Solution Methods for the Multi-trip Elementary Shortest Path Problem with Resource Constraints

We investigate the multi-trip elementary shortest path problem (MESPPRC) with resource constraints in which the objective is to find a shortest path between a source node and a sink node such that nodes other than the specified replenishment node are visited at most once and resource constraints are not violated. After each visit to the replenishment node, which we take to be the sink node in our study, resource consumption levels can be reset to a certain initial value. As this problem arises primarily as a subproblem in decomposition-based algorithms for a wide variety of practical applications, we illustrate it in the context of an integrated routing and scheduling problem with capacitated and time restricted vehicles. We propose exact and heuristic algorithms and evaluate the performance of these in a branchand-price framework.

[1]  Saïd Salhi,et al.  A multi-phase constructive heuristic for the vehicle routing problem with multiple trips , 2003, Discret. Appl. Math..

[2]  G. Laporte,et al.  A tabu search heuristic for periodic and multi-depot vehicle routing problems , 1997, Networks.

[3]  Alfredo Olivera,et al.  Adaptive memory programming for the vehicle routing problem with multiple trips , 2007, Comput. Oper. Res..

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

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

[6]  Ted K. Ralphs,et al.  A Branch-and-Price Algorithm for Combined Location and Routing Problems Under Capacity Restrictions , 2009 .

[7]  Simon Spoorendonk,et al.  A Branch-and-Cut Algorithm for the Elementary Shortest Path Problem with a Capacity Constraint , 2008 .

[8]  Renato F. Werneck,et al.  Robust Branch-and-Cut-and-Price for the Capacitated Vehicle Routing Problem , 2006, Math. Program..

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

[10]  Nicos Christofides,et al.  An algorithm for the resource constrained shortest path problem , 1989, Networks.

[11]  Mark S. Daskin,et al.  Location-Routing Problems with Distance Constraints , 2007, Transp. Sci..

[12]  Michel Gendreau,et al.  Vehicle Routeing with Multiple Use of Vehicles , 1996 .

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

[14]  M H Farahi,et al.  AN ALGORITHM FOR THE SHORTEST PATH PROBLEM , 2005 .

[15]  Alan Mercer,et al.  A tabu search algorithm for the multi-trip vehicle routing and scheduling problem , 1997, Eur. J. Oper. Res..

[16]  Irina Dumitrescu,et al.  Constrained path and cycle problems , 2002 .

[17]  Zeliha Akca.  Integrated location, routing and scheduling problems: Models and algorithms , 2009 .

[18]  Niklas Kohl,et al.  An Optimization Algorithm for the Vehicle Routing Problem with Time Windows Based on Lagrangian Relaxation , 1997, Oper. Res..

[19]  Jorge J. Moré,et al.  Digital Object Identifier (DOI) 10.1007/s101070100263 , 2001 .

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

[21]  Moshe Dror,et al.  Note on the Complexity of the Shortest Path Models for Column Generation in VRPTW , 1994, Oper. Res..