A STUDY ON THE SOLUTION APPROACH FOR THE VEHICLE ROUTING WITH BACKHAULS PROBLEM
徐俊誠、吳泰熙
E-mail: [email protected]
ABSTRACT
IN THE TRADITIONAL VEHICLE ROUTING PROBLEMS WITH BACKHAUL (VRPB), IT IS ASSUMED THAT
BACKHAULING CUSTOMERS CANNOT BE VISITED UNLESS ALL THE LINEHAULING CUSTOMERS HAVE BEEN VISITED. THIS ASSUMPTION BECOMES IMPRACTICAL FOR SOME LOCAL INDUSTRIES IN TAIWAN, IN WHICH, SOME CUSTOMERS REQUIRE BOTH THE LINEHAULING AND BACKHAULING SERVICE. USING THE
TRADITIONAL TRANSPORTATION PLAN WOULD SURELY COMMIT SOME EXTRA TRANSPORTATION COST.
IN THIS STUDY, WE HAVE RELAXED THE CONSTRAINT REGARDING THE VISITING SEQUENCE FOR THE LINEHAULING AND BACKHAULING CUSTOMERS, AND PROPOSE A NEW MATHEMATICAL MODEL FOR THE REVISED VRPB (RVRPB). IN ADDITION, THE CONDITION THAT SOME CUSTOMERS REQUIRE SPECIFIC SERVICE TIME WINDOWS IS ALSO CONSIDERED. A SIMULATED ANNEALING ALGORITHM IS PROPOSED TO INCREASE THE SOLVING EFFICIENCY FOR THE REVISED VRPB. SA PARAMETERS THAT CAN OBTAIN GOOD SOLUTION IN A REASONABLE AMOUNT OF TIME ARE DETERMINED THROUGH SOME EXPERIMENTS. FROM THE COMPUTATIONAL RESULTS, IT CAN BE OBSERVED THAT IN SOME INDUSTRIES THE PROPOSED RVRPB MODEL DOES REDUCE THE TRANSPORTATION COST.
Keywords : VRPB, VRPBTW, SIMULATED ANNEAL ALGORITHM.
Table of Contents
第一章 緒論--P1 1.1 研究背景與動機--P1 1.2 研究目的--P3 1.3 研究範圍與限制與假設--P3 1.3.1 研究範圍與限制--P3 1.3.2 研 究假設--P4 1.4 研究架構--P5 第二章 文獻回顧--P6 2.1 車輛途程問題--P7 2.1.1 VRP數學模式--P7 2.1.2 VRP文獻探討--P9 2.2 時窗限制下車輛途程問題--P10 2.2.1 VRPTW數學模式--P10 2.2.2 VRPTW文獻探討--P11 2.3 傳統回程取貨之車輛途程問 題--P13 2.3.1 VRPB數學模式--P13 2.3.2 VRPB和VRPBTW相關文獻探討--P15 2.4 模擬退火法--P19 2.4.1 模擬退火演算 法--P20 2.5 小節--P23 第三章 改良型車輛途程含取貨問題--P24 3.1 改良型VRPB數學模式--P24 3.2 改良型VRPB數學模式求 解--P26 3.2.1 數學模式測試--P26 3.2.2 傳統型與改良型VRPB結果比較--P28 3.2.3 改良型VRPB與VRP結果比較--P30 3.3 改 良型VRPBTW數學模式--P30 3.4 改良型VRPBTW數學模式求解--P32 3.4.1 模式自我測試--P32 3.4.2 網路例題測試--P34 3.5 小結--P36 第四章 改良型車輛途程含取貨問題之模擬退火啟發式方法--P37 4.1 起始途徑建構--P39 4.2 途徑間鄰域解改 善--P41 4.3 途程內鄰域解改善--P45 4.4 跳脫機制--P48 第五章 考量時窗之車輛途程含取貨問題之啟發式方法--P49 5.1 起始 途徑建構--P49 5.2 途程內鄰域解改善--P51 第六章 結果分析--P53 6.1 VRPB測試例題--P53 6.1.1 與數學模式之求解效率比 較--P54 6.1.2 SA啟發式求解--P55 6.2 VRPBTW測試例題--P62 6.2.1 與數學模式之求解效率比較--P63 6.2.2 SA啟發式求 解--P64 第七章 結論與建議--P69 7.1 結論--P69 7.2 建議--P70
REFERENCES
1. 申生元,"時窗限制車輛途程問題",國立交通大學,工業工程與管理研究所博士論文,民國八 十九年一月。 2. 吳泰熙和張欽智,"以 禁忌搜尋法求解推銷員旅行問題" ,大葉學報 第六卷 第一期,87-99 民國八十六年 3. 杜世文,"多目標與模糊時窗貨物配送啟發式演算 法研究",國立交通大學碩士論文,民國八十 一年六月 4. 黃金智,"隨機型車輛途程解法之研究"大葉大學工工所,民國八十八年七月 5.
