The Vehicle Routing Problem with Discrete Split Delivery and Time Windows

The Discrete Split Delivery Vehicle Routing Problem with Time Windows (DSDVRPTW) consists of designing the optimal set of routes to serve, at leas t cost, a given set of customers while respecting constraints on vehicles’ capacity and customer time windows. The delivery request of a customer consists of several discrete items which cannot be split further. The problem belongs to the class of split delivery problems since each cust omer’s demand can be split in orders, i.e. feasible combinations of items, and each customer can be visited by more than one vehicle. In this work, we model the DSDVRPTW as a mixed integer linear program, assuming that all feasible orders are known in advance and that each vehicle can serve at most one order per customer. Remarkably, service time at customer’s location dep ends on the serviced combination of items, which is a modeling feature rarely found in literatur e. We present a branch-and-price algorithm, analyzing the implications of the classical Dantzig-Wolfe reformulation. Preliminary computational results on instances based on Solomon’s data set are discussed.

[1]  Dag Haugland,et al.  A tabu search heuristic for the vehicle routing problem with time windows and split deliveries , 2004, Comput. Oper. Res..

[2]  B. Golden,et al.  Models and branch-and-cut algorithms for pickup and delivery problems with time windows , 2007 .

[3]  Moshe Dror,et al.  Savings by Split Delivery Routing , 1989, Transp. Sci..

[4]  Martin Desrochers,et al.  Vehicle routing and scheduling with time windows , 1986 .

[5]  A column generation algorithm for a vehicle routing problem with economies of scale and additional constraints , 2007 .

[6]  Giovanni Righini,et al.  New dynamic programming algorithms for the resource constrained elementary shortest path problem , 2008, Networks.

[7]  Cyrille Gueguen Méthodes de résolution exacte pour les problèmes de tournées de véhicules , 1999 .

[8]  Alain Hertz,et al.  A Tabu Search Algorithm for the Split Delivery Vehicle Routing Problem , 2003, Transp. Sci..

[9]  Guy Desaulniers,et al.  Branch-and-Price-and-Cut for the Split-Delivery Vehicle Routing Problem with Time Windows , 2008, Oper. Res..

[10]  Steve Y. Chiu,et al.  Effective Heuristic Procedures for a Field Technician Scheduling Problem , 2001, J. Heuristics.

[11]  José-Manuel Belenguer,et al.  A Lower Bound for the Split Delivery Vehicle Routing Problem , 2000, Oper. Res..

[12]  Maria Grazia Speranza,et al.  A column generation approach for the split delivery vehicle routing problem , 2011, Networks.

[13]  Gerard Sierksma,et al.  Routing helicopters for crew exchanges on off-shore locations , 1998, Ann. Oper. Res..

[14]  Martin W. P. Savelsbergh,et al.  An Optimization-Based Heuristic for the Split Delivery Vehicle Routing Problem , 2008, Transp. Sci..

[15]  Martin W. P. Savelsbergh,et al.  Branch-and-Price: Column Generation for Solving Huge Integer Programs , 1998, Oper. Res..

[16]  Michel Gendreau,et al.  Vehicle Routing with Time Windows and Split Deliveries , 2003 .

[17]  Mingzhou Jin,et al.  A two-stage algorithm with valid inequalities for the split delivery vehicle routing problem , 2007 .

[18]  Giovanni Righini,et al.  Symmetry helps: Bounded bi-directional dynamic programming for the elementary shortest path problem with resource constraints , 2006, Discret. Optim..

[19]  Hiroshi Nagamochi,et al.  A DP-based Heuristic Algorithm for the Discrete Split Delivery Vehicle Routing Problem , 2007 .

[20]  Gilbert Laporte,et al.  A Tabu Search Heuristic for the Vehicle Routing Problem , 1991 .

[21]  Moshe Dror,et al.  Vehicle routing with split deliveries , 1994, Discret. Appl. Math..

[22]  Martin W. P. Savelsbergh,et al.  Worst-Case Analysis for Split Delivery Vehicle Routing Problems , 2006, Transp. Sci..

[23]  Hanif D. Sherali,et al.  The Decomposition Principle , 2011 .

[24]  Si Chen,et al.  The split delivery vehicle routing problem: Applications, algorithms, test problems, and computational results , 2007, Networks.

[25]  George B. Dantzig,et al.  Decomposition Principle for Linear Programs , 1960 .

[26]  Jacques Desrosiers,et al.  Selected Topics in Column Generation , 2002, Oper. Res..

[27]  K. Lemmens,et al.  To split or not to split: that is the question , 2007 .