customer i s defined as the time between the a r r i v a l of customer demand and the completion of service. The concluding chapter w i l l discuss the res u l t s of the 5 above comparison. This evaluates the performance of the decision rules in the actual business si t u a t i o n . Additional areas of investi g a t i o n are discovered as side r e s u l t s of the experiments. 6 CHAPTER II REVIEW OF DOLL'S WORK This chapter i s divided i n t o three sections. The f i r s t section gives a formal d e f i n i t i o n of the vehicle-scheduling problem, the research problem. The second section involves a detailed explanation of Doll's decision rules upon which t h i s research i s based. The l a s t section i s a summary of Doll's experiments and res u l t s on his hypothetical case. 2 • 1 _he__ehicle_Sc_e A vehicle-scheduling problem can be stated as follows: To develop schedules and following these schedules, dispatch vehicles of known capacity to serve a set of customers, each at a known location and with a known requirement for some commodity, subject to the constraints that: (a) the requirements of a l l the customers must be met; (b) the t o t a l load allocated to each vehicle may not exceed i t s capacity; (c) the t o t a l time for each vehicle to complete i t s tour may not exceed some predetermined l e v e l . The objective of the solution i s the minimization of the 7 t o t a l cost of delivery. This cost may be the sum of costs associated with the f l e e t size and the costs of completing the delivery tours. Since most of the relevant factors i n vehicle-scheduling ( such as the location of customers, customer requirements, the number of vehicles and the size of vehicles ) do change with time , the problem i s often dynamic. The present research w i l l therefore address i t s e l f to such dynamic vehicle-scheduling problems. In solving a dynamic vehicle-scheduling problem, two decisions are involved: (a) that of developing schedules; (b) that of when to dispatch. Decisions are made to achieve the objective of maximizing p r o f i t s by accounting for both vehicle cost e f f i c i e n c y and customer service q u a l i t y . D o l l has developed two sets of decision rules, one f o r scheduling and the other for the dispatch of vehicles. These rules w i l l be summarized as follows. 2.2 DollJ_s_ Decision^ 2.2.1 Scheduling Decision fiules A schedule i s an ordered set expressed i n the form ( D-S_- 8 Sp~ ... -S -D ) where D denotes the depot and S-,, S 0 , . S denote the n-̂  customers served i n this schedule. When constructing a schedule by any of the h e u r i s t i c s described below, the f e a s i b i l i t y conditions must be checked. These conditions are that a schedule i s feasible i f the sum of the customer requirements on the schedule i s less than the vehicle capacity and i f the time required by the schedule i s l e s s than the time remaining i n the day. Doll's scheduling decision rules contain the time saved h e u r i s t i c and the closest customer h e u r i s t i c . Reasons for selecting these two h e u r i s t i c s and the pertinent l i t e r a t u r e review are given i n Doll's t h e s i s 1 0 . 2.2 . 1 ( 1 ) Closest Customer Heuristic ( C.C.H. ) This h e u r i s t i c was developed by O ' N e i l 2 0 and adopted by Doll. For t h i s decision h e u r i s t i c , the f i r s t customer selected i s the one closest to the depot and the subsequent customers selected are those closest to the l a s t selected customer. This h e u r i s t i c requires the following information: (a) the number of vehicles available; (b) the capacity of the vehicles; (c) the current time; (d) the end of day time; 9 (e) the number of customers; (f) the location of customers in r e l a t i o n to the depot; and to each other; (g) the requirements of the customers. The functioning of th i s h e u r i s t i c i s a r e p e t i t i v e process. F i r s t the customer closest to the depot i s added to the schedule and i t i s tested for f e a s i b i l i t y . If i t i s not f e a s i b l e , the next closest customer demand i s t r i e d u n t i l a customer i s found which i s a fe a s i b l e addition to the schedule, or u n t i l a l l customers have been t r i e d . If i t i s feasible, then the customer clos e s t to the customer just added to the schedule, i s next added to the schedule and the new schedule i s tested for f e a s i b i l i t y . The same procedure i s repeated u n t i l no more customer can be added to the schedule because of l i m i t a t i o n s set by vehicle capacity and/or the time remaining i n the day. If another vehicle i s available and customer demands remain to be serviced, t h i s scheduling process w i l l be repeated for the next vehicle. 2.2.1(2) Travel Time Saved Heuristic ( T.S.H. ) Another scheduling h e u r i s t i c of Doll's was f i r s t introduced by Dantzig and Ramser9 as a part of a lin e a r programming formulation of the t r a v e l l i n g salesman problem. It was subsequently improved and removed from the linear programming context by Clarke and Wright 7. This h e u r i s t i c begins with the 10 assumption that a l l customers are on separate schedules including only one customers. This schedule takes the form ( D- S ,-D ) where S. denotes the i - t h customer on the schedule. Then 1 x customers are included on a common schedule based on the amount of scheduled travel time saved by th e i r i n c l u s i o n . This i s done by arranging in descending order the travel time saved, which i s the time difference between serving two customers separately from the depot and serving them sequentially on the same schedule. This h e u r i s t i c requires the same information l i s t e d in 2.2.1 (1) i n addition to the computation of a t r a v e l time saved matrix. If LL J , J and D-; n denote the travel times between the depot and customer i , between customer i and j , between customer j and the depot respectively, then, the time required to serve customer i and j separately i s 2D- _+2D^ -^the time required to serve them in one schedule i s D0̂ _+D_^-j+D j 0 , Hence, the time saved i s ( 2D .+2D. ) - ( D_ . + D. -+D . _) , or D. _•+_•_; _ k o , i 0,o ' v 0 , 1 1,0 0.° o»iT-»D 0»° , where the distance matrix i s assumed to be symmetrical. After c a l c u l a t i n g the time saved matrix, t h i s h e u r i s t i c proceeds r e p e t i t i v e l y as follows. The pair of customers with the largest time saved value i s included i n a schedule, provided that a l l f e a s i b i l i t y conditions stated above are s a t i s f i e d . If the schedule i s not fea s i b l e , the time saved value of t h i s pair of customers i s removed from further consideration, and the remaining pairs of customers are considered by following the previous procedure. After the i n i t i a l pair of customers i s selected, the time saved matrix i s searched to add another 11 customer to the beginning or the end of the schedule. This new customer i s selected on the basis of largest time saved when combined with the f i r s t customer or the l a s t customer on the schedule and the selection should not vi o l a t e the f e a s i b i l i t y conditions. This procedure i s repeated u n t i l no more customers or vehicles are available. After schedules are formulated, the next decision i s on the dispatch of vehicles. An application of dispatching decision rules determines when a vehicle should be dispatched to follow a schedule. These rules a f f e c t the customer service c r i t e r i a d i r e c t l y and they a f f e c t the t r a v e l time of the vehicles i n d i r e c t l y . Before a vehicle can be dispatched , the following conditions must be s a t i s f i e d : (a) at least one customer demand exists to be served; (b) at least one vehicle i s available f o r dispatching; (c) at least one schedule e x i s t s that can be completed by the end of the current day. When the above conditions are s a t i s f i e d , Doll's decision rules can be applied to the dispatching of vehicles. His rules are as follows. 12 2 . 2 . 2 D i s p a t c h i n g D e c i s i o n R u l e s R u l e 1: DISPATCH IF EI__ < ME T h i s r u l e r e q u i r e s t h a t t h e s c h e d u l e s t o be f o l l o w e d a t t a i n s a minimum l e v e l o f e f f i c i e n c y ME b e f o r e a v e h i c l e i s d i s p a t c h e d . Here, the e f f i c i e n c y i n d e x , E l j r , i s d e f i n e d as t h e s c h e d u l e time per customer s e r v e d i n s c h e d u l e K. The maximum e f f i c i e n c y i n d e x , ME, i s a d e c i s i o n r u l e parameter, the n u m e r i c a l v a l u e of which i s p r e - d e f i n e d . The i m p o s i t i o n of a maximum l i m i t on E3J£ w i l l ensure t h a t the t o t a l d a i l y t r a v e l t ime does not exceed some maximum v a l u e . R u l e 2 : DISPATCH VEHICLES IF B > MB T h i s r u l e r e q u i r e s t h a t more th a n some s p e c i f i e d minimum number of customer demands have been r e c e i v e d b e f o r e a v e h i c l e i s d i s p a t c h e d . Here, B, the c u r r e n t b a c k l o g , g e n e r a t e s the d e l a y i n s e r v i n g an o r d e r . Parameter MB, t h e minimum b a c k l o g , i s the d e c i s i o n r u l e parameter which, w i t h a p r e - d e f i n e d v a l u e , c o n t r o l s the f u n c t i o n i n g o f t h i s d e c i s i o n r u l e c o n d i t i o n . Under t h i s r u l e , the s e r v i c i n g o f customer demands i s o f t e n d e l a y e d u n t i l t h e r e i s a s u f f i c i e n t l y l a r g e number of customers a w a i t i n g s e r v i c e . T h i s r u l e w i l l i n c r e a s e the e f f i c i e n c y of the s c h e d u l e but t h e mean s e r v i c e time per customer i s expected to i n c r e a s e as t r a v e l time per customer i s d e c r e a s e d . 13 Rule 3: ONLY WHEN ONE OR BORE VEHICLES ARE DISPATCHED IS THE NEIT SECTOR CONSIDERED. This rule requires that a vehicle or vehicles must be dispatched within the geographic sector of customer locations currently being considered. The geographical sectors can be defined as dividing a square or c i r c u l a r region into S equal segments, or subdividing the whole region into S i r r e g u l a r subregions according to the density of customer requirements. To apply t h i s decision rule, consider f i r s t l y the customers i n sector number one. Vehicles are dispatched to these customers i f the dispatching f e a s i b i l i t y conditions are met. After vehicles are dispatched to serve customer requirements in sector one, the customer requests in sector two w i l l be considered. The process continues u n t i l at least one vehicle i s dispatched to a l l S sectors, then i t s t a r t s again i n sector number one. As expected, the within sector condition increases mean service time because of the delays of customer requests i n sectors not currently being considered, but i t decreases t r a v e l time because of the increase in customer requests density. The three decision rules l i s t e d above w i l l require a knowledge of three parameters: (a) the maximum e f f i c i e n c y index, ME; (b) the minimum backlog per sector, MB; 14 (c) the number of sectors, S. I t i s possible to eliminate one or more of the constraints i n the three decision rules by assigning d i f f e r e n t numerical values to t h e i r associated parameters. For instance, to allow vehicles to be dispatched without a consideration of the e f f i c i e n c y l e v e l , ME can be set to some large numerical value. To eliminate any backlog, a value of zero can be applied to MB, and by setting the number of sectors S to one, the sectoring constraint w i l l be eliminated. 