Production , Manufacturing and Logistics Stochastic single vehicle routing with a predefined customer sequence and multiple depot returns

We study the routing of a single vehicle that delivers multiple products under stochastic demand. Specifically, we investigate two practical variations of this problem: (i) The case in which each product type is stored in its dedicated compartment in the vehicle, and (ii) the case in which all products are stored together in the vehicle's single compartment. Suitable dynamic programming algorithms are proposed to determine the minimum expected (routing) cost for each case. Furthermore, the optimal routing policy is derived by developing appropriate theorems. The efficiency of the algorithms is studied by solving large problem sets.

[1]  George B. Dantzig,et al.  The Truck Dispatching Problem , 1959 .

[2]  Mauro Birattari,et al.  Hybrid Metaheuristics for the Vehicle Routing Problem with Stochastic Demands , 2005, J. Math. Model. Algorithms.

[3]  A Assad,et al.  MODELING AND IMPLEMENTATION ISSUES IN VEHICLE ROUTING , 1988 .

[4]  Bruce L. Golden,et al.  VEHICLE ROUTING: METHODS AND STUDIES , 1988 .

[5]  Nicos Christofides,et al.  Combinatorial optimization , 1979 .

[6]  Richard F. Hartl,et al.  D-Ants: Savings Based Ants divide and conquer the vehicle routing problem , 2004, Comput. Oper. Res..

[7]  Christian Blume,et al.  Computer-integrated manufacturing technology and systems , 1985 .

[8]  E. R. Petersen STOCHASTIC VEHICLE ROUTING PROBLEM WITH RESTOCKING. , 2000 .

[9]  Gilbert Laporte,et al.  STOCHASTIC VEHICLE ROUTING. , 1996 .

[10]  Gilbert Laporte,et al.  Routing problems: A bibliography , 1995, Ann. Oper. Res..

[11]  Michel Gendreau,et al.  An Approximation Algorithm for the Traveling Salesman Problem with Backhauls , 1997, Oper. Res..

[12]  Gilbert Laporte,et al.  Models and exact solutions for a class of stochastic location-routing problems , 1987 .

[13]  Dimitris Bertsimas,et al.  A Vehicle Routing Problem with Stochastic Demand , 1992, Oper. Res..

[14]  A Assad,et al.  VEHICLE ROUTING WITH SITE DEPENDENCIES. VEHICLE ROUTING: METHODS AND STUDIES. STUDIES IN MANAGEMENT SCIENCE AND SYSTEMS - VOLUME 16 , 1988 .

[15]  G. L. Nemhauser,et al.  Tight bounds for christofides' traveling salesman heuristic , 1978, Math. Program..

[16]  Nicola Secomandi,et al.  Comparing neuro-dynamic programming algorithms for the vehicle routing problem with stochastic demands , 2000, Comput. Oper. Res..

[17]  Eugene L. Lawler,et al.  Traveling Salesman Problem , 2016 .

[18]  Moshe Dror,et al.  Vehicle Routing with Stochastic Demands: Properties and Solution Frameworks , 1989, Transp. Sci..

[19]  Bruce L. Golden,et al.  Stochastic vehicle routing: A comprehensive approach , 1983 .

[20]  Paolo Toth,et al.  The Vehicle Routing Problem , 2002, SIAM monographs on discrete mathematics and applications.

[21]  M. Dror Modeling vehicle routing with uncertain demands as a stochastic program: Properties of the corresponding solution , 1993 .

[22]  Nicola Secomandi,et al.  A Rollout Policy for the Vehicle Routing Problem with Stochastic Demands , 2001, Oper. Res..

[23]  Ioannis Minis,et al.  Single vehicle routing with a predefined customer sequence and multiple depot returns , 2008, Eur. J. Oper. Res..

[24]  Αντώνιος Ταταράκης A class of single vehicle routing problems with predefined customer sequence and depot returns , 2007 .

[25]  G. Clarke,et al.  Scheduling of Vehicles from a Central Depot to a Number of Delivery Points , 1964 .

[26]  George L. Nemhauser,et al.  The Traveling Salesman Problem: A Survey , 1968, Oper. Res..

[27]  Moshe Dror,et al.  Stochastic Inventory Routing: Route Design with Stockouts and Route Failures , 1989, Transp. Sci..