In this paper, we consider a combined terminal location and ship routing problem at So¨dra 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.
In this paper, the integrated planning of production and distribution for a pulp company is considered. The tactical decisions included regard transportation of raw materials from harvest areas to pulp mills; production mix and contents at pulp mills; inventory; distribution of pulp products from mills to customers and the selection of potential orders and their levels at customers. The planning period is one year and several time periods are included. As a solution approach we make use of two different heuristic approaches. The main reason to use heuristics is the need for quick solution times. The first heuristic is based on a rolling planning horizon where iteratively a fixed number of time periods is taken into consideration. The second heuristic is based on Lagrangian decomposition and subgradient optimization. This provides optimistic bounds of the optimal objective function value, that are better than the LP relaxation value, which can be used as a measure of the heuristic (pessimistic) solution quality. In addition we apply the proposed rolling horizon heuristic in each iteration of the subgradient optimization. A number of cases based on real data is analyzed which shows that the proposed solution approach is simple and provides high quality solutions.
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