2.3 Summary of, Doll; s.. Experiments and Results To evaluate the scheduling and the dispatching decision rules, Doll designed a set of simulation experiments defined with d i f f e r e n t customer request rates. At a given customer request rate, customer demands were generated according to a negative exponential probability d i s t r i b u t i o n with uniformly distributed units of requirements. In each of these problems, the location of each customer was represented by a grid point on a coordinate plane with the depot as the o r i g i n . They scattered on the plane following a given p r o b a b i l i t y d i s t r i b u t i o n function. Assumptions were also made on loading and unloading time, i n i t i a l number of vehicles and their capacity. In each of the experiments performed, schedules were developed and vehicles were dispatched to follow these schedules according to d i f f e r e n t solution methods to solve one of the hypothetical problems defined. These solution methods were generated from Doll's decision rules by using one of the two 15 scheduling h e u r i s t i c s with the other factors held constant, or using d i f f e r e n t values of the dispatching rule parameters with the other factors held constant, or imposing a l l dispatching conditions at the same time. The mean t r a v e l time per customer, the mean time to serve a customer and the standard deviation of the time to serve a customer were collected as simulaton output and i n each experiment, they were used to measure the effectiveness of the solution methods. These three performance measures are used because the mean t r a v e l time per customer i s d i r e c t l y related to the operating cost of the vehicle f l e e t ; the mean time to serve a customer i s a measure of service q u a l i t y ; and the standard deviation of the time to serve a customer i s a measure of the r e l i a b i l i t y of service. Analysis of Doll's experiments can be summarized as follows: (a) The time saved h e u r i s t i c always has less mean tr a v e l time per customer than the closest customer h e u r i s t i c . Also, the time saved h e u r i s t i c produces a lower value of standard deviation of the time to serve a customer. However, the closest customer h e u r i s t i c provides consistently lower mean time to serve a customer. (b) The dispatching decision rules have r e l a t i v e l y l i t t l e e ffect on the t r a v e l time per customer. Increasing the maximum e f f i c i e n c y parameter results i n the largest reduction of t r a v e l time per customer and also in the largest increase of the mean and the standard 16 deviation of the time to serve a customer. Increasing the number of sectors results in a reduction of the mean and the standard deviation of the time required to serve a customer, but i t has v i r t u a l l y no ef f e c t on mean tr a v e l time. In general, as mean t r a v e l time per customer decreases, there i s an increase in the mean and the standard deviation of the time required to serve a customer. However, combinations of dispatching rule parameters ( with both the ME and MB parameters functioning ) resu l t i n reducing mean tr a v e l time and mean service time below the expected values. It was noted that the maximum e f f i c i e n c y parameter, ME, causes a large increase i n the standard deviation of service time in some circumstances. This causes an unacceptable maximum service time. Two ef f e c t s of d i f f e r e n t customer request rates on the performance of the decision rules were discovered. F i r s t l y , as the customer request rate increases toward the maximum capacity of the vehicle f l e e t , the performance of d i f f e r e n t decision rules converges toward the same mean tr a v e l time per customer and mean service time per customer, and some decision rules produce a service rate less than the customer request rate and thus saturate the f l e e t at high customer request rates. Secondly, at the maximum customer request rate, the closest customer h e u r i s t i c should not be used because i t res u l t s i n excessive delays for 17 customers f a r from the depot. The following recommendations were offered by Doll for possible application of his decision rules: (a) If minimizing mean t r a v e l time i s important, use the time saved h e u r i s t i c and a high value for the backlog parameter. (b) If minimizing mean service time i s important, use the closest customer h e u r i s t i c and a sectoring dispatching rule, unless the f l e e t i s operating near saturation. In t h i s case, the time saved h e u r i s t i c should be used. (c) For a given operating s i t u a t i o n , i t i s possible to improve operations by, say, reducing backlog and adding sectoring to improve mean service time while maintaining a s a t i s f a c t o r y mean t r a v e l time. 18 CHAPTER I I I METHOD OF ANALYSIS I n t h i s c h a p t e r , an a c t u a l b u s i n e s s s i t u a t i o n i s p r e s e n t e d and the computer s i m u l a t i o n model i s d e s c r i b e d t o g e t h e r w i t h a comparison of t h e d i f f e r e n c e s between these two systems. 3 . 1 _ _ _ _ _ S o u r c e ALLTRANS EXPRESS LTD. ( Vancouver ) p r o v i d e d an a c t u a l b u s i n e s s s i t u a t i o n r e q u i r i n g t h e s o l u t i o n of a dynamic v e h i c l e - s c h e d u l i n g problem. ALLTRANS was s e l e c t e d because i t has a l a r g e volume o f d e l i v e r y s e r v i c e s and the company made i t s d a t a r e a d i l y a v a i l a b l e f o r t h i s r e s e a r c h . F o l l o w i n g i s a d e s c r i p t i o n o f t h e d e l i v e r y s e r v i c e s o f f e r e d by ALLTRANS t o i t s customers. D a i l y customer r e q u e s t s a r e dynamic i n n a t u r e . D i s p a t c h e r s d e v e l o p s c h e d u l e s and f o l l o w i n g t h e s e s c h e d u l e s , v e h i c l e s a r e d i s p a t c h e d as soon as p o s s i b l e t o s e r v e e x i s t i n g customer r e q u e s t s . U s u a l l y , one t h i r d of t h e customer r e q u e s t s handeled on a g i v e n day were r e c e i v e d d u r i n g t h e working hours of the p r e v i o u s day, and t h e r e m a i n i n g r e q u e s t s were r e c e i v e d a f t e r the working hours of the p r e v i o u s day. I n d e v e l o p i n g a s c h e d u l e , f a c t o r s such as customer l o c a t i o n , a r r i v a l t i m e and the amount t o be d e l i v e r e d are c o n s i d e r e d . The l o a d i n g l i m i t o f each d e l i v e r y t r u c k i s 550 c u b i c f e e t . The Vancouver a r e a has been 1 9 sectored as shown i n FIGDRE_I11^1 . Usually, customers located i n the same sector w i l l be included in the same schedule u n t i l no more load can be put on t h i s truck, and another schedule w i l l be developed to serve the remaining customers. Cn the other hand, i f loading l i m i t i s not reached after loading for a l l customers located i n a s p e c i f i e d sector, customers i n nearby sectors w i l l be added to the schedule. Each of the delivery trucks i s loaded af t e r mid-night, and i s ready to leave the depot immediately after the driver obtains the work order from the dispatcher on the following day. This therefore excludes the loading time from the schedule time. Drivers report to work at the depot at 8:30 a.m. and f i n i s h work at approximately 3:30 p.m. each day, having a coffee break in the morning and a lunch break at noon time. Usually, a driver can only f i n i s h two schedules a day at most, one in the morning and one in the afternoon. A sample of actual schedules obtained from the records of ALLTRANS i s presented as APPENDIX I. This sample contains scheduling and dispatching information for six days. In these schedules, 201 customers located in the central area of Vancouver City with varying demand volumes were served. A number of delivery trucks were dispatched according to schedules developed by the company. Customer information from the ALLTRANS records included: (a) location of a customer; FIGURE 1 l l i l ALLTRANS' SECTORING OF CITY VANCOUVER AND LOCATION OF CUSTOMERS ON RECORDS PC1 o 21 (b) amount of customer demand, in terms of weight; (c) for each truck, a r r i v a l time at and departure time from the location of a customer, ( hence the traveling time from one location to another and the unloading time at each location ) . However, the a r r i v a l time of a customer request i s not included in these records. The above raw information was converted into a suitable form for a simulation model which i s presented i n section 3.3 . 3.2 _ource_D_ta__odification Several data modifications were implemented to enable a comparison of computer simulated results with the vehicle- scheduling solutions of ALLTRANS. These modifications are: (a) The number of simulation days i s taken as s i x . With the exclusion of coffee and lunch time, drivers are supposed to work f i v e hours a day. (b) Unloading time for each customer i s taken as 10 minutes which i s the mean unloading time derived from the sample supplied by ALLTRANS. For reasons given in the f i r s t section of t h i s chapter, loading time i s not included in a schedule. (c) Amounts of customer demands recorded i n terms of 22 weight have been converted into volume. This i s done by assuming that a l l commodities delivered by one truck i n any given schedule have the same density together with the fac t that each delivery truck i s at least 98 per cent f u l l y loaded. Information on the percentage loading of trucks has been supplied by dispatchers of ALLTRANS. (d) The time at which customer demands occur has not been recorded. In order to compare the e f f i c i e n c y i n customer service, occurance times of customer demands which are served on the same day by ALLTRANS are assumed to ar r i v e at the beginning of the day. (e) From the given records, t r a v e l time information can only be obtained for certain pairs of locations. In the simulation model, t r a v e l time i s estimated by an empirical equation derived for the Greater Vancouver Region. TT = 3.85+0.00313 (x+y)+0.0106 (HYP0)-2.4 (HYPO)2 where TT i s the t r a v e l time i n units of minutes; HYPO = (x 2+y2) i/2; (HYPO)2 = (x2+y 2)•10" 6; x and y are the x-coordinate and y-coordinate of the location point on a Vancouver map, with the depot as the o r i g i n (0,0) . 23 S c a l e f o r x and y i s 240 g r a p h i c u n i t s t o one m i l e . 