A combined terminal location and ship routing problem

Abstract

In this paper, we consider a combined terminal location and ship routing problem at Södra Cell AB. The purpose is to supply the customers' annual demand for pulp products while minimizing the distribution costs. Customers are supplied with various pulp products from pulp mills in Scandinavia by ships, trains, or lorries. The ship routes go from the pulp mills to terminals in Europe. From each terminal, the products are transported to customers by lorry, train, or barge. Some customers can be supplied directly from the pulp mills by trains or lorries. We have developed a mathematical model to select which terminals to use and, at the same time, determine the shipping routes. The mixed integer programming model was solved directly using a commercial solver. When the number of routes generated is large, the time required to obtain an optimal solution is too long. Hence, we have developed heuristics in order to obtain an acceptable solution in reasonable time. In addition to the basic case, five different scenarios were tested. Our heuristics provide solutions that are within 0.12% of the optimal ones.

Keywords:

• mixed integer programming
• facility location
• transportation
• ship routing