The Solution Of Cooperative Games And Its Application In Inventory Cost Allocation

Using cooperative games,the allocation of joint replenishment inventory cost is studied in this paper.In view of the uncertainty of inventory demands,the demands can be expressed as interval values,so the joint replenishment inventory problem with interval demands is regarded as interval values cooperative games.In this paper,we focus on the solutions of interval values cooperative games,and the interval values cooperative games prenucleolus and nucleolus with player excess are defined.Some properties are proved.For the inventory cost allocation problems with strategy selection and cooperation,considering the strategies of retailers' ameliorating technology,the inventory cost with ameliorating technology sharing and joint replenishment is studied by using biform games theories.The main achievements are as follows:In this paper,the solution of interval values cooperative games and its properties are studied.The definition about player excess of interval values cooperative games is given,and then the quadratic programming models based on player excess are established to get the solutions of interval values cooperative games with crisp collations and the interval values cooperative games with infinite fuzzy coalitions respectively,which consider the efficiency and individual rationality.Some properties of solutions are proved.The model of joint replenishment inventory cost allocation with interval demands is constructed.Considering the joint replenishment inventory cost problem as an interval values cooperative game,an interval inventory cost cooperative game is defined in this paper,and the properties of the characteristic function of this game is discussed.Further the solution given in this paper is used to distribute inventory cost,which verifies the applicability and validity of the solution and expends a new idea for the interval inventory cost allocation at the same time.The game model of joint replenishment inventory cost with ameliorating technology sharing is constructed.Since there may be both strategy selection and cost allocation in inventory problem,the competition and cooperation of retailers is studied by biform games theories and a n-person biform game model with ameliorating technology sharing and joint replenishment is established.Then using stochastic programming models,retailers' pure strategy Nash equilibriums about ameliorating rate in competition stage can be obtained.By the allocation rule of cooperative games,the joint replenishment inventory cost is distributed.Finally,the validity of the biform game model is verified by numerical example analysis,and the relationship between retailers' confidence indexes and equilibrium solution is obtained.