50 sample l o c a t i o n p o i n t s were p i c k e d t o t e s t t h e r e l i a b i l i t y of t h i s t r a v e l time e s t i m a t i o n e q u a t i o n . T r a v e l t i m e between each p a i r of c o n s e c u t i v e p o i n t s was o b t a i n e d from t h e s u p p l i e d r e c o r d s . There was s i g n i f i c a n t c o r r e l a t i o n between the a c t u a l t r a v e l time and the e s t i m a t e d t r a v e l time. ( C o r r e l a t i o n c o e f f i c i e n t i s 0.837 w i t h 50 degrees of freedom.) t h i s shows t h a t the model i s r e l i a b l e . 3.3 I nput_Da t a Customer i n f o r m a t i o n i n p u t e x t r a c t e d from ALLTRANS r e c o r d s i s g i v e n i n APPENDIX_I. These r e c o r d s c o n t a i n i n f o r m a t i o n on 201 customer r e q u i r e m e n t s , i n 28 s c h e d u l e s , and f o r a p e r i o d of s i x days. These 201 customer r e q u i r e m e n t s came from 90 d i f f e r e n t c u s t o m e r s , one o f them r e q u e s t e d s e r v i c e f i v e t i m e s , a n o t h e r one r e q u e s t e d s e r v i c e t h r e e t i m e s , and a n o t h e r f i v e r e q u e s t e d s e r v i c e t w i c e w i t h i n these s i x days. The number of customers s e r v e d per day ranges from 17 t o 57. Per s c h e d u l e i n f o r m a t i o n o b t a i n e d from a n a l y z i n g t h e 28 s c h e d u l e s r e c o r d e d i s g i v e n i n 1&B L E _ I I I . 1 . I n t h i s t a b l e , (1) t h e number o f customers s e r v e d i n a s c h e d u l e i s d e f i n e d as t h e number o f customers c o n t a i n e d i n a s c h e d u l e ; (2) s c h e d u l e time per customer s e r v e d i n a s c h e d u l e i s d e f i n e d as the average s e r v i c e t i m e ( i n c l u d i n g t r a v e l t ime and u n l o a d i n g time ) ; and (3) u n l o a d i n g time per customer i s d e f i n e d as t h e u n l o a d i n g time a t each customer l o c a t i o n . A c c o r d i n g t o t h e above r e s u l t s , and i n o r d e r t o de v e l o p a t T A B L E I I I . l A N A L Y T I C A L RESULTS OF DATA S U P P L I E D BY ALLTRANS RANGE MEAN S T A N D . D E V . ( 1 ) N O . OF C U S T . SERVED 1 - 2 0 7 4 IN A S C H E D . * ( 2 ) S C H E D . T I M E PER C U S T . 1 4 - 3 4 21 10 SERVED IN A SCHED. ( 3 ) UNLOADING T IME PER 1 - 3 0 9 4 C U S T . T IME MEASURED IN M I N U T E S . * IN THE G I V E N S A M P L E , THE S E R V I C E TIME FOR ONE C U S T . IS 6 0 M I N U T E S . T H I S HAS BEEN CONSIDERED AS AN E X C E P T I O N A L C A S E , HENCE THE C U S T . I S EXCLUDED I N D E - R I V I N G MEAN AND STANDARD D E V I A T I O N OF TH IS T I M E . 25 least one schedule i n every simulation day, values of decision rule parameters are set as given i n T_B_E_III_2 based on Doll's decision rules. 3.4 Com_)_t er_Simulat ion__odel In t h i s research, the scheduling s i t u a t i o n posed above i s solved with a numerical simulation model using Doll's decision rules. As simulation i s a method of symbolically representing a r e a l s i t u a t i o n , any number of solution methods can be applied to the problem. The model used i n t h i s research i s a modification of Doll's. Doll's simulation program, written i n the computer simulation language c a l l e d GASP 2 1, contains the following parts: (a) generation of the input stream, e.g. the a r r i v a l of customer demands, by means of a random number generator according to the pr o b a b i l i t y d i s t r i b u t i o n functions defined; (b) application of the decision rules to the scheduling and dispatching decisions; (c) c o l l e c t i o n of s t a t i s t i c s on the simulation r e s u l t s . To accomodate the research problem under study, part (a) of Doll's program was replaced by a sub-program which reads i n collected information about customer demands, but part (b) and part (c) remain unchanged. This simulation program i s event TABLE I I 1 . 2 RANGE OF PARAMETER V A L U E S IN THE E X P E R I M E N T S DESIGNED RANGE ME MB *S 2 0 - 3 0 0 - 17 1 - 17 * THE D E C I S I O N RULE OF SECTORING DEPENDS ON SECTORING MECHANISM RATHER THAN VALUES OF PARAMETER S . D I F F E R E N T SECTORING M E C H A N - ISM ARE DESCRIBED IN SECT ION 3 . 5 OF T H I S C H A P T E R . 27 oriented which means that simulation time i s counted from event to event, ignoring model action between events. There are six basic types of events i n thi s simulation model: (a) an i n i t i a l i z a t i o n event, (b) a vehicle available event. (c) a customer occurrence event. (d) an end of day event. (e) the end of simulation event. (f) a change of sectoring event. The i n i t i a l i z a t i o n event i n i t i a t e s the simulation by i n i t i a l i z i n g the programmer defined variables as well as the necessary GASP variables. Customer information for the day i s read i n ( SUBROUTINE REDATA ). If a vehicle available event occurs, the vehicle available l i s t i s updated ( SUBROUTINE VEHUP ) and the l i s t s of available vehicles are put in working arrays for use by the decision rule process ( SUBROUTINE VEHCUS ). If a customer occurrence event occurs, the customer available l i s t i s updated ( SUBROUTINE CUSUP ) and the l i s t s of available customers and available vehicles are put in working arrays for use by the decision r u l e 28 process { SUBROUTINE VEHCUS ). Schedules are then formulated according to the decision rules { SUBROUTINE DECRUI ). The vehicles assigned to the schedules are removed from the vehicle available l i s t s . A vehicle available event i s generated when the schedule ends. S i m i l a r l y , the customers assigned to the schedules are also removed from the customer available l i s t s . The sectoring mechanism i s invoked when a change of sectoring event occurs ( SUBROUTINE VEHCUS ). Details on the sectoring mechanism are given i n section 3.5 . For each schedule developed, the per schedule s t a t i s t i c s are recorded ( SUBROUTINE UPDATE ). When an end of day event occurs, d a i l y s t a t i s t i c s are recorded { SUBROUTINE ENDAY ) . The l i s t s of available customers and available vehicles are stored i n working arrays to be used i n the next day by the decision rule process (SUBROUTINE VEHCUS ). The end of simulation event terminates further simulation. The program then computes the f i n a l s t a t i s t i c s which are subseguented printed ( SUBROUTINE ENDSIM ). FIGU_E_III_2 i s a macro flow chart of t h i s simulation. 3.5 Ex_erimental_Desi_n Details on the design of each set of experiments are given i n t h i s section. This includes: (a) scheduling h e u r i s t i c used; (b) values assigned to the dispatching decision rule parameters; and (c) methods of sectoring. 29 EVENTS ENDSIM t CUSUP 111 VEHCUS I DECRUL VE.HUP ENDAY UPDATE I REDATA FIGURErlU. »2 MACRO FLOW CHART OF THE SIMULATION MODEL 30 Four sets of experiments are designed for t h i s study. This set of experiments attempts to test the ef f e c t of using d i f f e r e n t values for MB. In these experiments, scheduling decision rules being tested include C.C.H. and T.S.H.. For each of these h e u r i s t i c s , parameter values for ME and S are fixed as 10000 and 1 respectively to avoid any influence from the two associated decision rule conditions. The parameter value of MB varied within the range from 0 to 17, a range which i s r e a l i s t i c i n terms of source data and an understanding of Doll's decision rules. These experiments are l i s t e d i n TABLE_III_3. SET_B__ This set of experiments i s designed to test the effect of using d i f f e r e n t values for ME. This set of experiments i s s i m i l a r to SET A, but the parameter of ME i s allowed to vary while MB i s fixed at 0. The range of ME i s set between 20 and 30. Experiments are l i s t e d i n TABLE_III_JI. SET_C_ This set of experiments i s designed to test the effect of using scheduling decision rules with d i f f e r e n t sectoring mechanisms. As i n SET A and SET B, both scheduling h e u r i s t i c s are tested, and parameter values of ME and MB are fixed respectively as 10000 and 0 to preclude t h e i r influence. Sectoring mechanisms considered i n these experiments include: S(1) The entire area i s considered as one sector. ( These experiments are i d e n t i c a l to two experiments in SET A and SET B, hence are not duplicated. ) TABLE 1 1 1 . 3 L I S T I N G OF EXPERIMENTS IN SET A EXP N O . S C H E D . D E C I S I O N RULE D ISPATCHING RULE PARAMETER S ME MB { 1 ) CLOSEST C U S T . H E U R I S T I S 1 lOOOO 0 (2 ) CLOSEST C U S T . H E U R I S T I C 1 1 0 0 0 0 5 13) CLOSEST C U S T . H E U R I S T I C 1 1 0 0 0 0 10 ( 4 ) CLOSEST C U S T . H E U R I S T I C 1 1 0 0 0 0 1 5 (5 ) T IME SAVED H E U R I S T I C 1 1 0 0 0 0 0 ( 6 ) T I M E SAVED H E U R I S T I C 1 100C0 5 17) T IME SAVED H E U R I S T I C 1 1 0 0 0 0 10 ( 8 ) TIME SAVED H E U R I S T I C 1 1 0 0 0 0 1 5 * IN D I F F E R E N T SECTORING MECHANISM USED THE CONTENT OF EXPERIMENTAL D E S I G N E D . ARE DESCRIBED I—1 TABLE I I I . h L I S T I N G OF EXPERIMENTS IN SET B E X P . S C H E D . D E C I S I O N RULE D ISPATCHING RULE PARAMETER N O . - S ME MB ( 1 ) CLOSEST C U S T . H E U R I S T I S 1 3 0 0 ( 2 ) CLOSEST C U S T . H E U R I S T I C 1 2 5 0 ( 3 ) CLOSEST C U S T . H E U R I S T I C 1 2 3 0 ( 4 ) CLOSEST C U S T . H E U R I S T I C 1 2 1 0 ( 5 ) T IME SAVED H E U R I S T I C 1 3 0 0 ( 6 ) T IME SAVED H E U R I S T I C 1 2 5 0 ( 7 ) T IME SAVED H E U R I S T I C 1 2 3 0 ( 8 ) T IME SAVED H E U R I S T I C 1 2 1 0 * D I F F E R E N T SECTORING MECHANISM USED ARE DESCRIBED IN THE CONTENT OF EXPERIMENTAL D E S I G N E D . 33 S(2) The entire area i s divided into two sectors which coincide with the second and thi r d coordinate quadrants shown i n FIGURE_III.3. S(3) ALLTRANS sectoring scheme i s followed ( FIGURE S (4) Based on the algorithm developed by C h r i s t o f i d e s 5 , a new sectoring mechanism was developed as follows: Subdivide the whole area into elementary squares of 200x200 graphic units. ( This size was derived from the cl u s t e r i n g of customer demands. ) A l l customers being served i n the same day within the same elementary square are considered as one aggregated- customer where the demand of the aggregated-customer i s equal to the sum of the demands of those customers. Using h i s t o r i c a l data , fuse some elementary squares together as follows: minimize the area of the region of fused elementary squares such that the t o t a l area demand of the region does not exceed the loading l i m i t of each delivery truck , and the elementary squares have more than a single corner point in common. Area demand of each elementary square i s taken as the maximum value of the demands of the aggregated- customers i n the square. The subregions of the simulated area developed by th i s sectoring mechanism i s given i n FIGURE_III__5 . FIGURE I I I . 3 SECTORING OF THE SIMULATED AREA BY SECTORING MECHANISM S ( 2 ) FIGURE 111.I, SECTORING OF THE SIMULATED AREA BY SECTORING MECHANISM S ( 3 ) VJ1 FIGURE II \'.S SECTORING OF THE S IMULATED A REA BY SECTOR! NG MECHANISM S U ) TABLE I I I . 