Exact and Approximate Cost Functions for Product Aggregates
提出一种新技术，将大型多产品问题近似为仅含一个或少数聚合产品的简化模型，并给出闭合形式的聚合成本函数，应用于多期多产品生产平滑模型，大幅减少产品数量。
We show that certain large, multiproduct problems can be well approximated by smaller models of the same form, representing only one aggregate product (or a few such products). This reduction follows from a new technique to approximate the minimal cost of a special allocation or “disaggregation” problem, by a simple, closed-form aggregate cost function. This function, moreover, has the same form as the cost functions for the original, individual products. For special cases the “approximation” is exact. (This latter result is related to economic-theoretic research on aggregation with homothetic preferences.) The results are applied to a one-stage, multiperiod, multi-item production smoothing model, and then to a similar model of a two-stage system, yielding a reduction in the number of items to one or to relatively few.