Use of Lagrangian decomposition in supply chain planning

The integrated planning of transportation of raw material, production and distribution of products of the supply chain for a large pulp company is studied. The planning period is one year and a numbers of time periods are considered. The tactical decisions included in the model regard transportation of raw materials from harvest areas to pulp mills, production mix and contents at pulp mills, distribution of pulp products from mills to customers either via terminals or directly, and the selection of potential orders and their levels at customers. A mixed integer linear programming model for the supply chain problem is developed. The main solution method in this paper is a Lagrangian heuristic method based on Lagrangian decomposition. The heuristic divides the problem into two subproblems representing different physical stages in the supply chain, each including several time periods. The advantage of the proposed solution approach is that it generates feasible solutions of high quality in short time. A number of cases based on real data is analyzed.