A Stochastic Programming Model for Multi-Product Aggregate Production Planning Using Valid Inequalities

Abstract

In this study, a mixed integer, linear, multi-stage, stochastic programming model is developed for multi-product aggregate production planning (APP). An approximation is used with a model that employs discrete distributions with three and four values and their respective probabilities of occurrence for the random variables, which are demand and production capacity, each one for every product family. The model was solved using the deterministic equivalent of the multi-stage problem using the optimization software LINGO 19.0. The main objective of this research is to determine a feasible solution to a real APP in a reasonable computational time by comparing different methods. Since the deterministic equivalent was difficult to solve, a proposal model with bounds in some decision variables was developed using some properties of the original model; both models were solved for different periods. We demonstrated that the proposed model had the same solution as the original model but required fewer iterations and CPU time, which implies an advantage in real APP. Finally, a sensitivity analysis was performed at varying service levels finding that if the service levels increase, the cost increases as well.

Keywords

• aggregate production planning
• stochastic programming
• industrial engineering