需求为三角模糊数的联合订货模型及其成本分摊方法

A Joint Replenishment Model with Demands Represented by Triangular Fuzzy Numbers and Its Cost Allocation Method

研究需求不确定的多销售商企业联合订购同种产品的库存管理问题.首先,构建允许缺货的需求用三角模糊数表示的联合订货EOQ模型,解得各销售商的三角模糊数订货量及各联盟的订货周期和三角模糊数平均成本.其次,根据定义的类联盟单调性条件,提出计算三角模糊数合作博弈的三角模糊数比例剩余分配值的一种方法,利用该方法得出三角模糊数比例剩余分配值的下界值、平均值和上界值可分别直接由相关联盟值三角模糊数的下界值、平均值和上界值计算得到,证明了三角模糊数比例剩余分配值满足的一些重要性质.最后,将三角模糊数比例剩余分配值用于分摊联合订货成本,用一个数值算例说明所提出的模型和成本分摊方法的有效性及实用性.研究工作可为解决复杂库存管理问题提供新途径与新方法.

This paper investigates the problem of multi-retailer joint replenishment for single product under uncertain demand. First, a joint replenishment EOQ model with shortage and demands represented by triangular fuzzy numbers is constructed to find the retailers' optimal triangular fuzzy ordering quantities and the coalitions' cycle lengths and the triangular fuzzy average costs. Second, we develop a simplified method based on our defined coalition size monotonicity-like conditions to calculate the triangular fuzzy proportional surplus division value for a special subclass of triangular fuzzy cooperative games. The triangular fuzzy proportional surplus division value can be obtained through computing the mean and the lower and upper limits by using the mean and the lower and upper limits of the relevant triangular fuzzy coalitions' values, respectively. Some important properties of the triangular fuzzy proportional surplus division value are proven. Finally, the proposed triangular fuzzy proportional surplus division value is used to allocate the triangular fuzzy average costs. The applicability and effectiveness of the proposed model and method are demonstrated with a numerical example. This paper may provide a new way and method for solving complex inventory management problems.