Accession Number : ADA189418

Title :   The Prize Collecting Traveling Salesman Problem.

Descriptive Note : Management science research rept.,

Corporate Author : CARNEGIE-MELLON UNIV PITTSBURGH PA MANAGEMENT SCIENCES RESEARCH GROUP

Personal Author(s) : Balas, Egon

PDF Url : ADA189418

Report Date : Jul 1987

Pagination or Media Count : 28

Abstract : The following is a valid model for an important class of scheduling and routing problems. A salesman who travels between pairs of cities at a cost depending only on the pair, gets a prize in every city that he visits and pays a penalty to every city that he fails to visit, wishes to minimize his travel costs and penalties, while visiting enough to collect a prescribed amount of prize money. We call this problem the Prize Collecting Traveling Salesman Problem (PCTSP). This paper discusses structural, the convex hull of the solutions to the PCTSP. In particular, it identifies several families of facet defining inequalities for this polytope. Some of these inequalities are related to facets of the ordinary TS polytope, others to facets of the knapsack polytope. They can be used in algorithms for the PCTSP either as cutting planes or as ingredients of a Lagrangean optimum. Keywords: Traveling salesman problem; Facets; Polyhedral Combinations; Convex polytopes.

Descriptors :   *ROUTING, ALGORITHMS, COSTS, PENALTIES, SCHEDULING, TRAVEL, LAGRANGIAN FUNCTIONS

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE