A Branch-and-Cut Algorithm for the Non-Preemptive Swapping Problem

In the Swapping Problem (SP), we are given a complete graph, a set of object types and a vehicle of unit capacity. An initial state specifies the object type currently located at each vertex (at most one type per vertex). A final state describes where these object types must be repositioned. In general there exist several identical objects for a given object type, yielding multiple possible destinations for each object. The SP consists of finding a shortest vehicle route starting and ending at an arbitrary vertex, in such a way that each object is repositioned in its final state. This article exhibits some structural properties of optimal solutions and proposes a branch-and-cut algorithm based on a 0-1 formulation of the problem. Computational results on random instances containing up to 200 vertices and eight object types are reported.