5 L I S T I N G OF EXPERIMENTS IN SET C E X P . S C H E D . D E C I S I O N RULE DISPATCHING RULE PARAMETER N O . . * S E C T . M E C H . ME MB (1) CLOSEST C U S T . H E U R I S T I S SC 13 10000 0 (2) CLOSEST C U S T . H E U R I S T I C SI 21 10000 0 13) CLOSEST C U S T . H E U R I S T I C S I 3) 10000 0 ( 4 ) CLOSEST C U S T . H E U R I S T I C SI 41 10000 0 (5) T IME SAVED H E U R I S T I C SI 1) 10000 0 (6) T I M E SAVED H E U R I S T I C SC21 10000 0 (7) T IME SAVED H E U R I S T I C S I 3) 10C00 0 (.8) T I M E SAVED H E U R I S T I C SI 4} 10000 0 * D I F F E R E N T SECTORING MECHANISM USED ARE DESCRIBED IN THE CONTENT OF EXPERIMENTAL D E S I G N E D . 38 TABLE_III-_5 l i s t s the experiments in SET_C . _iI_L_;_. This set of experiments attempts to test the e f f e c t of a l l decision rules combined. Experiments in t h i s set are taken as "combinations" or "modifications" of experiments contained i n SETS A, B and C. By "combinations", i t i s meant that the experiments are designed by varying the scheduling decision rules and the parameter values for HE, MB and S at the same time. By "modifications", i t i s meant that some procedures i n an experiment are changed. For example, the length of a working day i s extended, or the decision rule process i s varied. The following miscellaneous experiments were performed: (1) Extend the working time l i m i t of each simulation day to 600 minutes to ensure same-day service. The scheduling h e u r i s t i c used was C.C.H.. Parameter values for ME, MB and S are 10000, 0 and 1 respectively. (2) Similar to (1) except that the scheduling h e u r i s t i c used was T.S.H instead. (3) In the application of sectoring mechanism S (3) ( ALLTRANS mechanism ), modify that part of the dispatching decision rule concerning the within sector condition as follows: THE NEXT SECTOR IS CONSIDERED IF VEHICLE DISPATCHING IS NOT POSSIBLE IN THE SECTOR BEING CONSIDERED UNDER THE PREDEFINED DISPATCHING DECISION 39 RULE CONDITIONS, EVEN IF NO VEHICLE HAS BEEN DISPATCHED IN THIS SECTOR. Use C.C.H., with ME and MB being 10000 and 0 respectively. This i s simply a modified experiment of experiment (3) in SET C, used to detect the e f f e c t of sectoring mechanism S (3) i n conjunction with the other parts of the decision r u l e s . (4) As in (3) but using T.S.H. , t h i s i s a modified experiment of experiment (7) in SET C. (5) and (6) In order to tes t the e f f e c t of o v e r - a l l application of Doll's decision rules, these two experiments apply C.C.H. and T.S.H., respectively, with ME=50, MB=0 and using sectoring mechanism S(4). (7) and (8) Similar to (5) and (6), these two experiments are designed to test the e f f e c t s of combining conditions of the dispatching decision rules. C.C.H. was used i n (7) and T.S.H. was used i n (8). ME was set at 25 while MB was set at 5 with sectoring mechanism S{1) active. 3.6 0 u tj_ u t_Dat a For each experiment performed, f i v e performance measures are c o l l e c t e d from the simulated r e s u l t s : 40 (a) mean t r a v e l time per customer; (b) mean service time per customer, where service time i s the sum of tr a v e l time and unloading time; (c) standard deviation of service time per customer; (d) mean delivery time per customer, where delivery time i s defined as the time between the receipt of a customer demand and the completion of service; (e) standard deviation of delivery time per customer. These f i v e measurements are basic components of a p r o f i t function which i s here unknown. However, i n order to achieve the objective of t h i s study, i t i s s u f f i c i e n t to test the effectiveness of the decision rule methods based on these measurements. Travel time per customer and the mean service time per customer are the short term variable costs of operating the vehicles. The standard deviation of service time per customer reveals the r e l i a b i l i t y of estimating vehicle operation cost based on the mean tr a v e l or service time per customer. Mean delivery time per customer measures the e f f i c i e n c y of customer services, and the standard deviation of delivery time per customer measures the r e l i a b i l i t y of service. In a competitive area, high service e f f i c i e n c y a t t r a c t s customers which in tern increases p r o f i t . 41 CHAPTER IV RESULTS AND ANALYSIS In t h i s c h a p t e r , t h e r e s u l t s of the computer s i m u l a t i o n e x p e r i m e n t s w i l l be d i s c u s s e d and the performance of the v e h i c l e s c h e d u l i n g a c c o r d i n g t o Doll»s d e c i s i o n r u l e s w i l l be e v a l u a t e d . 4 . 1 Sta ti„ics_of_Data_S„£lied_by_ALLTRANS I n o r d e r t o compare the a c t u a l s o l u t i o n s o f ALLTRANS and t h e d e c i s i o n r u l e s o l u t i o n s , the same s t a t i s t i c s a b s t r a c t e d from the s i m u l a t i o n program were e x t r a c t e d from t h e data s u p p l i e d by ALLTRANS . These a r e : (a) mean t r a v e l t i m e per customer; (b) mean s e r v i c e t ime per customer; (c) s t a n d a r d d e v i a t i o n o f s e r v i c e time per customer; (d) mean d e l i v e r y time per customer; (e) s t a n d a r d d e v i a t i o n o f d e l i v e r y time per customer. TABLE IV.1 summarizes t h e above s t a t i s t i c s . 42 4.2 Comparison of a c t u a l and S i m u l a t e d Data Mean t r a v e l t i m e per customer, mean and s t a n d a r d d e v i a t i o n of s e r v i c e time per customer, mean and s t a n d a r d d e v i a t i o n of d e l i v e r y t i me per customer o b t a i n e d from the s i m u l a t e d d a t a p r o v i d e d by the s i m u l a t i o n model a r e l i s t e d i n TABLE_IV^2 t o T_BL__IV_.6. A comparison o f the s t a t i s t i c s t a ken on the a c t u a l and t h e s i m u l a t e d d a t a shows the f o l l o w i n g : (a) Mean t r a v e l t i m e per customer f o r the f o r m a l d e c i s i o n r u l e s o l u t i o n s i s not s i g n i f i c a n t l y d i f f e r e n t from t h a t o f ALLTRANS * s s o l u t i o n s . (b) Mean service time per customer request for the formal decision rule solutions i s also found to be not s i g n i f i c a n t l y d i f f e r e n t from that of ALLTRAN S's solutions. This follows from the r e s u l t of i n s i g n i f i c a n t difference in mean t r a v e l time per customer between the two solutions because service time i s defined as the sum of t r a v e l time and unloading time, the l a t t e r having a fixed value of 10 minutes. (c) Compared with ALLTRANS's solutions, over 78 per cent of the thirty-two simulation experiments performed, produced much smaller standard deviation of service time per customer. Where sectoring mechanism was operative, especially ALLTRANS mechanism (code S(3)), the measures of mean t r a v e l time per customer, mean T A B L E I V . 1 S T A T I S T I C S OF DATA S U P P L I E D BY A L L T R A N S MEAN STANDARD D E V I A T I O N TRAVEL T IME PER C U S T . 12 - S E R V I C E TIME PER C U S T . 2 1 10 DEL I V . TIME PER C U S T . 151 106 T IME MEASURED IN M I N U T E S . T A B L E I V . 2 RESULES OF EXPERIMENTS WITH A P P L I C A T I O N OF CLOSEST CUSTOMER H E U R I S T I C WITH S= l T R A V . T I M E T O T . N O . TRAV . S E R V I C E T IME D E L I V E R Y TIME PER DAY OF TIME PER C U S T . PER C U S T . ME MB MEAN S . D . C U S T . SERVED PER C U S T . MEAN S . D . MEAN S . D . lOOOO 0 7 2 9 176 1 8 9 13 2 3 6 132 70 1 0 0 0 0 5 6 7 3 1 8 4 185 12 2 2 6 154 9 3 1 0 0 0 0 10 6 4 3 2 1 8 1 7 9 11 2 1 7 1 7 9 130 1 0 0 0 0 15 617 2 0 1 1 7 4 11 2 1 7 7 196 159 3 0 0 6 7 8 166 183 12 2 2 5 147 9 7 2 5 0 6 4 4 2 2 2 178 12 2 2 7 155 125 2 3 0 6 1 2 2 8 5 1 7 4 11 2 1 9 156 152 ' 2 1 0 5 0 4 3 0 2 1 5 1 10 2 0 12 2 5 5 1 8 8 T IME MEASURED IN M I N U T E S . TABLE IV .3 RESULES OF EXPERIMENTS WITH APPLICATION OF TIME SAVED HEURISTIC WITH S=l TRAV.TIME TOT.NO. TRAV. SERVICE TIME DELIVERY TIME PER DAY OF TIME PER CUST. PER CUST. CUST. PER ME MB MEAN S . D . SERVED CUST. MEAN S . D . MEAN S . D . lOOOO 0 706 166 187 13 23 5 129 67 10000 5 660 169 185 11 21 5 140 86 10000 10 644 226 185 11 21 7 169 104 10000 15 626 202 179 11 21 7 194 116 30 0 677 171 185 12 22 5 141 84 25 0 667 217 186 11 21 7 142 88 23 0 574 243 168 10 20 9 204 178 21 0 575 229 171 10 20 8 175 166 TIME MEASURED IN MINUTES. T A B L E I V . 4 RESULES OF D IFFERENT SECTORING WITH A P P L I C A T I O N OF CLOSEST H E U R I S T I C MECHANISM CUSTOMER WITH MB=0 ME=10000 S E C . M E C H . T R A V . T I M E PER DAY T O T . N O . GF C U S T . SERVED T R A V . TIME PER C U S T . S E R V I C E TIME PER C U S T . D E L I V E R Y TIME PER C U S T . MEAN S . D . MEAN S . D . MEAN S . D . S( 1 ) 7 2 9 1 7 6 1 8 9 13 2 3 6 132 70 S (2 ) 5 7 1 130 1 5 1 13 2 3 5 152 1 1 3 S<3) 9 3 2 2 8 19 19 29 72 1 0 1 59 S ( 4 ) 5 2 8 3 7 6 138 13 2 3 16 4 2 1 3 0 3 TIME MEASURED IN MINUTES TABLE IV.5 RESULES OF DIFFERENT SECTORING MECHANISM WITH APPLICATION OF TIME SAVED HEURISTIC WITH MB=0 ME=lCOOO SEC.MECH. TRAV^TIME PER DAY TOT.NO. OF CUST. SERVED TRAV. TIME PER CUST. SERVICE TIME PER CUST. DELIVERY TIME PER CUST. MEAN S.D. MEAN S.D. MEAN S.D. sen 706 166 187 13 23 5 129 67 S(2 J 573 131 153 12 22 5 156 114 SI3) 93 228 19 19 29 72 102 60 S(4J 515 369 133 13 23 17 418 294 TIME MEASURED IN MINUTES TABLE I V . 6 RESULTS OF MISCELLANEOUS EXPERIMENTS CONTAINING IN SET D . N O . T R A V . T I M E PER DAY T O T . N O . OF TRAV. TIME S E R V I C E TIME PER C U S T . D E L I V E R Y TIME PER C U S T . MEAN S . D . C U S T . SERVED PER C U S T . MEAN S . D . MEAN S . D . (1 ) 7 6 6 2 3 0 2 0 1 13 2 3 7 1 4 4 82 (2 ) 7 4 4 2 2 0 2 0 1 12 22 6 139 8 3 ( 3 ) 7 5 2 1 5 5 1 7 8 15 2 5 5 148 8 0 1 4 ) 7 6 0 1 6 2 181 15 2 5 5 146 75 ( 5 ) 5 2 8 3 7 6 1 3 8 13 2 3 16 4 2 1 3 0 3 ( 6 ) 5 1 5 3 6 9 1 3 3 13 2 3 17 4 1 8 2 9 4 (71 6 4 5 2 4 8 1 8 0 11 2 1 8 1 5 9 140 (8 ) 6 6 3 2 0 7 1 8 5 11 2 1 7 152 9 4 T IME MEASURED IN M I N U T E S . 