A branch-price-and-cut algorithm for the workover rig routing problem

In an onshore oil field, the productivity of oil wells decreases when they require maintenance. To restore full productivity at a well, it must be visited by a specially equipped vehicle, called a workover rig. Given a set of wells needing maintenance and a heterogeneous fleet of workover rigs, the workover rig routing problem (WRRP) consists of finding rig routes that minimize the total production loss of the wells over a finite horizon. The wells have different loss rates, require various services, and may not be serviced within the horizon due to rig availability. The rigs have initial positions and do not have the same equipment. This paper presents the first exact algorithm for the WRRP, namely, a branch-price-and-cut algorithm that relies on some of the most recent techniques introduced for the vehicle routing problem with time windows. Our computational experiments show that this exact algorithm can solve practical-sized instances in reasonable computational times.

[1]  Jacques Desrosiers,et al.  Cutting planes for branch‐and‐price algorithms , 2009, Networks.

[2]  Adam N. Letchford,et al.  A new branch-and-cut algorithm for the capacitated vehicle routing problem , 2004, Math. Program..

[3]  Roberto Roberti,et al.  An exact solution framework for a broad class of vehicle routing problems , 2010, Comput. Manag. Sci..

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

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

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

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

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

[9]  Raf Jans.  Classification of Dantzig-Wolfe reformulations for binary mixed integer programming problems , 2010, Eur. J. Oper. Res..

[10]  Glaydston Mattos Ribeiro,et al.  A comparison of three metaheuristics for the workover rig routing problem , 2012, Eur. J. Oper. Res..

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

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

[13]  Guy Desaulniers,et al.  Multi-depot vehicle scheduling problems with time windows and waiting costs , 1996, Eur. J. Oper. Res..

[14]  Roberto Roberti,et al.  New Route Relaxation and Pricing Strategies for the Vehicle Routing Problem , 2011, Oper. Res..

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

[16]  Glaydston Mattos Ribeiro,et al.  A Grasp with Path-Relinking for the Workover Rig Scheduling Problem , 2010, Int. J. Nat. Comput. Res..

[17]  David Pisinger,et al.  Subset-Row Inequalities Applied to the Vehicle-Routing Problem with Time Windows , 2008, Oper. Res..

[18]  Louis Anthony Cox,et al.  Wiley encyclopedia of operations research and management science , 2011 .

[19]  J. Desrosiers,et al.  BRANCH-PRICE-AND-CUT ALGORITHMS , 2011 .

[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..

[22]  Jacques Desrosiers,et al.  The Vehicle Routing Problem with Time Windows: State-of-the-Art Exact Solution Methods , 2010 .

[23]  Adam N. Letchford,et al.  A branch-and-cut algorithm for the capacitated open vehicle routing problem , 2007, J. Oper. Res. Soc..

[24]  Celso C. Ribeiro,et al.  Scheduling workover rigs for onshore oil production , 2006, Discret. Appl. Math..

[25]  Alain Hertz,et al.  The capacitated team orienteering and profitable tour problems , 2007, J. Oper. Res. Soc..