Affinely Adjustable Robust Model for Multiperiod Production Planning Under Uncertainty
针对需求概率分布未知的多产品多周期生产规划问题，提出仿射可调鲁棒优化模型，通过线性决策规则得到始终可行的最优解，数值实验表明其在平均成本、标准差和最坏情况成本上优于传统鲁棒和确定性模型。
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.