Integer programming based approaches for multi-trip location routing

Abstract

The multi-trip location routing problem consists in selecting the depots to open and the routes that should be performed to serve a set of clients at minimum cost. The multi-trip variant considers the possibility for a vehicle to perform more than a single route during the planning period, and hence it applies typically to cases in which the trips are performed within a small geographic area and involves for example the transportation of perishable goods. As a consequence, the inherent complexity of the problem increases as it has now to determine which routes should be assigned to the vehicles. In this paper, we explore an improved network flow formulation for this problem, and we compare it with another compact formulation proposed in the literature. We describe also an iterative rounding heuristic that relies on this model. We show through computational experiments on benchmark instances that the model provides good lower bounds, and that it can be used both by commercial solvers and heuristics to derive good quality solutions for the problem.