The maximum benefit Chinese postman problem and the maximum benefit traveling salesman problem

Abstract

This paper introduces the maximum benefit Chinese postman problem (MBCPP) and the maximum benefit traveling salesman problem (MBTSP). For the MBCPP a benefit is realized each time a link of a directed graph is traversed. The MBCPP relaxes the constraint of the Chinese postman problem that each link be traversed.at least once and finds a tour of maximum total net benefit. For the MBTSP a benefit is derived when a node is visited and a cost is incurred when a link is traversed. The MBTSP relaxes the constraint of the traveling salesman problem that each node be visited exactly (or at least) once and finds a tour of maximum total net benefit. Both problems are formulated as linear integer programming problems. A solution algorithm is given that repeatedly solves a relaxation of the formulation as a minimum cost flow problem using a branch-and-bound procedure. Computational examples are presented.