Research On Fixed Cost And Resource Allocation With Different Interaction Modes Among Decision Making Units

Fixed cost and resource allocation,the most common managerial problems in modern economic society,have a significant value for and far-reaching influence on relevant entities.Theoretically,the fixed cost should be allocated in line with the causation principle,that is,the decision making units(DMUs)will afford the fixed cost according to their usages of and gains from the common platform.However,particularly when assigning the fixed cost,we often have the problem that the causes cannot be determined precisely.Then one mostly has to use production-or activity-related distribution criteria to address the fixed cost allocation problem.Additionally,there exists a set of comparable and homogeneous entities that are operating under the same central decision maker in many managerial applications.An essential problem frequently faced by the decision maker is achieving particular production goals or satisfying pre-specified regulations through planning and managing entities' productions.In view of this background,it is of vital importance and significant value for determining an equitable and reasonable mechanism,which can allocate fixed input resources and set pre-specified output targets across DMUs in a fair manner.It is acknowledged that the fixed cost allocation is targeted on expense occurred in the past,while the resource allocation problem focuses on production planning in the future.One must take the interaction among a set of competitive DMUs into account for both fixed cost allocation problem and resource allocation problem,as the interaction modes reflect different behavioral tendencies and decision preferences.And as results,the interaction modes will further affect the fixed cost and resource allocation mechanism and results.In view of this consideration,this thesis studies the fixed cost and resource allocation problem considering different interaction modes among DMUs.The thesis starts from the relative efficiency analysis using data envelopment analysis(DEA)theory.This thesis contains six chapters,and the main contents are summarized as follows:Chapter 1 first discusses the research background and research problem,and then introduces the DEA technique,including methodology introduction,basic concepts,and some fundamental models.Afterward,it reviews some relevant DEA-based fixed cost and resource allocation studies in the existing literature.In the end,it discusses the research methodology,research contents,research significance and structure organization.Chapter 2 and 3 considers the extra-DMU interaction,and study the fixed cost allocation problem by adopting competitors' opinion and defending competitors'utility,respectively.By focusing on the peer appraisal among DMUs,Chapter 2 proposes a DEA cross-efficiency game approach for allocating the fixed cost.To this end,each DMU is considered as a game player and the cross-efficiency increment is defined as the characteristic function.Further,Chapter 2 takes the Shapley value as an equitable distribution for the total cross-efficiency increment and accordingly calculates the associated common weights.The common weights can be further used to determine an equal and unique fixed cost allocation scheme.Taking the feasibility of possible fixed cost allocation plans into consideration,Chapter 3 proposes a new concept called non-egoistic principle,which implies that each DMU should propose its allocation proposal in such a way that the maximal cost would be allocated to itself.Based on the non-egoistic principle,this chapter gives a constraint condition on allocated cost and post-allocation efficiency for individual DMUs.Then it integrates a goal programming method with the DEA methodology to propose a new model under a set of common weights,and the final allocation scheme is determined in such a way that the efficiency scores are maximized for all DMUs.Chapter 4 mainly considers the interaction among internal sub-units within DMUs,and extends the traditional fixed cost allocation problem to situations where the DMUs have a two-stage network structure.Chapter 4 first determines the possible relative efficiency while taking the internal structure and possible allocated costs into account.It shows that there exists an efficient allocation set based on a set of common weights,using which all DMUs and their two sub-units can be simultaneously efficient.However,there are alternative allocation plans in the efficient allocation set.Afterward,it calculates a proportional size allocation plan by taking the size of operation units into account.By repeatedly minimizing the deviation between the efficient allocations and size allocations,the proposed method can guarantee a unique allocation plan for all DMUs and sub-units.With consideration of the extra-DMU interaction of preserving the status quo,Chapter 5 studies the input resource allocation and output target setting problem.Through revising the traditional establishment condition for common weights and efficiency invariance principle,this chapter proposes a new resource allocation and target setting approach.In general,the proposed method will generate two schemes,with one being generated using a set of common weights for all DMUs in such a way that the change of efficiencies is minimized,while the other is generated by strictly keeping efficiency scores unchanged yet having similar or even identical weights on input-output measures for each DMU to the utmost extent.Finally,Chapter 6 concludes this thesis.It not only summarizes the whole research and the main innovations,but also discusses some drawbacks and limitations,which will imply possible revenue for future research.This thesis studies the fixed cost and resource allocation problem considering different interaction modes among DMUs,and it contributes to the existing literature mainly in the following aspects:first,it develops a DEA cross-efficiency game approach for fixed cost allocation,which takes advantage of peer appraisal and takes the competition and cooperation relationship among DMUs into account.Further,it proposes a non-egoistic principle,which considers the feasibility issue of possible fixed cost allocation schemes.Also,it extends the traditional fixed cost allocation problem to situations with two-stage network structures and accordingly proposes a two-stage DEA-based fixed cost allocation approach.Lastly,it explores the efficiency invariance principle under a common set of weights and proposes a resource allocation and target setting scheme simultaneously adopting the principles of common weights and efficiency invariance.