Research Of Common Cost Allocation In Two-stage Series System From The Efficiency Perspective

The problem of common cost allocation has always been an important issue in enterprise production activity.It is aslo a hot issue in the research field of management science.The traditional researches about this topic are usually allocating the common cost from the prospective of profits or revenue.By contrast,the allocation method based on data envelopment analysis(DEA)comprehensively considers multiple inputs and multiple outputs of decision making units(DMUs).In this thesis,we consider the efficiency and fairness,use DEA method,game theory,robust optimization and other method or theory to provide three allocation methods.The main contents are as follows:Firstly,we propose a step-by-step allocation method based on game theory.We use the existed Minmax model to allocate the common cost among different DMUs.Then establishing Leader-Follower DEA model to determine the common cost allocation between two stages of DMUs.In order to gurantee the fairness,we use the average of the cost allocation obtained from the Leader-Follower DEA models that each stage is regarded as leader.This method fits for the intra-organizational hierarchically allocation,in which situation,the senior decision maker only allocate the common cost among different DMUs,and the decision makers of each DMU decide the cost between their two stages.Secondly,we design a cross efficiency algorithm to obtain the common cost allocation.After establishing the additive two-stage DEA model,we choose the average of each DMU's cross efficiency as the iteration variable and prove that all the DMU's cross efficiency will reach 1 when the iteration stops.We use the averge cost of each DMU's cost as the final cost allocation and prove the all DMUs can find at least one set of weight to make themselves Pareto efficient.Since the cross efficiency consider both the “self-evaluation” and “peer-evaluation”,it can be said that the obtained cost allocation is fair.This method is used to allocate the common cost among different enterprises or different sub-enterprises that are under a centralized organization.Then,we combine common weight DEA model with the DMU's satisfaction and present a new method to allocate the common cost.We prove that all DMUs can find at least one cost allocation to make themselves Pareto efficient under an appropriate set of common weight.The efficient cost allocation set are also given.In order to find a fair allocation in this set,we define the DMU's satisfaction of the cost allocation.Through maximizing the minmal satisfaction,we can get the final cost allocation.This method can be used when the central authority wants to use common weight to evaluate all DMUs and decide the cost allocation.After presenting the above three methods of common cost allocation,we expand the DMUs to the two-stage series system with shared inputs.We prove that the previous three methods can also be used in such systems.The numberical example shows that these methods are suitable.We also point out that the shared inputs should be divided into two stage to obtain more accurate and reasonalbe results.Finally,we consider the uncertainty in output data and establish a robust efficiency evaluation model and cost allocation model based on the common weight DEA model with DMU's satisfaction.The output data is allowed to fluctuate among the nominal value in a small range,and the results is valid at a relative high probability.Since we have taken the data uncertainty into consideration at the very beginning of the modelling,the results derived from this model are reliable and robust.This thesis present different methods to allocate the common cost among different DMUs and stages.The findings have great practical significance to the common cost allocation scheme mechanism design.We can provide siginificant choice and suggession for the decision maker to help them make more clear and reasonable task and plan.In addition,our researches not noly expand the research of common cost allocation in both theory and practice,but aslo broaden the application fields of DEA theory.