An SKU Decomposition Algorithm for the Tactical Planning in the FMCG Industry

In this paper we address the optimization of the tactical planning for the Fast Moving Consumer Goods (FMCG) industry, in which numerous trade-offs need to be considered over possibly thousands of Stock-Keeping Units (SKUs). An MILP model for the optimization of this tactical planning problem is proposed. This model is demonstrated for a case containing 10 SKUs, but is intractable for realistically sized problems. Therefore, a decomposition algorithm based on decomposing the model into single-SKU submodels is proposed in this paper. To account for the interaction between SKUs, slack variables are introduced into the capacity constraints. These slack variables initially allow the capacity to be violated. In an iterative procedure the cost of violating the capacity is slowly increased, and eventually a feasible solution is obtained. Even for the relatively small 10 SKU case, the required CPU time could be reduced from 4427s to 472s using the algorithm. Moreover, the algorithm was used to optimize cases of up to 1000 SKUs, whereas the full model is intractable for cases of 25 or more SKUs. The solutions obtained with the algorithm are typically within a few percent of the global optimum.