Affinely adjustable robust model for multiperiod production planning under uncertainty

Demand forecasting is an important factor in production planning, but future demand is not easy to forecast in practice. We consider a multiperiod, multiproduct production planning problem under demand uncertainty with constrains for raw materials, manufacturing capacity, and inventory. Under the assumption that probability distribution of demand is not available, two types of robust optimization models are proposed. First, a robust counterpart is developed to determine the here-And-now decision. Next, an affinely adjustable robust counterpart is developed to determine the wait-And-see decisions by approximating a robust solution with a linear decision rule. The robust models find an optimal solution that is always feasible and less sensitive against all realized demand within a given uncertainty set, in order to minimize production, procurement, inventory, and lost sales costs even in the worst case. Numerical studies demonstrated that, without knowing probability distribution of future demand, the affinely adjustable robust counterpart approach could outperform the robust counterpart and deterministic model in terms of the average cost, the standard deviation of the realized cost, and the worst-case scenario cost. The proposed method is much better than the others, especially when penalty cost due to lost sales is high and unknown demand is left skewed.