Research On Interval Cross-Efficiency Evaluation Method And Additive Multi-stage DEA Model

Cross-efficiency evaluation in data envelopment analysis (DEA) is proposed for increasing discrimination power of the classic DEA method, in which efficient DMUs cannot be further classified and ranked. However, in the computation of cross-efficiencies the optimal weights from classic DEA model are used. The possible existence of multiple optimal weights may lead to the non-uniqueness of cross-efficiency scores, which becomes one of flaws in the cross-efficiency evaluation that may limit its usefulness. In addition, the ultimate cross-efficiency results by simply averaging aggregation in the method are not Pareto optimal such that DMUs have no motivation to accept it. The non-uniqueness of cross-efficiencies and their aggregation issues in the method have affected its applications of the cross-efficiency evaluation. The first part of this dissertation is to deal with the non-uniqueness and aggregation issues in the cross-efficiency evaluation, including Chapter 2,3 and 4. To be specific, Chapter 2 discusses the cross-efficiency non-uniqueness issues, introduces an alternative interval cross-efficiency strategy, and defines cross-efficiency intervals, dominance relations and ranking ranges for DMUs. The interval cross-efface strategy successfully avoids the cross-efficiency non-uniqueness issue, and does not require decision makers’ preference on choosing aggressive or benevolent secondary goals. The definitions of dominance relations and ranking ranges for DMUs are useful for assessing the stability of the cross-efficiency scores. Chapter 3 deals with cross-efficiencies aggregation issue, and introduces the stochastic multicriteria acceptability analysis (SMAA-2) method to aggregate all DMUs’interval cross-efficiencies in the interval cross-efficiency matrix, giving up the simply averaging in the traditional cross-efficiency evaluation. In Chapter 4, a cross-ranking method is visited and improved based upon the proposed interval cross-efficiency evaluation strategy.Research on multi-stage DEA is conducted in the second part of the dissertation, i.e., Chapter 5. One of the unique features of the classic DEA model is that it does not make any assumptions on the DMUs’ inter structure. This property makes DEA a general and robust method. However, the classic DEA leaves out information about the internal structure, which often reveals process improvement opportunities. In addition, few industrial production system consist of only a single-stage process. Recently, the classical DEA has been extended to multi-stage systems. One useful feature of the multi-stage DEA model is that it can estimate the technical efficiencies for a DMU as well as the stages inside it. In Chapter 5, we study the multi-stage DEA models and find that the decomposition weights in the multi-stage model with additive efficiency decomposition can be non-increasing in the sequence of stage, which can bias the estimation of DMU’s overall and stages efficiencies. We create taxonomy for the multi-stage DEA models and examine when the decomposition weights can be non-increasing. As an alternative, a two-stage DEA model with constant decomposition weights and an improved heuristic algorithm for solving it are proposed.Contributions of the dissertation are as follows.1) Interval cross-efficiency evaluation strategy is introduced to address the cross-efficiency non-uniqueness issue and difficulty of choosing secondary goals.2) Cross-efficiency intervals, dominance relations and ranking ranges for DMUs in the interval cross-efficiency matrix are defined, which may be useful for assessing the stability of the cross-efficiency scores. 3) Giving up the simply averaging aggregation, the stochastic multicretieria acceptability analysis (SMAA-2) is introduced to aggregate the interval cross-efficiency matrix.4) It is found that decomposition weights in the additive multi-stage DEA model can be non-increasing, which may bias the DMUs’overall and stage efficiencies estimation.5) An additive two-stage model with constant weights are proposed as an alternative and an improved heuristic algorithm is provided for solving the problem.