An application of the multi-stage Monte Carlo optimization algorithm to aggregate production planning

Abstract

The restrictions to the use of analytical optimization approaches in the production and inventory management domain are widely recognized. Most significant among these restrictions is the limitation imposed by the need to model the real system by simple functions (normally linear or quadratic) if an optimal solution is to be obtained. In situations where such a simplified model does not provide a sufficiently accurate representation of reality, a possible alternative is to use a numerical search method. Many such methods have been developed and applied; however, many of these methods are not appropriate when dealing with functions of large numbers of variables or functions of non-convex form. This paper proposes the use of a Monte-Carlo-based search method for such problems, which include many production and inventory systems. The multi-stage Monte Carlo optimization algorithm (MSMCO) is described, and its use is illustrated by its application to the classical linear decision rule model of Holt et al. Results of this study indicate that, although not guaranteeing a strictly optimal solution, a very good near-optimal solution may be obtained within a manageable number of function evaluations. It is therefore proposed that the algorithm is likely to perform well with less well-behaved functions, such as might be the case in the general multi-item, multi-period production planning problem.