Abstract: 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.

Key words: joint replenishment, EOQ model, cost allocation, interval-valued cooperative game, Shapley value