Branch and Price and Cut for the Split-Delivery Vehicle Routing Problem with Time Windows and Linear Weight-Related Cost

This paper addresses a new vehicle routing problem that simultaneously involves time windows, split delivery, and linear weight-related cost. This problem is a generalization of the split delivery vehicle routing problem with time windows (SDVRPTW), which consists of determining a set of least-cost vehicle routes to serve all customers while respecting the restrictions of vehicle capacity and time windows. The travel cost per unit distance is a linear function of the vehicle weight and the customer demand can be fulfilled by multiple vehicles. To solve this problem, we propose an exact branch-and-price-and-cut algorithm, where the pricing subproblem is a variant of the resource-constrained elementary shortest path problem. We first prove that at least one optimal solution to the pricing subproblem is associated with an extreme delivery pattern, and then we design a tailored and novel label-setting algorithm to solve the pricing subproblem. Computational results show that our proposed algorithm can handle ...

[1]  Yuchun Xu,et al.  Development of a fuel consumption optimization model for the capacitated vehicle routing problem , 2012, Comput. Oper. Res..

[2]  Miguel A. Figliozzi,et al.  Vehicle Routing Problem for Emissions Minimization , 2010 .

[3]  Marius M. Solomon,et al.  Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints , 1987, Oper. Res..

[4]  Michel Gendreau,et al.  Production , Manufacturing and Logistics An exact algorithm for a vehicle routing problem with time windows and multiple use of vehicles , 2009 .

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

[6]  Natashia Boland,et al.  Accelerated label setting algorithms for the elementary resource constrained shortest path problem , 2006, Oper. Res. Lett..

[7]  Guy Desaulniers,et al.  Enhanced Branch and Price and Cut for Vehicle Routing with Split Deliveries and Time Windows , 2009, Transp. Sci..

[8]  Andrew Lim,et al.  An adaptive ejection pool with toggle-rule diversification approach for the capacitated team orienteering problem , 2013, Eur. J. Oper. Res..

[9]  Andrew Lim,et al.  The single vehicle routing problem with toll-by-weight scheme: A branch-and-bound approach , 2012, Eur. J. Oper. Res..

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

[11]  Yiyo Kuo,et al.  Optimizing goods assignment and the vehicle routing problem with time-dependent travel speeds , 2009, Comput. Ind. Eng..

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

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

[14]  Guy Desaulniers,et al.  Tabu Search, Partial Elementarity, and Generalized k-Path Inequalities for the Vehicle Routing Problem with Time Windows , 2006, Transp. Sci..

[15]  Giovanni Righini,et al.  A Branch-and-Price Approach to the Vehicle Routing Problem with Simultaneous Distribution and Collection , 2006, Transp. Sci..

[16]  Jay M. Rosenberger,et al.  A Branch-and-Price-and-Cut Method for Ship Scheduling with Limited Risk , 2008, Transp. Sci..

[17]  Stefan Irnich,et al.  Shortest Path Problems with Resource Constraints , 2005 .

[18]  Jacques Desrosiers,et al.  The Pickup and Delivery Problem with Time Windows , 1989 .

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

[20]  Gilbert Laporte,et al.  A branch-and-price algorithm for the Vehicle Routing Problem with Deliveries, Selective Pickups and Time Windows , 2009, Eur. J. Oper. Res..

[21]  Yiyo Kuo,et al.  Using simulated annealing to minimize fuel consumption for the time-dependent vehicle routing problem , 2010, Comput. Ind. Eng..

[22]  Jean-François Cordeau,et al.  Branch and Cut and Price for the Pickup and Delivery Problem with Time Windows , 2009, Transp. Sci..

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

[24]  Michel Gendreau,et al.  An exact algorithm for the elementary shortest path problem with resource constraints: Application to some vehicle routing problems , 2004, Networks.

[25]  Michel Gendreau,et al.  Vehicle dispatching with time-dependent travel times , 2003, Eur. J. Oper. Res..

[26]  Jun Zhang,et al.  A Scatter Search for Multi-Depot Vehicle Routing Problem with Weight-Related Cost , 2011, Asia Pac. J. Oper. Res..

[27]  Andrew Lim,et al.  A Capacitated Vehicle Routing Problem with Toll-by-Weight Rule , 2009 .

[28]  Teodor Gabriel Crainic,et al.  Fleet management and logistics , 1998 .

[29]  de Ag Ton Kok,et al.  Analysis of Travel Times and CO2 Emissions in Time‐Dependent Vehicle Routing , 2012 .

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

[31]  Cynthia Barnhart,et al.  Using Branch-and-Price-and-Cut to Solve Origin-Destination Integer Multicommodity Flow Problems , 2000, Oper. Res..

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

[33]  M. Dror,et al.  Split delivery routing , 1990 .

[34]  Tom Van Woensel,et al.  A study on carbon reduction in the vehicle routing problem with simultaneous pickups and deliveries , 2012, Proceedings of 2012 IEEE International Conference on Service Operations and Logistics, and Informatics.

[35]  Bahar Yetis Kara,et al.  Energy Minimizing Vehicle Routing Problem , 2007, COCOA.

[36]  A. Palmer.  The development of an integrated routing and carbon dioxide emissions model for goods vehicles , 2007 .

[37]  Martin Desrochers,et al.  A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows , 1990, Oper. Res..

[38]  Matteo Salani,et al.  Branch and price for the vehicle routing problem with discrete split deliveries and time windows , 2011, Eur. J. Oper. Res..

[39]  Jacques Desrosiers,et al.  A Unified Framework for Deterministic Time Constrained Vehicle Routing and Crew Scheduling Problems , 1998 .

[40]  Giovanni Righini,et al.  A branch-and-cut-and-price algorithm for the multi-depot heterogeneous vehicle routing problem with time windows , 2011 .

[41]  Gleb Belov,et al.  A branch-and-cut-and-price algorithm for one-dimensional stock cutting and two-dimensional two-stage cutting , 2006, Eur. J. Oper. Res..

[42]  Gilbert Laporte,et al.  The time-dependent pollution-routing problem , 2013 .

[43]  Zhixing Luo,et al.  Branch-and-price-and-cut for the multiple traveling repairman problem with distance constraints , 2014, Eur. J. Oper. Res..

[44]  Tom Van Woensel,et al.  Branch and Price for the Time-Dependent Vehicle Routing Problem with Time Windows , 2013, Transp. Sci..

[45]  J. Desrosiers,et al.  A dynamic programming algorithm for the shortest path problem with time windows and linear node costs , 1998 .

[46]  Gilbert Laporte,et al.  The Pollution-Routing Problem , 2011 .

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

[48]  Gilbert Laporte,et al.  An adaptive large neighborhood search heuristic for the Pollution-Routing Problem , 2012, Eur. J. Oper. Res..

[49]  Glaydston Mattos Ribeiro,et al.  A branch-price-and-cut algorithm for the workover rig routing problem , 2011, Comput. Oper. Res..