Applying a relax-and-fix approach to a fixed charge network flow model of a maritime inventory routing problem

Abstract

This work presents a Relax-and-Fix algorithm to solve a class of single product Maritime Inventory Routing Problems. The problem consists of routing and scheduling a heterogeneous fleet of vessels to supply a set of ports, respecting lower and upper limits of inventory at production and consumption ports, along with a time horizon. A fixed charge network flow is used to model the problem, and valid inequalities are incorporated into the formulation, providing tight bounds and enabling the Relax-and-Fix algorithm to obtain good solutions in reasonable processing times. Three MIP-based local search procedures are proposed for improving solutions. Tests performed on a set of benchmark instances from the literature show that the solution approach can be effective for solving the problem.