An integer programming approach for the rural postman problem with time dependent travel times

Abstract

The Chinese Postman Problem is a famous and classical problem in graph theory. This paper introduces a new variant of this problem, namely Rural Postman Problem with Time Dependent Travel Times, which is motivated from scheduling with time dependent processing times. An arc-path formulation of the problem is given and strong valid inequalities are derived. A subset of constraints in this formulation has a strong combinatorial structure, which is used to define the polytope of arc-path alternation sequence. The facial structure of this polytope is investigated and facet defining inequalities are presented which may be helpful to tighten the integer programming formulation. Computational results that verifies the effect of facet defining and strong valid inequalities are presented. © 2011 Springer-Verlag.