49 s e r v i c e t i m e per customerand s e r v i c e time per customer s t a n d a r d d e v i a t i o n a r e l a r g e . Hence emphasis s h o u l d be put on a n a l y z i n g the d e s i g n o f the s e c t o r i n g mechanism r a t h e r t h a n t h e e f f i c i e n c y of the f o r m a l d e c i s i o n r u l e performance. F u r t h e r d i s c u s s i o n w i l l f o l l o w i n s e c t i o n 4.3. Mean d e l i v e r y time per customer f o r the f o r m a l d e c i s i o n r u l e s o l u t i o n s ranges from 101 t o 421 minutes, of which 44 per c e n t f e l l below the v a l u e of 151 which i s the mean d e l i v e r y time per customer from ALLTRANS*s s o l u t i o n s . T h i s shows t h a t an a p p l i c a t i o n of the d e c i s i o n r u l e s can i n some c a s e s r e s u l t i n h i g h e r s e r v i c e q u a l i t y by r e d u c i n g the time taken to s a t i s f y customer demand. However, t h e assumptions r e g u a r d i n g the r e c e i p t t i m e o f customer demands, as o u t l i n e d i n c h a p t e r I I I , must be k e p t i n mind. The r e c e i p t t i m e can o n l y be assumed, making t h e v a l i d i t y of comparison q u e s t i o n a b l e . The s t a n d a r d d e v i a t i o n o f d e l i v e r y t i m e per customer o f t h e f o r m a l d e c i s i o n r u l e s o l u t i o n s ranges from 59 t o 303 m i n u t e s , and t h a t of ALLTRANS's s o l u t i o n s i s 105 minutes. As noted, t h e experiments which r e s u l t i n low mean d e l i v e r y t ime per customer a l s o r e s u l t i n low d e l i v e r y time per customer s t a n d a r d d e v i a t i o n , s u g g e s t i n g t h a t an a p p l i c a t i o n o f t h e d e c i s i o n r u l e s 50 improves both the e f f i c i e n c y and t h e r e l i a b i l i t y of s e r v i c e . F u r t h e r e f f e c t s o f the d e c i s i o n r u l e s w i l l be d i s c u s s e d i n the next s e c t i o n . I n summary, the comparison o f f o r m a l d e c i s i o n r u l e s o l u t i o n s and ALLTRANS* s s o l u t i o n s does not i n d i c a t e as g r e a t an improvement i n s o l v i n g the s c h e d u l i n g problem as exp e c t e d . One n o t a b l e p o i n t i s t h a t , i n ALLTRANS* s c h e d u l i n g problem, t h e r e were many customers l o c a t e d near the boundary of the a r e a t o be s e r v e d , and some of them are s e p a r a t e d from o t h e r customer l o c a t i o n s by r e l a t i v e l y l o n g d i s t a n c e s . T h i s c h a r a c t e r i s t i c i n customer l o c a t i o n l e d to t h e f o r m u l a t i o n of many d e c i s i o n r u l e based s c h e d u l e s c o n t a i n i n g o n l y one customer. These s c h e d u l e s i n c r e a s e t h e mean t r a v e l time per customer to a v a l u e which can be r a t h e r l a r g e . D e t a i l e d d i s c u s s i o n on t h i s p o i n t i s g i v e n i n t h e l a s t s e c t i o n of t h i s c h a p t e r . • 3 Per f ormance_of _ D o l l J _ s _ D e c i s i o n _ R u l e The t h i r t y - t w o e x p e r i m e n t s performed were de s i g n e d t o p r o v i d e d a t a f o r comparing t h e two s c h e d u l i n g h e u r i s t i c s , t h e c l o s e s t customer h e u r i s t i c and t i m e saved h e u r i s t i c , and to i d e n t i f y the e f f e c t s of t h e d e c i s i o n r u l e parameters on the s o l u t i o n s d e v e l o p e d . A d i s c u s s i o n based on t h e a n a l y s i s of e x p e r i m e n t a l r e s u l t s l i s t e d i n TABLE_IV_.2 t o TABLE_IV._6 i s g i v e n below: 51 4,3.1 Effects of the Scheduling Heuristics and the Dispatching Decision Rule Parameters ME and MB J/ABJLJLIliZ l i s t s the differences i n performance measures res u l t i n g from the scheduling h e u r i s t i c s used in a l l experiments except those which were designed for testing the results of altered work policy or the application of the modified decision rules. The re s u l t s are as follows: (a) When the sectoring mechanism designed i n th i s research i s i n a c t i v e , ( in a l l experiments using sectoring mechanism S(1) or S (2) , ) T.S.H. always generates shorter mean tr a v e l time per customer than C„ C. H., although the difference i s small. T.S.H. also produces a lower mean service time per customer, and usually r e s u l t s in lower values of both service time standard deviation per customer and mean delivery time per customer, as well as delivery time standard deviation per customer. The implication i s that solution methods with T.S.H active are more preferable i n solving t h i s scheduling problem. (b) When the sectoring part of the dispatching decision rule i s i n a c t i v e , the mean tr a v e l time per customer ( also the mean service time per customer ) decreases and the mean delivery time per customer increases as the value of MB becomes- larger. However, service time standard deviation per customer i s r e l a t i v e l y unaffected by the value of t h i s parameter, as opposed T A B L E I V . 7 SUMMARY OF D I F F E R E N C E S I N PERFORMANCE MEASURES DUE TO THE SCHEDULING H E U R I S T I C S USED IN THE E X P E R I M E N T S E X P E R . D E S I G N D I F F E R E N C E IN PERFORMANCE MEASURES { C C . L E S S T . S . ) T R A V . T I M E MEAN S E R . S . D . O F S E R . MEAN D E L . S . D . O F D E L . ME MB S PER T IME T IME TIME TIME C U S T . PER C U S T . PER C U S T . PER C U S T . PER C U S T . lOOOO 0 S ( l ) 0 . 4 9 0 . 4 9 0 . 2 8 3 . 3 1 3 . 0 8 1 0 0 0 0 5 S( 1) 0 . 4 4 0 . 4 4 0 . 4 7 1 3 . 7 2 7 . 3 7 1 0 0 0 0 10 S ( l ) 0 . 6 9 0 . 6 9 - 0 . 0 4 9 . 2 1 2 6 . 1 5 1 0 0 0 0 1 5 S ( l ) 0 . 2 9 0 . 2 9 0 . 1 7 2 . 0 6 4 3 . 2 5 30 0 S U ) 0 . 2 9 0 . 2 9 - 0 . 0 9 6 . 4 7 1 3 . 6 3 25 0 S ( l ) 0 . 1 9 0 . 19 0 . 4 8 1 3 . 1 2 3 6 . 8 5 2 3 0 S<1> 0 . 6 2 0 . 6 2 1 . 1 5 - 4 7 . 2 4 - 2 5 . 9 9 21 0 S ( i ) 0 . 0 1 0 . 0 1 3 . 9 7 7 9 . 7 5 2 2 . 4 1 1 0 0 0 0 0 S ( 2 ) 0 . 2 1 0 . 2 1 0 . 0 4 - 3 . 8 4 - 1 . 0 6 1 0 0 0 0 0 S ( 3 ) 0 0 0 - 0 . 1 8 - 0 . 0 9 1 0 0 0 0 0 S<4) - 0 . 3 0 - 0 . 3 0 - 0 . 2 9 2 . 7 0 9 . 2 8 5 0 0 S ( 4 ) - 0 . 2 9 - 0 . 2 9 - 0 . 2 9 2 . 7 0 9 . 2 8 25 5 S d l - 0 . 0 2 - 0 . 0 2 1 . 5 6 7 . 0 9 4 5 . 4 3 TIME MEASURED IN M I N U T E S . 53 to the delivery time standard deviation per customer which increases as i t s value increases. These re s u l t s imply that i f the operating cost of the vehicle f l e e t ( to which mean t r a v e l time per customer and mean service time per customer are d i r e c t l y related) i s important, then a s u f f i c i e n t l y large value should be assigned to MB. If i t i s desirable to compromise the operating cost for higher e f f i c i e n c y in service in order to attra c t customers, then MB should be set to a smallest value possible. (c) When the sectoring part of the dispatching decision rules i s inactive, the mean t r a v e l time per customer ( also the mean service time per customer ) decreases and the mean delivery time per customer usually increases as the value of ME becomes smaller. A larger value of t h i s parameter usually r e s u l t s i n smaller service time standard deviation per customer and smaller d e l i v e r y time standard deviation per customer. These imply that i f the mean t r a v e l time per customer or the mean service time per customer i s important, then a small enough value should be assigned to ME. If the mean delivery time per customer i s more important, then ME should be set to a largest value possible. 54 4.3.2 Sectoring E f f e c t The performance measures l i s t e d i n TABLE., IV. 4 and T_BLE_IV_5 indicate that a l l f i v e measures are affected by the sectoring mechanism. Comparing the re s u l t s of the experiments using sectoring mechanism S{1) and S (2) , the l a t t e r mechanism leads to a decrease in mean travel time per customer, mean and standard d i v i a t i o n of service time per customer while i t increases the delivery time per customer mean and standard deviation. This suggests that increasing the number of sectors w i l l y i e l d a reduction i n t r a v e l time and hence mean service time per customer, but an accompanying loss i n customer service quality w i l l probably occur. When sectoring mechanism S (3) i s used i n conjunction with either one of the two scheduling h e u r i s t i c s , about 19 minutes mean t r a v e l time per customer ( hence about 29 minutes mean service time per customer ) i s achieved with only 19 customers being served within the entire six day period. This makes the low value in mean delivery time per customer meaningless. It appears that sectoring mechanism S (3) ( ALLTBASS's sectoring ) as a part of the decision rule conditions i s not appropriate i n solving t h i s scheduling problem. In another words, th i s sectoring mechanism simply does not combine well with the other parts of the decision rules. The res u l t s of experiments (3) and (4) i n SET D support t h i s conclusion. As seen i n TABL.E_I.Vi8, solution based on C.C.H. produces a mean tr a v e l time per customer of 15 minutes ( hence mean service time per customer i s T A B L E I V . 8 SUMMARY OF R E S U L T S OF EXPERIMENTS USING SECTORING MECHANISM S I 3 ) EXPERIMENTAL DESIGN T R A V . T IME PER C U S T . MEAN S E R . TIME PER S . D . O F S E R . T I M E PER MEAN D E L . T IME PER S . D . O F D E L . T IME PER TOTAL NO. OF C U S T . ME MB s D E C . RULES C U S T . C U S T . C U S T . C U S T . SERVED lOOOO 0 S ( 3 ) D O L L ' S D . R . WITH C . C . 19 29 72 101 5 9 19 1 0 0 0 0 0 S ( 3 ) MODIF IED D . R .WITH C . C . 15 25 5 148 8 0 178 1 0 0 0 0 0 S<3) D O L L ' S D . R . WITH T . S . 19 29 7 2 102 6 0 19 1 0 0 0 0 0 S ( 3 ) MODIF IED D . R .WITH T . S . 15 2 5 5 146 75 181 T IME MEASURED IN M I N U T E S . 56 25 minutes ) with a t o t a l of 178 customers being served i n six days. With T.S.H., mean t r a v e l time per customer i s 15 minutes ( hence mean service time per customer i s 25 minutes ) with a t o t a l of 181 customers being served in six days. This means that, the decision r u l e s were unable to operate under sectoring mecha nism S (3) . More important are the r e s u l t s of the experiments using sectoring mechanism S{4). This sectoring mechanism was designed with due consideration of the problem structure as well as in s i g h t into the operation of the decision rules. I t i s seen in T_BL__IV_9 that when C.C.H. i s used, sectoring mechanism S (4) can achieve a reduction in mean travel time and hence mean service time per customer as compared to those with an inoperative sectoring mechanism ( by using sectoring mechanism S(1) ). At the same time, mean delivery time per customer increases very rapidly. However, when T.S.H. i s used, mean t r a v e l time and hence mean service time per customer showed an increase together with an increase in mean delivery time per customer as compared to the results of the experiments using sectoring mechanism S(1). The unexpected increase in mean t r a v e l time and mean service time per customer can be explained by the design of t h i s sectoring mechanism i t s e l f . With t h i s sectoring mechanism, the area being served i s subdivided into smaller regions according to the clustering of customer demands. In this scheduling problem, customer demands are concentrated i n the down-town area, thus increasing the density of customers within small areas in the subregions located in down-town d i s t r i c t s . Such subdivision of the area can accomplish a more e f f i c i e n t TABLE I V . 9 COMPARISON ON RESULTS OF EXPERIMENTS USING SECTORING MECHANISM S I D AND S<4) R E S P E C - T I V E L Y E X P E R I M E N T A L D E S I G N T R A V . TIME MEAN S E R . S . D . O F S E R . MEAN D E L . S . D . O F D E L . ME MB s SCHEDULING H E U R I S T I C USED PER C U S T . T IME PER C U S T . T IME PER C U S T . T IME PER C U S T . T IME PER C U S T . lOOOO 0 S ( l ) C . C . 13 2 3 6 1 3 2 7 0 1 0 0 0 0 0 S<4) C . C . 13 2 3 16 4 2 1 3 0 3 1 0 0 0 0 0 SI 1) T . S . 13 2 3 5 129 6 7 1 0 0 0 0 0 S I 4 ) T . S . 