A Maritime Pulp Distribution Problem

In this paper, a path flow model and solution method for a maritime pulp distribution problem is presented and analyzed. Unlike many other models for maritime distribution chains, the customers are not located at the ports, but different modes of transportation are needed in order to deliver the pulp. This means that the model proposed also incorporates the distribution planning from the ports to the customers as well as direct deliveries from the pulp mills. For the distribution, a fleet of long‐term time‐chartered ships are used, but additional ships can also be chartered on the spot market. The problem is modeled as a mixed integer linear program and solved using a branch‐and‐price method. Due to the complexity of the problem, the solution strategy is divided into two phases, where the first emphasizes the generation of schedules for the time‐chartered ships while the second deals with decisions regarding the chartering of ships on the spot market. To generate the schedules, a network based on clusters is constructed, and a modified k‐shortest path algorithm is developed to solve the problem. The algorithm penalizes parts of schedules already generated, making the generated schedules more diversified than general k‐shortest path algorithms.