Mathematical models for a ship routing problem with a small number of ports on a route

Abstract

This paper presents an industrial ship routing problem with split loads faced by a steel company that exports its steel products to neighboring countries. The problem considers two types of ships: ships with contracts of affreightment and spot ships. It also considers other practical constraints, such as cargo–cargo and cargo–ship compatibility and the minimum loading amount for using a ship. Due to high surcharges for multiple port visits, each ship is allowed to visit at most two loading and two unloading ports. Herein, arc flow-based and path flow-based mathematical models are proposed to solve the problem. Computational experiments show that the path flow model is more efficient than the arc flow model. The path flow model can reduce the computational time by 67% on average and find optimal solutions to real-world ship routing problems in acceptable computational time in most cases.