The open capacitated arc routing problem

  • Authors:

  • Fábio Luiz Usberti;Paulo Morelato França;André Luiz Morelato França

  • Affiliations:

  • School of Electrical and Computer Engineering, Campinas State University, 13083-852 Campinas, SP, Brazil;Department of Mathematics, Statistics and Computing, São Paulo State University, 19060-900 Presidente Prudente, SP, Brazil;School of Electrical and Computer Engineering, Campinas State University, 13083-852 Campinas, SP, Brazil

  • Venue:
  • Computers and Operations Research
  • Year:
  • 2011

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Abstract

The Open Capacitated Arc Routing Problem (OCARP) is a NP-hard combinatorial optimization problem where, given an undirected graph, the objective is to find a minimum cost set of tours that services a subset of edges with positive demand under capacity constraints. This problem is related to the Capacitated Arc Routing Problem (CARP) but differs from it since OCARP does not consider a depot, and tours are not constrained to form cycles. Applications to OCARP from literature are discussed. A new integer linear programming formulation is given, followed by some properties of the problem. A reactive path-scanning heuristic, guided by a cost-demand edge-selection and ellipse rules, is proposed and compared with other successful CARP path-scanning heuristics from literature. Computational tests were conducted using a set of 411 instances, divided into three classes according to the tightness of the number of vehicles available; results reveal the first lower and upper bounds, allowing to prove optimality for 133 instances.