13 2 3 17 4 1 8 2 9 4 T IME MEASURED IN MINUTES 58 performance for C.C.H. than for T.S.H.. I t i s evident that the performance of the decision rules depends largely on the s p e c i f i c a t i o n of sectoring. The number of sectors and t h e i r geographic l i m i t s depend on the area size and the expected demand density, while i n d i v i d u a l sector would be defined by the s p a t i a l d i s t r i b u t i o n of customer demands. Theoretically, the d e f i n i t i o n of each sector should be changed dynamically to allow the most e f f i c i e n t use of each vehicle i n solving a s p e c i f i c scheduling problem. In practice, however, sectors cannot be dynamically redefined. A powerful sectoring mechanism i s d i f f i c u l t to obtain, but i t should be problem oriented. 4.3.3 Effect of Combinations of Decision Rule Conditions Experiments (5) and (6) in SET D, using C.C.H. and T.S.H. respectively, have been performed with ME=50, MB=0 and sectoring mechanism S(4) active. In choosing values for ME and MB, several preliminary experiments were performed. These experiments had to be terminated because when ME was set to 50 or l e s s , the backlog of customer requests grew to a point where the assigned computer memory space was exceeded. Similar phenomena occurred i f ME was set larger than 0. These computational problems are caused by the f a c t that for the six day period, the 201 customer requests were scattered in 17 sectors. During the simulated period, there was usually only a limited number of customer requests for delivery to most of these 17 sectors. Hence, when r e l a t i v e l y low 59 HE or r e l a t i v e l y l a r g e MB v a l u e s were used i n c o n j u n c t i o n w i t h s e c t o r i n g mechanism S ( 4 ) , i t was i m p o s s i b l e t o d e v e l o p s c h e d u l e s and d i s p a t c h v e h i c l e s t o f o l l o w them. Hence, the e x p e r i m e n t s f a i l e d t o f i n d out whether a c o m b i n a t i o n of s e v e r a l d i s p a t c h i n g d e c i s i o n r u l e parameters can m i n i m i z e t h e t r a d e - o f f between low mean t r a v e l t i me and low mean d e l i v e r y time. The r e s u l t s o f e x p e r i m e n t s (5) and (6) i n SET D were found t o be c l o s e t o those o f t h e e x p e r i m e n t s i n SET C u s i n g s e c t o r i n g mechanism S(4) w i t h ME and MB i n o p e r a t i v e . As l i s t e d i n T_BLE_I__10, a comparison o f the r e s u l t s o f e x p e r i m e n t s (7) and (8) i n SET D t o t h o s e of the f o u r e x p e r i m e n t s u s i n g e i t h e r s c h e d u l i n g h e u r i s t i c and s e c t o r i n g mechanism S ( 1 ) , w i t h ME=25 and MB=0 or ME=10000 and MB=5 i n d i c a t e s the f o l l o w i n g : (a) When C.C.H. i s used: w i t h ME=25 and BB=5, t h e r e i s a 1 minute d e c r e a s e i n t r a v e l t i m e per customer { hence a l s o i n mean s e r v i c e time per customer ) accompanied by a 5 minutes i n c r e a s e i n mean d e l i v e r y time per customer compared t o t h e r e s u l t s of experiment w i t h ME=10000 and MB=5. There i s a l s o a 1 minute d e c r e a s e i n t r a v e l time per customer ( so i s mean s e r v i c e time per customer ) t o g e t h e r w i t h a 4 minutes i n c r e a s e i n mean d e l i v e r y t i m e per customer as compared to the r e s u l t s of the experiment w i t h ME=25 and MB=0. The s t a n d a r d d e v i a t i o n of s e r v i c e time per customer and th e s t a n d a r d d e v i a t i o n o f d e l i v e r y time per customer i n c r e a s e as compared to both e x p e r i m e n t s . T A B L E I V .10 T R A D E - O F F BETWEEN LOW MEAN TRAVEL TIME AND LOW MEAN D E L I V E R Y TIME BY MEANS OF COMBINATION OF CONDITIONS OF D I S P A T C H - ING D E C I S I O N RULES EXPERIMENTAL D E S I G N T R A V . MEAN S . D . O F MEAN S . D . O F TIME S E R . S E R . D E L . D E L . SCHEDULING PER T IME TIME T IME TIME H E U R I S T I C C U S T . PER PER PER PER ME MB S USED C U S T . C U S T . C U S T . C U S T . 25 5 S i l l C . C . 11 21 8 159 140 25 0 sen C . C . 12 22 7 155 125 10000 5 SI 1] C . C . 12 22 6 154 93 25 5 SI 1] T . S . 11 21 7 152 94 25 0 SI 1] T . S . 11 21 7 142 8 8 10000 5 S i l l T . S . 11 21 5 140 8 6 T IME MEASURED I N M I N U T E S . 61 (b) When T.S.H. i s used: with ME=25 and MB=5, there i s no change i n travel time per customer ( also i n mean service time per customer ) as compared to the res u l t s of the other two experiments. For mean delivery time per customer, there i s a 12 minutes increase compared to the r e s u l t of the experiment with ME= 10000 and MB=5, and a 10 minutes increase as compared to that of the experiment with ME=25 and MB=0. In most cases, the standard deviation of service time per customer and standard deviation of delivery time per customer increase as compared to both experiments. These re s u l t s demonstrate that c e r t a i n combination of conditions of the dispatching decision rules can minimize the trade-off required between low mean travel times and low mean delivery times to serve customers. 4.4 0ther_Ex£eriments aPPENDIX_II l i s t s the pertinent schedule time information on i n d i v i d u a l schedules from s i x d i f f e r e n t experiments. In the f i r s t pair of experiments with ME=10000,MB=0 and sectoring mechanism S(1) act i v e , 52 per cent of the schedules served contain only one customer when C.C.H. i s used. This changes to 46 per cent when T.S.H. i s used. These singleton schedules ( i.e„, schedules containing only one customer ) tend to increase the mean tr a v e l time per customer. The generation of the singleton schedules re s u l t s from a broad dispersion of customer demands in t h i s given problem. 62 The second pair of experiments chosen take on parameter values of ME=50, MB=0 and active sectoring mechanism S(4), using C.C.H. and T.S.H. respectively. About 30 per cent of the schedules were found to be singleton schedules, suggesting that th i s sectoring mechanism f a i l e d to eliminate singleton schedules. With sectoring mechanism S (4) active, the area being served i s subdivided into smaller regions which aggregate customer demands. Rejection of singleton schedules i n a region increases the backlog of customer demands, because according to Doll's dispatching rules, no vehicle can be dispatched to the next sector unless at least one vehicle has been dispatched in the sector being considered. In the third pair of experiments which has ME = 25 and MB = 5, with sectoring mechanism S(1) active , using C.C.H. and T.S.H. respectively, i t i s found that each schedule contains at least 3 customers. Travel time per customer was reduced from 13 to 11 minutes as compared to the r e s u l t s of the f i r s t pair of experiments. This shows that given a r e s t r i c t i o n on the minimum l e v e l of e f f i c i e n c y and/or a minimum backlog of customer requests, singleton schedules w i l l be rejected as a result of the long travel time required. Of course, r e s t r i c t i o n in t r a v e l time per customer w i l l be accompanied by increasing time to s a t i s f y a customer afte r i t s a r r i v a l , when r e s t r i c t i o n in e f f i c i e n c y l e v e l and/or backlog of customer requests i s set. Another two experiments, using C.C.H. and T.S.H. respectively, and with WE=10000, MB=0,and sectoring mechanism S{1) active, were performed to investigate the scheduling 63 re s u l t s on extending the operation hours from f i v e to ten hours per day. I t i s found (see TABLE^IV.6 , experiments (1) and (2)) that by a l t e r i n g the work policy as discribed, no change occurs i n t r a v e l time ( hence mean service time ) per customer but there i s an increase in the standard deviation of service time per customer, and the mean and standard deviation of delivery time per customer . The conclusion i s that extending operation hours can only enable the completion of service for a l l customer requests occuring within the same day but the travel time ( hence mean service time ) per customer w i l l not be affected. 64 CHAPTER V CONCLUSIONS In t h i s s t u d y , D o l l ' s d e c i s i o n r u l e s have been s u c c e s s f u l l y a p p l i e d t o an a c t u a l s c h e d u l i n g s i t u a t i o n . The performance of D o l l ' s d e c i s i o n r u l e s on t h i s s p e c i f i c s c h e d u l i n g s i t u a t i o n i s summarized below, (a) For t h i s a c t u a l s c h e d u l i n g problem, D o l l ' s d e c i s i o n r u l e methods do not improve the s o l u t i o n s i n terms o f r e d u c i n g t r a v e l time per customer. A p p l i c a t i o n of t h e s e methods, however, can p o s s i b l y produce h i g h e r s e r v i c e q u a l i t y i n terms o f r e d u c i n g t h e time to s a t i s f y a customer r e q u i r e m e n t a f t e r i t s o c c u r r e n c e . I t i s found t h a t t h e volume and d i s p e r s i o n of customer r e q u e s t s i n t h i s s c h e d u l i n g problem a re p r o b a b l y not a p p r o p r i a t e f o r a l l o w i n g competent performance of the d e c i s i o n r u l e s . (b) Compared w i t h t h e c l o s e s t customer s c h e d u l i n g h e u r i s t i c , t h e time saved s c h e d u l i n g h e u r i s t i c r e s u l t s i n c o n s i s t e n t l y s h o r t e r mean t r a v e l time (hence mean s e r v i c e t i m e ) per customer and, i n many c a s e s , a s h o r t e r t i m e t o s a t i s f y a customer r e q u e s t a f t e r i t s o c c u r r e n c e . The time saved h e u r i s t i c i s t h e r e f o r e shows b e t t e r performance i n s o l v i n g t h i s s c h e d u l i n g problem. 65 (c) Both maximum e f f i c i e n c y condition and minimum backlog condition of the dispatching decision rules can a f f e c t the mean t r a v e l time ( hence mean service time ) per customer and mean time to s a t i s f y a customer request after i t s occurrence. These times cannot be j o i n t l y minimized. However the trade-off between them can be control by using d i f f e r e n t combinations of parameters of the dispatching decision rules, e s p e c i a l l y the maximum e f f i c i e n c y parameter and the minimum backlog parameter. (d) Geographical r e s t r i c t i o n i s found to have ef f e c t s on a l l f i v e performance measures, i e tr a v e l time per customer, mean and standard deviation of service time per customer, mean and standard deviation of delivery time per customer. The effect of t h i s r e s t r i c t i o n depends b a s i c a l l y on the design of a sectoring mechanism. For the vehicle-scheduling problem under study, i t i s most impossible to examine a l l important topics i n d e t a i l , me topics, however, should be mentioned as p o t e n t i a l l y u i t f u l areas for further research. They include: (a) Studies on the ef f e c t s of the within sector condition of the dispatching decision r u l e s , with emphasis on the design of a s p e c i f i c sectoring mechanism; (b) Studies on the use of combinations of conditions of 66 the dispatching decision rules to control the trade- off between mean t r a v e l times (or mean service times) per customer and mean times to s a t i s f y a customer request a f t e r i t s occurrence. 