Tight lower bounds for the Traveling Salesman Problem with draft limits

Abstract

In the present paper, we consider the Traveling Salesman Problem with Draft Limits (TSPDL), which is a variant of the Traveling Salesman Problem (TSP) arising in maritime transportation. We provide compact formulations of polynomial size developed by using the Reformulation-Linearization Technique (RLT) with one and two levels. In doing so, we recover time-dependent formulations of TSP and provide their factorization into products involving the decision variables and their complements. This factorization affords further RLT-lifting to the model of TSPDL by combining time-dependent and flow variables that lead to very tight linear relaxation. Computational results conducted on benchmark instances confirm the tightness of the lower bounds.