Improved Weighted Shapley Value Model for the Fourth Party Logistics Supply Chain Coalition

How to make the individual get the reasonable and practical profit among the fourth party logistics supply chain coalition system is still a question for further study. Considering the characteristics of the fourth party logistics supply chain coalition, this paper combines Shapley Value with Distribution according to Contribution, two methods in the application, and then adjusts the profit allocated to each member reasonably based on the actual coalition situation named improved weighted Shapley Value model. In this paper, we first analyze the fourth party logistics supply chain coalition profit allocation models, the classical Shapley value method. Then, we analyze the weight of individual enterprise in the coalition by the analytic hierarchy process. To each enterprise, the weight is determined by the investment risks, information divulging risks, and failure risks. Finally, the numerical study shows that the profit allocation method improved weighted Shapley value model is relatively rational and practical. Thus, the proposed combined model is a useful profit allocation mechanism for the fourth party logistics supply chain coalition that the contribution and risks are fully considered.

ALLOCATION OF FIXED COSTS: CHARACTERIZATION OF THE (DUAL) WEIGHTED SHAPLEY VALUE

The weighted value was introduced by Shapley in 1953 as an asymmetric version of his value. Since then several axiomatizations have been proposed including one by Shapley in 1981 specifically addressed to cost allocation, a context in which weights appear naturally. It was at the occasion of a comment in which he only stated the axioms. The present paper offers a proof of Shapley's statement as well as an alternative set of axioms. It is shown that the value is the unique rule that allocates additional fixed costs fairly: only the players who are concerned contribute to the fixed cost and they contribute in proportion to their weights. A particular attention is given to the case where some players are assigned a zero weight.

A TWO-STEP SHAPLEY VALUE FOR COOPERATIVE GAMES WITH COALITION STRUCTURES

In this paper, we study cooperative games with coalition structures. We show that a solution concept that applies the Shapley value to games among and within coalitions and in which the pure surplus that the coalition obtains is allocated among the intra-coalition members in an egalitarian way, is axiomatized by modified axioms on null players and symmetric players and the usual three axioms: efficiency, additivity and coalitional symmetry. In addition to the original definition, we give two expressions of this solution concept. One is an average of modified marginal contributions and the other is the weighted Shapley value of a game with restricted communication.