带有资源约束的模糊DEA线性生产博弈模型及分配

Fuzzy DEA linear production game model and allocation with resource constraints

Owen线性生产博弈假设生产技术和资源的边际贡献固定不变,但实际上,生产技术和资源边际贡献并非固定不变而是随生产改变.基于此,为了刻画具有模糊性和动态性的生产过程,提出模糊DEA线性生产博弈.首先构建2种合作水平(同时共享技术和资源、仅共享资源)、3种资源类型(最低资源、最佳资源、有效资源)和2种收益角度(乐观、悲观)构成的复杂生产模型,并通过上述3种因素解释合作生产具有互利性,资源带来的收益具有“先增后平”的变化趋势以及可能获得的最大收益区间;然后,利用α-核心求解此博弈,在特定情况下无需利用对偶理论即可得到α-核心分配,从而简化了计算步骤;最后,通过解决云服务虚拟机转化过程中建模和收益分配问题表明所提出模型和方法的实际意义与理论价值.

Owen’s linear production game makes a fixed assumption on the marginal contribution of production technology and resources.However,production technology and the marginal contribution of resources change with production all the time in fact.Based on this,in order to describe the production process with fuzziness and dynamics,this paper proposes a fuzzy DEA linear production game.Firstly,the complex production models composed of two cooperation scenarios(sharing technology and resources and sharing resources only),three resource types(the minimum resources,the optimum resources,the effective resources)and revenues from two perspectives(optimistic and pessimism)are established.This paper explains the mutual benefit of cooperative production,the change trend of“increase first and then smooth”in the revenue brought by resources,and the possible maximum revenue range by the above three factors.Secondly,α-core is used to solve this game,and it is found that theα-core allocation can be obtained without using duality theory in specific cases,which simplifies the calculation steps.Finally,the practical significance and theoretical value of this model and method are illustrated by solving the problems of modeling and revenue allocation in the process of cloud service virtual machine transformation.