联合订货区间值EOQ模型及变权Shapley值成本分摊方法

研究多个销售商企业组成联盟向一个供应商订购同种商品的联合订货问题。考虑到实际问题中很难预测到精确的需求，本文用区间表示单位时间需求量，研究允许缺货的销售商企业联合订货区间值EOQ模型，其中缺货完全回补。以联合订货平均成本最小为目标，结合连续有序加权集结算子求解出联合订货的周期、区间值订货量和区间值平均成本。定义变权Shapley值，给出区间值合作博弈的区间值变权Shapley值的求解方法，得出区间值变权Shapley值的表达式可直接利用相关联盟值的左、右端点计算得到。考虑联盟和局中人的相对重要性，结合需求率确定合成权重，提出基于区间值变权Shapley值的联合订货成本分摊方法。利用数值算例验证模型和方法的有效性。本文可为解决联合订货成本分摊问题提供决策参考。

Joint Replenishment Interval-Valued EOQ Model and Cost Allocation Approach Based on Variable-weighted Shapely Value

The joint replenishment problem with a single supplier and multiple retailers for a single product is investigated in this paper. According to the fact that it is difficult for retailers to predict the demands accurately in real situations, a joint replenishment interval-valued EOQ model of retailers whose demands are expressed with intervals is studied. It is assumed that the shortages are allowed and are completely backlogged. The aim of this paper is to determine the replenishment policy which minimizes the average joint cost. The optimal cycle, interval-valued ordering quantity and interval-valued average joint cost are obtained by using the continuous ordered weighted averaging (COWA) operator. Inspired by the variable-weighted theory and the Shapley value, the variable-weighted Shapley value is proposed and a simplified method is developed to obtain the formula of the interval-valued variable-weighted Shapely value by utilizing the lower and upper bounds of the relevant interval-valued coalitions' value, respectively.The method avoids the issues resulting from the Moore's interval subtraction. Then a cost allocation approach based on the interval-valued variable-weighted Shapely value is introduced. The synthetic weights of the interval-valued variable-weighted Shapely values are determined by considering the relative importance of coalitions and players, where the relative importance is reflected by the demand rate. The model and allocation approach proposed in this paper are illustrated with a numerical example to show the applicability and superiority.This paper can be taken as a reference for solving complex joint replenishment cost allocation problems.