Exact approach for the aggregate production plan problem of machine-dependent production systems by considering stochastic parameters

This paper considers the variability of specific parameters in the aggregate production plan (APP) problem for machine-dependent production systems. The core issue emerges when assessing the APP's configuration by considering such decisions as the staff size, overtime and subcontracting, and inventory accumulation while reducing the overall production costs. We developed a deterministic mathematical model (MILAPP) and a stochastic mathematical model (SMILAPP) with the minimisation cost as the objective function. The stochastic model's decisions are performed in one stage, considering a penalised objective function for unsatisfied and surplus demand due to demand variation. The stochastic model's solution strategy is referred to as the sample average approximation (SAA). The effectiveness of the proposed approach is tested in the case of a Colombian multinational corporation. The results show that the proposed approach, which considers the predicted contribution of products and the uncertainty of many parameters, is a strong reference for decision support of APP problems.