Solving the Prize-collecting Rural Postman Problem

Julián Aráoz, Elena Fernández and Oscar Meza

European Journal of Operational Research, 2009, vol. 196, issue 3, 886-896

Abstract: In this work we present an algorithm for solving the Prize-collecting Rural Postman Problem. This problem was recently defined and is a generalization of other arc routing problems like, for instance, the Rural Postman Problem. The main difference is that there are no required edges. Instead, there is a profit function on the edges that must be taken into account only the first time that an edge is traversed. The problem is modeled as a linear integer program where the system has an exponential number of inequalities. We propose a solution algorithm where iteratively we solve relaxed models with a small number of inequalities, that provide upper bounds, and we propose exact separation procedures for generating violated cuts when possible. We also propose a simple heuristic to generate feasible solutions that provide lower bounds at each iteration. We use a two-phase method with different solvers at each phase. Despite the difficulty of the problem, the numerical results from a series of computational experiments with various types of instances assess the good behavior of the algorithm. In particular, 75% of the instances were optimally solved with the LP relaxation of the model. The remaining instances were optimally solved on a second phase, most of them in small computation times.

Keywords: Integer; programming; Combinatorial; optimization; Arc; routing; problems (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (23)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:196:y:2009:i:3:p:886-896

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