Shapley值法的改进及其应用研究

Research on improvement and application of Shapley value

为了求解没有哑元的合作对策问题,以经典Shapley值法为基础,提出了改进的Shapley值求解模型,并通过证明和推理对该改进Shapley值解进行了描述和刻画,结果表明:改进的Shapley函数和经典Shapely函数在形式上具有一致性,可以认为:改进的Shapley函数是经典Shapely函数在模糊领域的一个自然延续和拓展。在此基础上,以单个制造商、单个分销商和单个零售商构成的三级供应链为背景,将改进Shapley值法运用到其利润分配问题中,并用一个算例说明了该改进Shapley解的实用性和可行性。

To solve no-dummy cooperative game, based on classical Shapley value method, the paper puts forward solution model ofimproved Shapley value, and describes and portrays the improved Shapley value solution by proving and reasoning. The results show the form ofimproved Shapley function and classical is consistent, so the improved Shapley function is natural renewal and expansion of classical function on fuzzy area. Based on this, this paper regards three-level supply chain as background, which contains single manufacturer, single distributor and single retailer, appling improved Shapley value method to allocate profits, an example is given to illustrate its applicability and feasibility.