Convex optimisation for aggregate production planning

Abstract

This paper presents a new solution approach to the problem of aggregate production planning (APP). As identified by many researchers, the APP cost function is convex and piecewise. Thus, the convex optimisation approach can be applied to the APP problem. Solving the APP problem using convex optimisation is attractive since it leads to an improved solution over the classical solution methods and it can be applied to a wider range of functions. The classical Linear Decision Rule model of APP is solved using convex optimisation and the resulting solution is compared to three solution approaches which have been historically used to solve this model. The results suggest that convex optimisation may be an effective approach for solving certain types of planning models.