Ship routing and scheduling with cargo coupling and synchronization constraints

The purpose of this paper is to introduce and solve a planning problem faced by shipping companies operating in a special segment of tramp shipping called project shipping. Project shipping differs from other more traditional tramp segments because the cargoes are more unique and usually transported on a one‐time basis. The special nature of the cargoes complicates the routing and scheduling. For instance, a cargo can be part of a process facility, but the shipping company cannot transport it unless other parts of the same facility are transported as well, even though these parts may have different origins. This creates an additional coupling constraint between the cargoes. In addition, the different parts might require synchronized delivery within some time window. We present a mathematical formulation for the problem and propose three alternative solution methods based on path flow formulations and a priori column generation. In one of the solution methods this is combined with a scheme for relaxing the complicating synchronization constraints and reintroducing them dynamically when needed. Computational results show that we are able to find optimal solutions to problems based on data obtained from a shipping company.