入出力項目間の相互作用を考慮したDEAにおける改善案計算法の提案

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Data Envelopment Analysis (DEA) is a method for measuring efficiency of a Decision Making Unit (DMU) by taking into account its characteristics. One of the feature emphasized in DEA is the capability of providing an improvement plan that makes an inefficient DMU efficient. It is assumed that all evaluation items can change independently in the calculation of an improvement plan. However, this assumption may not be realistic. Normally, some interactions between evaluation items should be assumed and the interaction may be described by equilibrium conditions. If this assumption does not hold, any improvement plans from DEA may not be applicable to a real problem since the improvement plans are impossible to carry out. In this study, a method for calculating improvements in a plan that allows interactions, including equilibrium conditions that are difficult to denote by closed forms, between evaluation items is proposed. Taylors first order expansion is used to approximate the interactions between evaluation items. If the interactions are expressed by linear functions, a problem that calculates an improvement plan is formulated as a nonlinear optimization problem with some constraints. In addition, a standard algorithm for solving nonlinear optimization problems can be applied to calculate the improvement plan due to convexity of an objective function and the constraints formulated. On the other hand, if the interactions are not expressed by linear functions or are expressed by equilibrium conditions, a problem for calculating an improvement plan is formulated as a fixed point problem. An algorithm for the fixed point problem is developed based on Kuhn-Tucker conditions. Lastly, two simple numerical examples are presented in this paper.JEL Classification: C61, C67

入出力項目間の相互作用を考慮したDEAにおける改善案計算法の提案

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