A minimax p-robust optimization approach for planning under uncertainty

Planning under uncertainty is one of the important issues in production planning. The development of mathematical models under uncertainty has long been studied in order to avoid the impact of uncertain factors and to maintain stable and excellent performance of manufacturing system. In this paper, we propose a minimax p-robust production planning problem in the presence of parameter uncertainty. Particularly, we apply p-robust measure to a multi-period production planning and inventory control problem considering a set of demand scenarios. A scenario based robust optimization problem is extended to a minimax p-robust optimization problem by combining a p-robustness measure and a minimax objective function. The proposed model is compared with a deterministic model and a minimax model using simulation experiments. The results show that the minimax p-robust solution improves the average cost compared to other approaches while maintaining similar level of worst-case cost from the minimax model.