A chance constrained programming approach for multi-product multi-stage integrated production planning under internal and external uncertainties

In industrial practice, making an efficient production planning for a multi-product multi-stage manufacturing network implies that various aspects of the uncertain environment have to be taken into account. In this paper, we address the uncertain conditions originating from internal and external factors including production efficiency, penalty cost of backorders and safety stock deviations, raw material supply and market demand. A novel chance constrained programming model with stochastic objectives and constraints is developed for the multi-product multi-stage integrated production planning problem incorporating the uncertainties. Then the proposed stochastic model is converted into an equivalent crisp mixed integer linear programming (MILP) problem by treating the stochastic objectives and constraints using a direct and an indirect approach. An industrial case is used for implementing and validating the proposed approach. The result indicates that the approach is flexible and that the trade-off between minimizing the cost and controlling the risk is efficient.