Cost Allocation Of Cooperative Game With Random Demand And Supply Uncertainty

ABSTRACT:With the rapid upgrading of products, different choices and customer personalized needs bring demand uncertainty to the retailers. Meanwhile, suppliers’variable capacity, random yield, product quality and supply disruption caused by natural disaster result in supply uncertainty. Supply and demand uncertainty makes it harder for the retailers to decide order quantity and control cost. Customers would be unsatisfied if the retailers’inventory does not meet their needs, while excess inventory will cause risk of occupation of funds and commodity depreciation. In this situation, retailers would choose to cooperate to reduce risk and seek for better profits, and this paper focuses on cost allocation in the cooperation.The paper analyses the cooperation between companies which face random demand and supply uncertainty using cooperative game theory, and gives a solution to the cost allocation of the cooperative game using the concept of core and Shapley value in cooperative game theory. It is an extension for the newsvendor game, the paper considers the impact of both supply and demand uncertainty to the cost allocation. A two-stage stochastic program model is built up:in the first step, retailers decide their own order quantity, in the second step retailers fulfill the needs of the customers and make commodity transfer decision. The companies reduce their cost and share risk through inventory transshipment.Using the duality approach, the core of the game is proved to be non-empty and an element in the core is found, which represents the cost allocation. It is proved that all companies benefit from the cooperation, and the grand cooperation has the lowest cost. Then we also use Shapley value to calculate cost allocation according to their "contribution", we also get a solution in this method. A case study is given, and the two methods are used to solve the problem, and result in two different solutions of cost allocation, a comparison is also made between the two different solutions.