67 BIBLIOGRAPHY 1. A l t r a a n , S.M., Bhagat, N . and Bodin, C., " E x t e n s i o n of the C l a r k e and Wright P r o c e d u r e f o r R o u t i n g T r u c k s " . Paper P r e s e n t e d a t t h e X V I I I I n t e r n a t i o n a l M e e t i n g of the I n s t i t u t e o f Management S c i e n c e s , Washington, D. C. , March 1971. 2. B a l i n s k i , M.L. and Quandt, R.E., "On an I n t e g e r Program f o r a D e l i v e r y Problem", „erations_Research , V o l . 1 2 , No.2, 1964. 3. Bowman, E.H., " C o n s i s t a n c y and O p t i m a l i t y i n M a n a g e r i a l D e c i s i o n Making", Manaaement_Science , V o l . 9 , 1963. 4. Bruggeman, J.M. and H e a t h i n g t o n , K.W., " S e n s i t i v i t y t o V a r i o u s P arameters of a Demand-Schedule Bus System Computer S i m u l a t i o n Model", T r a n s ^ o r t a t i c n_S^s terns P l a n n i n g , Report No. 293, Highway Research Board, 19697 5. C h r i s t o f i d e s , N., " F i x e d Routes and Areas f o r D e l i v e r y O p e r a t i o n s " , The I n t e r n a t i o n a l m J o u r n a l _ o f _ P h y s i c a l D i s t r i b u t i o n , V o l . 1 , No.2, F e b r u a r y 1971. 6. C h r i s t o f i d e s , N- and E i l o n , S., "An A l g o r i t h m f o r t h e V e h i c l e D i s p a t c h i n g Problem", Q p e r a t i o n a 1 R e s e a r c h Q u a r t e r l y , V o l . 2 0 , No.3, 1969. 7. C l a r k e , G. and W r i g h t , J.M., " S c h e d u l i n g of V e h i c l e s from a C e n t r a l Depot t o a Number of D e l i v e r y P o i n t s " , 0 „ r a t i o n s _ R e s e a r c h , V o l . 1 2 , No. 4, 1964. 8. C r o e s , G.A., "A Method of S o l v i n g T r a v e l l i n g Salesman Pr o b l e m s " , O p e r a t i o n s _ R e s e a r c h , V o l . 5 , No.6, 1958. 9. D a n t z i g , G.B- and Ramser, J.H., "The Truck D i s p a t c h i n g Problem", Management_Science , V o l . 6 , No. 1, 1959. 10. D o l l , C.L., l _ S i m u l a t i o n _ S t u d y _ o f _ a _ D j n a m i c _ V e h i c l e - „b„Miii__l_E£2]32_._! • Ph.d D i s s e r t a t i o n s , K r a n n e r t Graduate S c h o o l of I n d u s t r i a l A d m i n i s t r a t i o n , Purdue U n i v e r s i t y , West L a f a y e t t e , I n d i a n a , March 1974. 11. F l o o d , M., "The T r a v e l l i n g Salesman Problem", O p e r a t i o n s Research , V o l . 4 , No.1, 1956. 12. G a s k e l l , T . J . , "Bases f o r V e h i c l e F l e e t S c h e d u l i n g " , 2£§:£_._-i2r__Ll_Beŝ  , V o l . 1 8 , No.1, 1967. 13. Gordon, G. and Z e l i n , K., "A S i m u l a t i o n Study of Emergency Ambulance S e r v i c e i n New York C i t y " , T r a n s a c t i o n s _ N e w 68 Y o r k _ A c a _ e _ _ _ o f _ S c i e _ c e s , 1971. 14. Hays, R.L., The D e l i v e r y Problem . Report M SR 106, Graduate S c h o o l of I n d u s t r i a l A d m i n i s t r a t i o n , C a r n e g i e I n s t i t u e of T echnology, 1967. 15. H e a t h i n g t o n , K.W. and Bruggeman, J.M., "The Use of Computer S i m u l a t i o n t o A n a l y z e a Demand-Scheduled Bus System". Paper P r e s e n t e d a t t h e P i t t s b u r g h S i m u l a t i o n and M o d e l l i n g C o n f e r e n c e , A p r i l 1969. 16. H e a t h i n g t o n , K.w., M i l l e r , J . , Knox, S.R., H o f f , G.L. and Bruggeman, J . , "Computer S i m u l a t i o n s of a Demand- Scheduled Bus System O f f e r i n g Door-To-Door S e r v i c e " , i l E b a _ _ _ a s s _ T r _ _ _ _ _ r t a _ , Report No. 251, Highway R e s e a r c h Board, 1968. 17. Held, M. and K a r p , R.M., "A Dynamic Programming Approach t o Sequencing Problems", J o u r n a l _ o f _ t _ e _ S o c i e t _ _ o f I_^__t_i_l_and_A_£lie^ , V o l . 1 0 , No.1, 1962. 18. L i t t l e , J.D.C., Murty, K.G., Sweeney, D.W. and K a r e l , C. , "An A l g o r i t h m f o r t h e T r a v e l l i n g Salesman Problem", 2£6£5tions_Research , V o l . 1 1 , No.8, 1963. 19. Noonan, R. and Whinston, A., "An I n f o r m a t i o n System f o r V e h i c l e S c h e d u l i n g " , Software_A_e , December 1969. 20. O ' N e i l , B.F., A p p r o a c h e s t o t h e V e h i c l e S c h e . Ph.d D i s s e r t a t i o n s , K r a n n e r t Graduate S c h o o l of I n d u s t r i a l A d m i n i s t r a t i o n , Purdue U n i v e r s i t y , West L a f a y e t t e , I n d i a n a , August 1971. 21. P r i t s k e r , A.A.B.and K i v i a t , P . J . , S i m u l a t i o n s w i t h G A S P I I , P r e n t i c e - H a l l I n c . , Englewood C l i f f s , New J e r s e y , 1969. 22. Wagner, H.M., P_inci_les_gf^Q£erati^ns_Resea^ch * P r e n t i c e - H a l l I nc. , Englewood C l i f f s , New J e r s e y , "1965. 23. W i l s o n , N.M.H., Sussman, J.M., Hi g o n n e t , B.T. and Goodman, L.A., " S i m u l a t i o n o f a Computer-Aided R o u t i n g System (CARS) ", M A S S T r a n s p o r t a t i o n , Report No.318, Highway Research Board, 1970. APPENDIX I R e c o r d s o f S c h e d u l e s S u p p l i e d by ALLTRANS and Customer I n f o r m a t i o n O b t a i n e d f r o m These R e c o r d s Equipment No. /to ̂ 7 CASH AND DELIVERY RECORD Station Pro. No. Consignee Weight Total to Collect Remarks Pro No. Consignee Weight Total to Collect Remarks AV 7fct ff) fs<*€> /ff. An. ; . r ' SA/cY* m: ..TTT. W —r^^, ^ % ^ * «> •r jf ~f— /a. i . T# //r far 4; ^ jj K » U \\ ^ «» f t a. . • ^ / {&) i * / > / ' f fa /// ^. to / f i r , — * « • — ' *• o Equipment No. Driver's Name_ put t>*7 CASH AND DELIVERY RECORD Station Date 7- 7* Pro. No. Consignee Weight Total to Collect Remarks Pro No. Consignee Weight Total to Collect Remarks 0) ft A) rs*jff 1 t ~ r (j r If & - - • / / W . f '*? > 9 f fa.) / 7 9  w — ^ — -" r - -i i—1 Form No. 205-A Equipment No. CASH AND DELIVERY RECORD Station Pro. 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No. Consignee Weight Total to Collect 'T — Remarks Pro No. Consignee Weight Total to Collect Remarks SO f<4/> At.fr). zr*./r>. sj/rtu. /&/>C 9-'f84L./n. 0 70.- ML ftu> r* S3) f fa ^ r J.*V>. / A) fe? fa) /0 S V 64/ ft);ST /2»> ^ — - / — i r\ — o Form No. 205-A CASH AND DELIVERY RECORD Equipment No p6fj> o^^/ 7 Station Driver's Name 7~' xfostJllSU Date <7" °? ~ 7^ Pro. No. Consignee Weight Total to Collect Remarks Pro No. Consignee Weight Total to Collect Remarks £7779* 70 tJfit t 72) (F• r?~ /4 sr> cyrst to fy. M— # ; //) 4 . » 1 / //9r f —f- •— ' 7\)MJLA/U1JQJL. f / r f —0. ^ T fcl • r 1 dr. I* 7c, //> /.r<* TC p7 (CLL&A/VUUH to F •it a tn. //./.<- At. 1 t r 7J/>AJt 7<r, // //:<3^<* 37/: I t TO 7*9 /** a. / / // y.r: — r — t -f Form No. 205-A CASH AND DELIVERY RECORD Equipment No Driver's N a m e . Station Date £~<=$ ~73 Pro. No. Consignee Weight Total to Collect Remarks Pro No. Consignee Weight Total to Collect Remarks k6r97/ fl sss> 7s) " d./n dUiF 6 fa d.to. 77dArfb2^ S^OA^bJ. 7*f 7±> —** V *— r/i/» 9 d.to ( *• • — — " — • ^ J>S>f* /d) 0d.M /£. > ://> d./r) PAJ 7JI C7ay//ri {$/id( J7f Fa) § 7** lad.AT) S' styF&7 S SJ0 /?-) /J * SSa J. to St M S 77/ 7?lA.t Sfpi^Jrusif fr 7* y ? d to AdJn? / m Sk) £ (Sftfj/ 0.2 74) S) // -jf^./> } MS ?fd rat 77) / / A* St to // ^ /a4'.A 7 •— g v • t PA) 72 r f ^ fa 7f) /a d./y> / / ://"/? ' *? ML / /{ ; f 7 3 d *? / " vO' IV) CASH AND DELIVERY RECORD Equipment No PC(P S~6/ Station Driver's N a m e ^ f e * //jJ/T UduJ ft/f^J*. ' ^ " - ^ Pro. No. Consignee Weight Total to ^ Collect 1 ' l ^ f l " j Remarks Pro No. Consignee Weight Total to Collect Remarks MLJS/ 7<J*0 (7? 'af.Sri 0*/jty TD 9U A> /0 :df~J.#> . /0~/< t T# 626 ? / / 7 fa) S0 . 70 '1 7 sil /». c^/f/7^. M / /// ' f /0:22. d An M L £fa 1 lr*£a & 7L idt /? /to / / . \ 4l sf syj fA)6r art ACM £00 //./r 2d* d./r> M L tfo M? #7 ft: TD iff Art* 0Usi . M 7?) //i @0 /*.#>. 7/ 7~2 j./ri TD fw 7/\f~l j . / n . /<* > 7-OlJ A/y>. /i <£.CAM- T0 0/0 &utf 4-$0A^ r 7rJ r 1 fair aft fa) //•* d>£ d./yt. / / / r • X - J ,4 & TD M L 3-70 fa) TD 0Sf t 7/s) v r ' /fA*n — • %/ , . ter* ^m— Form No. 205-A CASH AND DELIVERY RECORD Equipment No f'Clp' — / Station Driver's Name N• T' It<*-*SLCLAJ Date 6/~ t ~ ^1 Pro. No. Consignee Weight Total to Collect Remarks Pro No. Consignee Weight Total to Collect Remarks TD/fT /f7)/L*>jLM£ *2-0O 7/) ^yi7/j^/c/ 7t/t 0.0 ~3 /to ra t/o 6tr 7V 9^ /r*. fi> . 7SIMA4/JM, tt/f. /^r 74) r *> J./y> 49t 4: 0rA-/y> . 9; /£/}.'»> TD 697 /tlo 7t) / i f , J M L 2/4 A). 7/)AJ4AJLHJ fir) /J fa. 7(^6 J .ffivvt. 7?) /0SJ1O a. fin . *=—f~ /* AT*, fin '7' _ f . & u > . t/6) /.* /«> f/r>. /? /rA/r) ?v /r<t &7' /•- r 2/ p./y> TO /1J, ///) //•• It? J fin . // f 'If J.") 70 //srz> a. /j > //) A to LA)7)A/J^JLJ, I £ WE -M- Tit M L ^r 7?) ///t 4.fi>. // BAI 711 » TD 6/9 90 7/t) /-c*/ p./n. /: M L 2oQ i ' 9 a/i 7t) f //cora.fii. // A. fit / /Ajt/A 31<7 7?) 70 < /0 a.fii. 70 ? 7ra.fi? BNjrr SuJ)/ XTUAA c276 ALAJnJ dUd/f) Form No. 205-A LASH AND DELIVERY RECORD Equipment No Station Driver's Name i~ Date Pro. No. Consignee Weight Total to Collect Remarks Pro No. Consignee Weight Total to Collect Remarks A S ) ^.to?. //*) / T J7A./r? f //.' #0 A.to . L / : ' r M L p/r ftr) / i /ft p. to) . A A to! /s&s A to. r terAto. f * i Lat-frf.to. /<* ? fz/>.to? 7 ' f -. vn Form No. 205-A Equipment No. pap t>*7 CASH AND DELIVERY RECORD Station Pro. No. Consignee Weight Total to Collect Remarks Pro No. Consignee Weight Total to Collect Remarks ML <7<& Q-fcC At.toi. Aft f*< O J . / V y ^ L<£7 7/) fc*2P / MLst7£> ' / fr//> / //) *3f~ A.to. / //••< >S~4*tot. M/ AJ..C J6L7 79, //^rA. to. //;. ZA/r? /Al fff r f?30 a. to. M L £ ± L & f /!f/»jdi2SJi set 77) / " 7/>i 3a d. to M/ 1? 7 //'i //> A.to . //; 2j *./?) * f / /fo/> //•' 3a A.Mo. /A £T~A.to. UL 'Jrtod. (/f/A/u/j if9 //r P.M. M L m -  7 7 /7L> t r 6', r /d? &o P./n. /* — f" ML r &) r /: //? />./y) . / ' />,/> ? . -r— ML 17* 7D ML SAC 7f) t f #-7& A.to. t > M <7Sa7/-u. Ml 6/3 ^)IJOE6 10/id 7jr / Pz> p. to). / / M/ fa£ /TT faitJ. S» 7* 7?r) r /•' 3 c p.to. / • -iC P./ y? /TAJ 7/7 yF— ///, r Pto. /• f n. Form No. 205 -A E q u i p m e n t N o . Dr iver 's N a m e _ CASH AND DELIVERY RECORD 7T AfMtSU S t a t i o n P r o . N o . Cons ignee Weight T o t a l to C o l l e c t R e m a r k s Pro N o . Cons ignee Weight T o t a l to C o l l e c t R e m a r k s TD <pd /llaJ/MUu7 ft) / / . ' 2C /f.fr) . To /ft>7 7^ / / // i If, f./yj. TD If/ fa 73) ft ;//io4./y). // 0 er* t f / cJt?f \/r>. IS w * ( f f - 0 Form No. 205-A Equipment No . . Driver's N a m e _ CASH AND DELIVERY RECORD 21 ${><L*>MJ Station Date fr-A-yf Pro. No. Consignee Weight Total to Collect Remarks Pro No. Consignee Weight Total to Collect Remarks TC *3Jt 7/) t9tf /.• la a. ML //?7 /Q/Ltot AJ>/t) —5^ —•=*— to C /j tyi. ryi. M 7JL7 7l) / • < 'AT*, /yj. to TC /?* 7(A) /f* u fTA./r? . 4; AD A to) r ML 4*'7 77-) a. AC A. to . 7 f; /A A \to , — / M/ (/ Bsif-pJ) TUT/* 70 /A A. to) . f to /l/tiyif/W 71&+ to / J^f A. to >~" S A. to TC 7/7 f iT . /jstto/s/tUAJ 7f) < <zr j-to. / A> [7AJ.IAJLAAM /  r 00 CUSTOMERS INFORMATION CUST. DAY LOCATION DEMAND NO. X Y 1 1 -1180.00 370.00 59.00 2 1 -1020.00 322.00 48.00 3 1 -369.00 -380,00 20.00 4 1 , -1292.00 416.00 132.00 5 1 -119.00 -822.00 244.00 6 1 -1321.00 400.00 44.00 7 1 -860.00 435.00 136.00 8 1 -1182.00 50.00 16.00 9 1 - 142.00 401.00 261,00 10 1 -1215.00 172.00 13.00 11 1 -1265.00 140.00 3.00 12 1 -1215.00 145.00 196.00 13 1 -1435.00 125.00 81.00 14 1 -1392.00 70.00 355.00 15 1 -356.00 247.00 17.00 16 1 -1427.00 397,00 259,00 17 1 -945.00 160.00 111.00 18 1 -1240.00 160.00 39.00 19 1 -1240.00 100.00 24.00 20 1 -1515.00 -260.00 34.00 21 2 -1210.00 115.00 11. 