Fair Allocation of profits or costs arising from joint participation by multiple individuals or entities with different purposes is essential for their continuing involvement and for their dissatisfaction reduction. In this research, fair allocation of the profits of forming a grand coalition in Three-Echelon Supply Chain (TESC) game that is composed of manufacturer, distributor and retailer, is studied. In particular, the solutions of the proportional method of profit, the proportional method of marginal profit, and Shapley value based on cooperative game theory are proved to be in the desirable characteristics of the core. The proportional method of profit and the proportional method of marginal profit are often used because of their ease of application. These methods distribute total profit in proportion to profits or marginal profits of each game participant. In addition, Shapley value can be defined as the average marginal profit when one game player is added at a time. Even though the calculation of the average of all possible marginal profits is not simple, Shapley value are often used as a useful method. Experiments have shown that the solution of the incremental method, which calculates the marginal cost of adding game players in the order of manufacturers, distributors and retailers, does not exist in the core.

Joint order and transportation system which can be used for the franchise business is considered. It is assumed that several agents exist on the same vehicle route and each agent has an EOQ inventory policy and the same order cycle. It is also assumed that transportation cost is proportional to the distance of farthest agent from the supplier. Various methods for rational and fair cost allocation such as line rule, AMEF, the Shapley value, nucleolus, and proportional method were researched and applied to the inventory transportation problem. The core is the basic condition for rational and fair cost allocation. Therefore, we examined if the solutions of various allocation methods are existed in the core through an example.

Cost allocation studies on the rational allocation method for the common cost of the joint products or services that provide different benefits to each economic entity under the constraints of the efficiency and fairness. Cooperative game theory is often used for cost allocation and studies on a fair and efficient allocation of the utility if some feasible utility for a whole or subset of the players in a game is given. This study shows a variety of cooperative game theory approaches and discusses the pros and cons of each approach.