Joint replenishment model with fuzzy demand and cost allocation approach based on egalitarian Shapley value
Joint replenishment is an effective way for retailers to save costs and increase profits since retailers can share fixed ordering costs and storage costs together.In real situations,it is difficult for retailers to predict the demands accurately due to the complexity of the market environment.Hence,the joint replenishment triangular fuzzy EOQ model without shortage is re-searched,where the demands of retailers are expressed with triangular fuzzy numbers.Then the cooperative game approach to allocate the corresponding joint replenishment costs is discussed.Combining with the measure method of average area of the triangular fuzzy number,we attain the joint replenishment strategy and triangular fuzzy average cost.There is not general method for solving triangular fuzzy cooperative games due to the irreversible subtraction of triangular fuzzy number.Hence,we develop an effective method to compute triangular fuzzy egalitarian Shapley values for a class of triangular fuzzy cooperative games through adding some coalition size monotonicity-like conditions,and the formula of triangular fuzzy egalitarian Shapley value is obtained.Moreover,some important properties of the triangular fuzzy egalitarian Shapley value are proven in detail.The triangular fuzzy egalitarian Shapley value is used to allocate the trian-gular fuzzy public costs since it balances efficiency and fairness.The validity and applicability of the proposed model and the cost allocation approach are demonstrated with a real example.
joint replenishmentcost allocationcooperative gameegalitarian Shapley value
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