黃聖峰,"考量回程取貨之車輛途程問題"大葉大學工工所,民國八十八年六月 6. 廖忠雄和黃敏亮,"物流中心之模糊多目標與混合型時 窗限制配送車輛途程問題之研究",第二 冊,625-632,中華民國工業工程學會八十四年會論文集。 7. 廖亮富,"含時窗限制式多部車量 途程問題解算之研究"'元智大學工業工程研究所,民國八十 七年六月。 8. 劉雅魁,"運用路線鄰域法求解車輛途程含回程取貨問題"國防 管理學院資源管理所,民國八十 七年六月。 9. Bramel, J. and SimchiLevi, D.,"On the Effectiveness of Set Covering Formulations for the Vehicle Routing Problem with Time Windows,"Operations Research,45,295-301 (1997)。 10. Chiang, W.C., "Simulated Annealing
Metaheuristics for the Vehicel Routing Problem with Time Windows," Anneals of Operations Research, 63, 3-27 (1996) 11. Christofides, N. and Eilon, S., "An algorithm for the vehicle dispatching problem ,"Operational Research Quarterly, 20, 309-318 (1969)。 12. Christofides, N., Mingozzi, A. and Toth, P., "State-space relaxation procedures for the computation of bounds to routing problems,"Networks, 11, 145-164 (1981)。
13. Christofides, N., Mingozzi, A. and Toth,P.,"Exact Algorithm for the Vehicle Rout -ing Problem base Spanning Tree and Shortest Path Relaxations,"Mathematics Progmm -ing, 20,255-282 (1969)。 14. Christophe, D., Jean-Yves, P. and Jean-Marc, R.,"A Tabu Search Heuristic for the Vehicle Routing Problem with Backhauls and Time Windows,"Transportation Science, 31, No.1, (1997) 。 15. Clarke, G. and Wright, J.
W.,"Scheduling of Vehicles from a Central Depot to a Number of Delivery Points,"Operations Research, 12, 568-581 (1964)。 16. Daniel, O. C., Golden, B. L., and Edward, A.W.,"Vehicle Routing with Backhauls: Models, Algorithms and Case Sstudies,"Vehicle routing:Methods and studies, B.L. Golden and A.A. Assad(Editors), (1988)。 17. Deif, I. And Bodin, L.,"Extension of the Clarke and Wright Algorithm for Solving the Vehicle Routing Problem with Backhauling,"In proceedings of the babson confer -ence on sofeware use In Trandportation and logistic management, A.E.Kidder,Bab -son Prak, MA, 75-96(1984)。 18. Desrochers, M. Desrosiers, J., and Solomon, M.,"A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows,"Operations Research, 40, 342-354 (1992)。 19. Duhamel, C., Potvin Jean-Yves and Rousseau, J.M.,"A Tabu Search Heuristic for the Vehicle Routing Rroblem with Backhauls and Time Windows,"Transportation Science, 31, 49-59 (1997)。
20. Fisher, M.L. and Jaikumar, R.,"A Generalized Assignment Heuristic for Vehicle Rout -ing Problems,"Networks, 11, 109-124 (1981)。 21.
