Temporal Aggregation in Production Planning

Abstract

In this paper, the problem of temporal aggregation in production planning is addressed. A single facility with multiple part types is considered. The planning horizon consists of a sequence of elementary time periods, and the demand for all part types is assumed to be known over these periods. The production planning problem consists of minimizing the holding and backlogging cost for all part types. Due to usual errors in demand forecasting, and due to the large size of the linear programming problem commonly encountered in such problems, there is a need for aggregating the production variables over the time horizon (typically, for weekly to monthly) to result in a hierarchical structure. We consider a two-level hierarchy composing a sub- problem at each level, and we propose an iterative technique which solves these sub-problems in sequence. A posteriori bounds are developed, which are useful in evaluating the performance of the iterative algorithm. Quick lover and upper bounds of the original problem are also developed. Finally, numerical results for numerous test cases are presented.