DEA-based Fixed Resource Allocation And Efficiency Evaluation On DMU With Fixed Resource

The problem of resource allocation,the most common managerial problem in modern economic society,have a significant value and far-reaching impact on relevant entities.With the development of social economic,"resources" are becoming scarce and limited.The scare and limited resource determines that any society must allocate the limited resource reasonably to all different kinds of fields,in order to achieve the effective utilization of all resources.That is,using less resource brings more goods and services as well as profit.Through an effective way in allocating the limited resource,enterprises can make more and better products and services.In addition,it can also realize the balance of supply and demand in different commodities,different varieties of the same kinds of goods,as well as the different producers of same commodity.Therefore,it is particularly important to design a fair,reasonable,and effective mechanism for resource allocationCurrently,most of the enterprises and originations allocate their resource through a series of financial indicator or the coordination among the enterprises departments,but these have no supports in mathematical theory.Data envelopment analysis(DEA),as a non-parametric mathematical approach,used to evaluate the relative performance of a group of homogenous DMUs,especially with multiple inputs and multiple outputs.At the same time,DEA can also estimate DMUs'production technology according to the production possible set,and,hence provides a reasonable theoretical basis for resource allocation.In addition,in practice we often encounter with the situation that some DMUs' total resources are fixed.For example,in the situation with fixed output,one DMU's increased output must on the basis of reducing other DMUs' outputs in making up his increment.However,traditional DEA models rarely consider the situation with fixed resources,and even the existing researches considering fixed output are rare and have obvious disadvantages.Hence,this dissertation will further study the DEA models in evaluating the DMUs' performance in the case of fixed outputs.This dissertation has six chapters,and the main contents for each chapter are displayed as follows.In the first Chapter,we first introduce the concept of the resource and resource allocation.Then,we introduce the DEA method,including methodology introduction,basic concepts,and several fundamental models.Afterwards,we further review some relevant DEA-based studies on resource allocation.Last,the research methodology,research contents,and the significance of the research are given.Chapter 2 provides a resource allocation method based on context-dependent DEA model,by firstly considering both resource category and each DMU's actual production technology.Specifically,we first review the traditional DEA-based resource allocation methods and point out the main disadvantages of previous studies.We found that previous studies have a strong assumption(e.g.,keep constant efficiency or become efficient in new production).Then,we use the concept of context-dependent DEA to construct each DMU's special production technology or production layer in order to reflect each DMU's changeable production after resource allocation and,hence,it could provide more accurate basis for the problem of resource allocation.Further,few studies have considered the characteristics of input resources.In real life,there are different kinds of input resources.For example,some resources may be inflexible and have fixed characteristics,while some other resources may be flexible and have variable characteristics.Last,consider above characteristics that have been neglected in previous studies,we combine context-dependent DEA and multi-objective linear programming(MOLP)to construct the corresponding model by comprehensively considering output,input,and firm's effectiveness in order to help the decision makers allocate the additional resources more reasonably.In Chapter 3,a new context-dependent DEA approach is developed to select the best cooperative partner in reallocating resources.That is,on the basis of Chapter 2 the context-dependent DEA is used to reallocate the available resource between cooperative partners.First,the context-dependent DEA is used to construct each partner's special production technology or production layer in order to reflect each partner's changeable production after resource reallocation.Then,using each partner's special production technology,we provide a new DEA model to select the best cooperative partner to reallocate their resources.Note that we consider two cooperative scenarios,namely,resources pooling only and best-practice sharing.In cooperation involving resource pooling only,the two cooperative partners only reallocate their pooled available inputs,whereas in cooperation involving best-practice sharing,the two cooperative partners,in addition to pooling their available input resources,can also share their production technology.Last,regarding the allocation of total revenue,we provide a fair allocation of total revenue to the two cooperative partners based on the Shapley value.Chapter 4 provides a new DEA method to allocate the emission reduction tasks.The new DEA method use each enterprise's previously observed production to construct its own production technology plan.First,we review previous studies about the allocation of emission reduction tasks and point out that previous studies rarely consider each enterprise's actual production after the emission reduction tasks are allocated.Then,we propose a new method to accurately assess the production,using each enterprise's previously observed production to construct its own production technology plan.With emission permits decreased,the enterprise can have new production strategy based on its own technology.Last,assuming emission permits can be freely bought and sold in the market,we show how each enterprise can determine the optimal amount of emission allowance that should be used for production,which may leave some allowance to be sold for extra profit or may require the purchase of permits from other firms.In the Chapter 5,we provide improved DEA models in evaluating DMUs'efficiency in the situation with fixed-sum resource.Based on the situation with fixed-sum output,previous studies have provided a common equilibrium efficient frontier and could guarantee the uniqueness of the common equilibrium efficient frontier by using a secondary goal approach.Through a simple counterexample,we first demonstrate that the secondary goal approach cannot always achieve uniqueness of the common equilibrium efficient frontier.Hence,we propose an algorithm based on the secondary goal approach to address the problem.The proposed algorithm is proven mathematically to be an effective approach guaranteeing the uniqueness of the common equilibrium efficient frontier.In addition,previous approaches mainly considered fixed-sum outputs by assuming a common input/output multiplier for all DMUs.We further propose to construct the common equilibrium efficient frontier by using different input/output multipliers(or weights)for each different DMU,which method could further decrease the decrement of fixed-sum out in achieving the common equilibrium efficient frontier.Last,the proposed algorithm and method are proven mathematically to be an effective by using two numerical examples.Chapter 6 makes conclusion and future research for this dissertation.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.