Fisher, M.L., Jornsten, O. and Madsen, O.B., "Vehicle Routing with Time Windows: Two Optimization Algorithms," Operations Research, 45, 488-492 (1997)。 22. Gendreau, M., Laport, G. and Vigo, D.,"Heuristics for the Traveling Salesman Problem with Pickup and Delivery,"
Computer & Operations, 26, 699-714 (1999)。 23. Gilbert, L.,"The Traveling Salesman Problem:An Overview of Exact and Approximate Algorithm"European Journal of Operational Research, 59, 231-247 (1992)。 24. Gilles, P.,"An Exact Constraint Logic Programming Algorithm for the Traveling Salesman Problem with Time Windows"Transportation Science, 32,No.1, Feb. (1998)。 25. Gillett, B.E. and Miller, L.R."A Heuristic Algorithm for the Vehicle Dispatch Problem,"Operations Research, 2, 340-349, (1974)。 26. Glover, F.,"Tabu search,part I,"ORSA journal on Computing, 1, 190-209 (1989) 。 27. Goetschalckx, M. and Jacobs-Blecha, C.,"The Vehicle Routing Problem with Backhauls
,"European Journal of Operational Research, 42, 39-51 (1989)。 28. Golden, E.B., Alfaro, J. and Schagger, J., "The Vehicle Rouing Problem with Backha -ulling:Two Approaches,"Proceedings of the XII Annual Meeting of S.E.TIMS, Myrtle Beach, S.C, 90-92 (1985)。 29. Gur
Mpsheiov,"Vehicle Routing with Pick-up and Delivery Tour-Partitioning Heurist -ics,"Computers Industrial Engineering, 34, 669-684 (1998)。 30.
Kohl, N. and Madsen, G.O.B., "An Optimization Algorithm for the Vehicle Routing Problem with Time Windows based on Lagrangian Relaxation,"Operational Research, 45, 395-406 (1997)。 31. Koskosidis, I.A.,"Optimization Based Models and Algorithms for Routing Civil Eng -ineering and Operations Reserch,"Ph.D. Dissertation, Dept. of Civil Engineering and Operations Research, University of Princetion (1988)。 32.
Lin, S. and Kernighan, B.W.,"An Effective Heuristic Algorithm for Traveling Sales -man Problem,"Operations Research, 21, 498-516(1973)。 33.
Little, J.D.C., Murty, K.G., Sweeney D.W. and Karel, C.,"Alghorithm for the Travel -ing Salesman Problem,"Operational Research, 11, 979 (1963)。 34. Mole, R. and Jameson, S.,"A Sequential Route-Building Employing a Generalized Sav -ings Criterion,"Operations Research Quarterly, 27, 503-511 (1976)。 35. Or, I.,"Traveling Salesman-Type Combinatiorial Problem and their Relation to the Logistics of Regional Blood Banking,"Ph.D thesis, Northwestern University, IL, (1976)。 36. Potvin Jean-Yves, Duhamel, C. and Guertin, F.,"A Genetic Algorithm for Vehicle Routing with Backhauling,"Applied Intelligence, 6, 345-355 (1996)。 37. Potvin Jean-Yves and Laporte, g.,"Genetic Algorithm for the Traveling Salesman Problem"Anneals of Operations Research, 63, 339-370 (1996)。 38. Reingold, E.M., Neivergelt, J. and Deo,
N.,"Combinatorial Algorithms:Theory and Practice (Prentice-Hall, Englewood Cliffs, N.J.),"(1977)。 39. Shoshana Anily and Gur Mpsheiov,"The Traveling Salesman Problem with Delivery and Backhauls,"Operations Research Letters, 16, 11-18 (1994)。 40. Solomon, M.M.,"Algorithm for the Vehicle Routing and Scheduling Problems with Time Window Constrain,"Operations Research, 35, 254-265 (1987)。 41. Thangiah, S.R., Potvin, J.Y. and Sun, T.,"Heuristic Approaches to Vehicle Routing with Backhauls and Time Windows," Computers and Operations Research, 23, 1043-1057 (1996)。 42. Toth, P. and Vigo, D., "An Exact Algorithm for the Vehicle Routing Problem with Ba -ckhauls, "Transportation Science, 31, 372-385 (1997)。 43. Yano, T., Chan, L. and Richter, K.M.,"Vehicle Routing at Routing at Quality Stores ,"Interfaces, 17(2), 52-63 (1987)。