Heuristics for the mixed swapping problem

In the swapping problem, to each vertex of a complete directed graph are associated at most two object types representing its supply and demand. It is assumed that for each object type the total supply equals the total demand. A vehicle of unit capacity, starting and ending its route at an arbitrary vertex, is available to carry the objects along the arcs of the graph. The aim is to determine a minimum cost route such that each supply and demand is satisfied. When some of the object types are allowed to be temporarily unloaded at some intermediate vertices before being carried to their final destination, the problem is called the mixed swapping problem. In this paper we describe constructive and improvement heuristics which were successfully applied to randomly generated instances with up to 10,000 vertices, with an average optimality gap not exceeding 1%.