Tramp Ship Routing with Bunker Optimization and Flexible Cargo Quantities: Case from Dry Bulk Shipping

Abstract

We study the Tramp Ship Routing and Scheduling Problem with Bunker Optimization (TSRSPBO). The TSRSPBO includes, in addition to the routing and scheduling of the vessels in the given fleet, decisions about how much to bunker (refuel) in which ports. Furthermore, the cargo quantities to be transported are given in an interval, which means that determining the optimal transport quantities also becomes a decision. We propose an arc flow model and a solution method based on a reformulation into a path flow model that uses all feasible vessel routes (columns) as input. For each route, we determine the optimal bunker amounts and cargo quantities along the route. The path flow solution method is tested on a set of instances generated based on data from our case company. The computational results show that the path flow solution method outperforms the arc flow model solved by a commercial solver. We also present how chartering managers may use this as decision support in the negotiation of freight contracts and bunker prices.