Solution of the aggregate production planning problem in a multi-stage-multi-product manufacturing system using functional space analysis and quadratic programming approaches

Abstract

This paper describes the functional space analysis and quadratic programming approaches for the solution of a vector space model of aggregate production planning in a multi-stage-multi-product manufacturing system. It is shown that both of these approaches can be used to determine the production planning strategies for the number of periods under consideration. Statistical inference techniques are used to determine whether the functional space analysis technique results in a global minimum. Tests carried out on two different sets of data show that the quadratic programming approach always results in a minimum cost solution, although it requires a large amount of computing power. Although complicated mathematics is required to formulate the problem and solve it, the resulting solution can be easily understood and applied to a practical manufacturing system.