00 22 2 -1392.00 70.00 12-00 23 2 -1316.00 170.00 339.00 24 2 -1890.00 -468.00 14. 00 25 2 -1090.00 -849.00 147.00 26 2 -874.00 317.00 1.00 27 2 -1 182.00 50. 00 289.00 28 2 -1148.00 434.00 35.00 29 2 -1269.00 82.00 14.00 30 2 -1211.00 -300.00 19.00 31 2 -1092.00 -848.00 85.00 32 2 -32.00 230.00 52.00 33 2 -978.00 340.00 40.00 34 2 -1019.00 264.00 42.00 35 2 -1400.00 -880.00 102.00 36 2 -852.00 317.00 19.00 37 2 -1449.00 308.00 373.00 38 2 -1098.00 425.00 26.00 39 2 -874.00 317.00 12.00 40 2 -1260.00 81.00 106.00 41 2 -1410.00 -450.00 7.00 42 2 -1182.00 50.00 22.00 43 2 -1400.00 -480.00 21.00 44 2 -1240.00 128.00 63.00 45 2 -1120.00 80,00 354.00 46 2 -1284.00 -562.00 264.00 47 2 -1460.00 70.00 11. 00 48 2 -370.00 -392.00 150.00 49 2 -1350.00 130.00 75.00 50 2 -1075.00 2.30,00 100 . 0 0 51 2 -1092.00 -858.00 7.00 52 2 -910.00 390.00 4. 00 53 2 -1400.00 -480.00 62.00 54 2 -1098.00 425.00 58 . 0 0 55 3 -974.00 -850.00 5 0 5 . 0 0 56 3 -910.00 318.00 25 0. 00 57 3 -1445.00 310.00 26 . 0 0 58 3 -1364.00 -700.00 1.00 59 3 -1242.00 -795.00 118 . 0 0 60 3 -1030.00 412.00 31. 0 0 61 3 -1092.00 -849.00 37 . 0 0 62 3 -885.00 402.00 41 . 0 0 63 3 -1094.00 -300.00 305 . 0 0 64 3 -1258.00 -860.00 17.00 65 3 -945.00 343.00 36 , 0 0 66 3 -1386.00 -480.00 46 . 0 0 6 7 3 -1632.00 -860.00 15-00 68 3 -1116.00 67.00 15 . 0 0 69 3 -1210.00 115.00 102 . 0 0 70 3 -1298.00 -850.00 230.00 71 3 -963.00 -768.00 53.00 72 3 -1540.00 -950.00 236 . 0 0 73 4 -1640.00 65.00 18 . 0 0 74 4 -1118.00 220.00 244 . 0 0 75 4 -1454.00 70.00 3 . 0 0 76 4 -20.00 -90.00 48.00 77 4 -1380.00 80.00 215 . 0 0 78 4 -1182.00 50.00 540. 00 79 4 -1410.00 472.00 2 . 0 0 80 4 -1455.00 25.00 122 . 0 0 81 4 -120.00 110.00 6 . 0 0 82 4 -28.00 229.00 32.00 83 4 -1532.00 87.00 64.00 84 4 -22.00 -65.00 85.00 85 4 -1118.00 220.00 118 . 0 0 86 4 -853.00 420.00 42 . 0 0 87 4 -1210.00 -885.00 35 . 0 0 88 4 -505.00 -652.00 190 . 0 0 89 4 -30.00 -59.00 18 . 0 0 90 4 -1956.00 72.00 19.00 91 4 -2394.00 57.00 3.00 92 4 -972.00 -850.00 6 . 0 0 93 4 -48.00 -509.00 172.00 94 4 -1458.00 436.00 15 . 0 0 95 4 -1676.00 148.00 83.00 96 4 -30.00 -60.00 6.00 97 4 -1178.00 130.00 57 . 0 0 98 4 -1210.00 -897.00 407 . 0 0 99 4 -1810.00 -760.00 3.00 100 4 -623.00 66.00 26 . 0 0 104 4 -1620.00 290.00 3 . 0 0 102 4 -2169.00 -110.00 1.00 103 4 -1417.00 -886.00 17.00 .104 4 -958.00 315.00 103 . 0 0 105 5 -958.00 165.00 14 . 0 0 106 5 -985.00 115.00 54 . 0 0 107 5 -1072.00 278.00 2 0 . 0 0 108 5 -958.00 165.00 14 . 0 0 109 5 -80.00 -500.00 12 . 0 0 100 110 5 -979.00 314.00 4 5 . 0 0 111 5 -1024.00 414.00 43.00 112 5 -1020.00 300.00 413.00 113 5 -872.00 391.00 34. 0 0 114 5 -955.00 312.00 62.00 115 5 -610.00 311.00 170.00 116 5 -913.00 180.00 176.00 117 5 -979.00 340.00 205.00 118 5 -1355.00 339.00 5 . 0 0 119 5 -352.00 198.00 2 5 . 0 0 120 5 -940.00 225.00 273.00 121 5 -1200.00 100.00 2 3.00 122 5 -958.00 262.00 7.00 123 5 -1083.00 383.00 6.00 124 5 -1211.00 -100.00 31.00 125 5 -1420.00 120.00 52.00 126 5 -1290.00 86.00 5 . 0 0 127 5 -991.00 388.00 106.00 128 5 -958.00 191.00 6.00 129 5 -1360.00 142.00 34.00 130 5 -1098.00 356.00 7 . 0 0 131 5 -1095.00 432.00 8 . 0 0 132 5 -1214.00 145.00 67.00 133 5 -1068.00 221.00 5.00 134 5 -932.00 282.00 8. 0 0 135 5 -932.00 425.00 394.00 136 5 -422.00 550.00 6 2 . 0 0 137 5 -1110.00 432.00 3.00 138 5 -1081.00 230.00 39.00 139 5 -1092.00 432.00 98.00 140 5 -1066.00 220.00 27.00 141 5 -1270.00 130.00 1 0 . 0 0 142 5 -910.00 390.00 29.00 143 5 -980.00 340,00 160.00 144 6 -1214.00 70.00 74.00 145 6 -805.00 -235.00 26.00 146 6 -1472.00 302.00 19.00 147 6 -1190.00 192.00 9 . 0 0 148 6 -910.00 390.00 25.00 149 6 -1686.00 146.00 9.00 150 6 -957.00 230.00 20.00 151 6 -1410.00 355.00 1.00 152 6 -878.00 375.00 2 9 . 0 0 153 6 -1190.00 52.00 8 . 0 0 154 6 -950.00 220.00 3.00 155 6 -1213.00 190.00 293.00 156 6 -1805.00 25.00 5. 00 157 6 -1290.00 140.00 3 7 . 0 0 158 6 -957.00 227.00 3 8 . 0 0 159 6 -1010.00 300.00 12.00 160 6 -1395.00 460.00 17.00 161 6 -1090.00 168.00 224.00 162 6 -720.00 392.00 5. 00 163 6 -1030.00 412.00 26 9 . 0 0 164 6 -990.00 340.00 1 0 . 0 0 165 6 -1100.00 60.00 10.00 166 6 -977.00 405.00 19.00 167 6 -958.00 165.00 15.00 168 6 -1380.00 80.00 5 1 . 0 0 169 6 -958.00 410.00 1 0 . 0 0 101 170 6 -915.00 318.00 25.00 171 6 -1700.00 100.00 7.00 172 6 -1182.00 50.00 32.00 173 6 -1075.00 413.00 1.00 174 6 -1144.00 136.00 6.00 175 6 -1298.00 82.00 4 . 00 176 6 -1788.00 70. 00 22.00 177 6 -1215.00 190.00 201.00 178 6 - 840.00 420.00 44.00 179 6 -1680.00 163.00 41. 00 180 6 -1261.00 141.00 23.00 181 6 -1474.00 300.00 41.00 182 6 -1462.00 70. 00 26.00 183 6 -1610.00 150.00 22.00 184 6 -1635.00 20.00 103.00 185 6 -1110.00 430.00 19.00 186 6 -1350.00 110.00 1 8 . 0 0 187 6 -1180.00 130.00 195.00 188 6 -760.00 530.00 9.00 189 6 -1300.00 175.00 17.00 190 6 -980.00 340.00 115.00 191 6 - 724.00 270.00 45.00 192 6 -980.00 345.00 2.00 193 6 -1220.00 355.00 14.00 194 6 -1190.00 432.00 7.00 195 6 -772.00 452.00 43.00 196 6 -958.00 325.00 41.00 197 6 -1350.00 140.00 4.00 198 6 -1300.00 131.00 1 3 . 0 0 199 6 -1318.00 372.00 3 1 . 0 0 200 6 -910.00 390.00 41.00 201 6 -1300.00 412.00 9.00 APPENDIX II S c h e d u l e Time I n f o r m a t i o n o f S i x E x p e r i m e n t s TRAVEL TIME INFORMATION ON INDIVIDUAL SCHEDULES IN THE EXPERIMENT WITH ME=100QO» MB=Q AND SECTORING MECHANISM S ( l ) t USING CLOSEST CUSTOMER HEURISTIC DAY SCHEDULE TOTAL NO.OF CUST. S C H E D . TIME NO. SCHEDULE SERVED IN / CUST, TIME THE SCHED. 1 1 137.94 6 22.99 1 2 41.78 1 41.78 1 3 43.77 1 43 . 77 1 4 154.79 8 19.35 1 5 88.20 3 29.40 1 6 47.08 1 47.08 2 7 44.67 1 44.67 2 8 47.08 1 47.08 2 9 46.08 1 46.08 2 10 251.67 13 19.36 2 11 224.71 12 18.73 2 12 62 .01 2 31.01 2 13 71.44 2 35.72 2 14 49.54 1 49.54 2 15 49 .57 1 49.57 3 16 48.50 1 48.50 3 17 41.36 1 41.36 3 18 49.53 1 49.53 3 19 168.35 8 21.04 3 20 134.27 6 22.38 3 21 55.93 1 55.93 4 22 50.23 1 50.23 4 23 44.00 1 44.00 4 24 47.93 1 47.93 4 25 239.75 13 18.44 4 26 232.48 11 21.13 4 27 4 3.77 1 43.77 4 28 78.55 3 26.18 4 29 51.93 1 51.93 5 30 40.80 1 40.80 5 31 40.89 I 40.89 5 32 43.74 1 43.74 5 33 233.64 14 16.69 5 34 13 4.86 6 22.48 5 35 139.63 7 19.95 5 36 121.69 6 20.28 5 37 81.87 3 27.29 6 38 44.42 1 44.42 6 39 38.61 1 38.61 6 40 49.82 I 49.82 6 41 202.25 12 16.85 6 42 249.74 15 16.65 6 43 248.28 14 17.73 6 44 58.13 2 29.06 TRAVEL TIME INFORMATION ON INDIVIDUAL SCHEDULES IN THE EXPERIMENT WITH ME=lQOQQt MB=Q AND SECTORING MECHANISM S ( l ) , USING TIME SAVED HEURISTIC DAY SCHEDULE TOTAL NO.OF CUST. SCHED. TIME NO. SCHEDULE SERVED IN /CUST. TIME THE SCHED. 1 1 136.18 6 22.69 1 2 41 .78 1 41.78 1 3 43.77 1 43.77 1 4 14 0.83 7 20.12 1 5 82.22 3 27.41 1 6 59.21 2 29.60 2 7 44.67 1 44.67 2 8 47.08 1 47.08 2 9 46.68 1 46.68 2 10 165.61 8 20 . 70 2 11 138.17 6 23.03 2 12 230.98 12 17.77 2 13 71.44 2 35.72 2 14 62.91 2 31.45 3 15 48.50 1 48.50 3 16 41.36 1 41.36 3 17 49.53 1 49.53 3 18 132.99 6 22. 16 3 19 118.67 5 23.73 3 20 93.34 4 23.34 4 21 50.24 1 50.24 4 22 44.00 1 44.00 4 23 47.93 1 47.93 4 24 247.66 12 20.63 4 25 121.52 5 24.30 4 26 173.28 9 19.25 4 27 44.78 2 22.39 4 28 43.77 1 43.77 5 29 40.80 1 40.80 5 30 40.89 1 40.89 5 31 43.74 1 43.74 5 32 253.17 15 16.88 5 33 100.58 5 20.12 5 34 200.13 11 18.19 5 35 74.84 3 24.95 5 36 3 5.73 1 35.73 5 37 42.87 1 42.87 6 38 44.42 1 44.42 6 39 38.61 1 38.61 6 40 49.82 1 49.82 6 41 259.86 15 17.32 6 42 222.47 13 17. 11 6 43 219.42 13 16.88 TRAVEL TIME INFORMATION ON INDIVIDUAL SCHEDULES IN THE EXPERIMENT WITH ME =50, MB=0 AND SECTORING MECHANISM S(4) T USING- CLOSEST CUSTOMER HEURISTIC DAY SCHEDULE TOTAL NO.OF CUST. SCHED. TIME NO. SCHEDULE SERVED IN / CUST, TIME THE SCHED. 1 1 41.78 1 41.78 1 2 29.25 1 29.25 1 3 32.27 1 32.27 1 4 37.89 1 37.89 3 5 48.50 1 48.50 3 6 77.89 3 25.96 3 7 40.53 1 40.53 3 8 16 0.18 9 17.79 3 9 90.96 4 22.74 3 10 87.52 4 21. 88 3 11 158.96 9 17.66 3 12 106.04 5 21.21 3 13 63.47 2 31. 73 4 14 90.91 4 22 . 73 4 15 159.78 8 19.97 4 16 155.29 7 22. 18 4 17 90.62 3 30.21 4 18 41.49 1 41.49 4 19 94.45 5 18.88 4 20 105.98 6 17 . 66 4 21 63.38 2 31.69 5 22 48.48 1 48.48 5 23 88.09 3 29.36 5 24 55.53 2 27.77 5 25 128.19 7 18.31 5 26 131.28 7 18.75 5 27 73.05 3 24.35 5 28 132.61 7 18.94 5 29 106.73 5 21 -35 5 30 97.94 4 24.48 6 31 107.23 5 21.45 6 32 44.58 1 44.58 6 33 126.59 5 25.32 6 34 49.82 1 49. 82 6 35 88.76 4 22.19 6 36 82.76 4 20.69 6 37 30.83 1 30.83 TRAVEL TIME INFORMATION ON INDIVIDUAL SCHEDULES IN THE EXPERIMENT WITH ME =50, MB=0 AND SECTORING MECHANISM S{4) t USING TIME SAVED HEURISTIC DAY SCHEDULE TOTAL NO.OF CUST. SCHED. TIME / NO. SCHEDULE SERVED IN / CUST. TIME THE SCHED. 1 1 41.78 1 41.78 1 2 29.25 1 29.25 1 3 3 2.27 1 32.27 1 4 37.89 1 37.89 3 5 48.50 1 48.50 3 6 77.89 3 25.96 3 7 40.53 1 40.53 3 8 159.66 9 17.74 3 9 90.29 4 22.5 7 3 10 87.29 4 21.82 3 11 118.16 6 19.69 3 12 106.04 5 21.21 3 13 63.47 2 31.73 4 14 90.91 4 22.73 4 15 157.86 8 19.73 4 16 155.28 7 22.18 4 17 90.62 3 30.20 4 18 41.49 1 41.49 4 19 93.94 5 18.79 4 20 105.98 6 17.66 4 21 63.38 2 31.69 5 22 48.47 1 48.47 5 23 88.09 3 29.36 5 24 55.53 2 27.76 5 25 128.12 7 18.30 5 26 130.71 7 18.67 5 27 73.04 3 24.35 5 28 13 2.03 7 18.86 5 29 10 6.73 5 21.34 5 30 97.31 4 24.33 6 31 106.96 5 21.39 6 32 44.58 1 44.58 6 33 126.40 5 25.2 8 6 34 49.82 1 49.82 6 35 74.38 3 24.79 6 36 67.53 3 22.51 6 37 30.83 1 30.83 TRAVEL TIME INFORMATION ON INDIVIDUAL SCHEDULES IN THE EXPERIMENT WITH ME =25, MB=5 AND SECTORING MECHANISM S ( l ) , USING CLOSEST CUSTOMER HEURISTIC DAY SCHEDULE TOTAL NO.OF CUST. SCHED. TIME / NO. SCHEDULE SERVED IN / CUST. TIME THE SCHED. 1 1 137.94 6 22.99 1 2 109.48 5 21.89 1 3 94.59 4 23.65 1 4 9 7.32 4 24.33 2 5 144.57 6 24.09 2 6 124.98 5 24.99 2 7 146.71 6 24.45 2 8 164.01 8 20.50 2 9 152.29 8 19.04 3 10 123.61 5 24.72 3 11 121.13 5 24.2 3 4 12 161.67 7 23.09 4 13 116.13 5 23.23 4 14 123.47 5 24.69 4 15 179.78 9 19.97 4 16 164.73 8 20.59 5 17 140.94 6 23.48 5 18 88.44 4 22.11 5 19 162.36 8 20.29 5 20 181.08 10 18.11 5 21 151.88 8 18.98 5 22 12 4.08 6 20.67 6 23 144.18 6 24.03 6 24 144.10 6 24.01 6 25 116.35 5 23.26 6 26 174.26 10 17.43 6 27 142.89 8 17.86 6 28 141.86 7 20.26 TRAVEL TIME INFORMATION ON INDIVIDUAL SCHEDULES IN THE EXPERIMENT WITH ME =2 5, MB=5 AND SECTORING MECHANISM S (1) , USING TIME SAVED HEURISTIC DAY SCHEDULE TOTAL NO.OF CUST. SCHED. TIME / NO. SCHEDULE SERVED IN / CUST. ..TIME THE SCHED. 1 1 13 6.18 6 22.69 1 2 109.47 5 21.89 1 3 94.29 4 23.57 2 4 116.85 5 23.3 7 2 5 14 5.97 6 24.33 2 6 118.07 5 23.61 2 7 165.21 8 20.65 2 8 125.29 6 20.88 2 9 91.68 4 22.92 3 10 109.01 5 21.80 3 11 123.61 5 24. 72 3 12 12 0.87 5 24. 17 3 13 12 3.01 5 24.60 4 14 12 2.35 5 24.46 4 15 98.52 4 24.63 4 16 95.99 4 23.99 4 17 200.36 9 22.26 4 18 94.99 4 23.75 4 19 129.21 6 21.53 5 20 118.28 5 23.65 5 21 95.82 4 23.95 5 22 72.60 3 24.20 5 23 224.46 13 17.27 5 24 195.68 11 17.78 5 25 74.84 3 24.95 6 26 116.32 5 23.26 6 27 72.83 3 24.27 6 28 118.55 5 23.71 6 29 217.63 12 18.14 6 30 178.95 10 17.89 6 31 172.66 10 17.26

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