An Exact Approach to the Relaxed Combined Production Planning Model
Código: WPE – 178
Maria Cristina Nogueira Gramani
Paulo M. França
Marcos N. Arenales
Two fundamental processes usually arise in the production planning of several industries. One of them consists of deciding how many final products of each type have to be produced in each period of the planning horizon, the well known lot sizing problem. The other process consists of cutting rectangular plates in order to produce smaller pieces used in the assembly of final products, the much studied cutting stock problem. In this paper we propose to join these two problems in order to obtain a global optimum solution. Toward this goal, we formulated a novel combined mathematical programming model that captures the synergy in solving both problems in conjunction. Due to the great complexity of the proposed problem, we have relaxed the model and solved it by an exact approach – using the simplex method with the column generation technique. We present some sets of computational tests, analyzed over three different aspects. These results demonstrate that, by combining the problems, it is possible to obtain significant gains compared to the usual industrial practice.