Fixed Costs Allocation using Cross-Efficiency Evaluation and Game Theory

Subject Areas : Statistics

Mostafa  Davtalab-olyaie ¹ (Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, 8731753153, I R Iran,)
Fatemeh  Ghandi ² (Department of Mathematics, Shahid Rajaee Teacher Training University, Lavizan, Tehran)
Farideh  Davtalab-Olyaie ³ (Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan)

Received: 2020-01-14 Accepted : 2020-09-17 Published : 2021-07-23

Keywords: تخصیص هزینه‌‌های ثابت, نظریه بازی‌, تحلیل پوششی داده‌ها, ارزیابی کارایی متقاطع,

Abstract :

In many applications, there are some fixed costs for constructing the common platform of an organization which must be shared by all decision making units (DMUs). It is important how one should allocate such costs among all competing DMUs. Data envelopment analysis (DEA), which is a useful tool to evaluate the relative efficiency of DMUs, has been successfully used in allocating fixed costs among DMUs. Two main approaches have been proposed to allocate fixed costs that are based on maintaining or improving the relative efficiency of DMUs. In fixed costs allocation, one however needs to take into account both competitive and cooperative aspects among all DMUs. Therefore, it seems more reasonable to apply a peer-evaluation method in evaluating the efficiency of DMUs. To this end, we use cross-efficiency evaluation in DEA to allocate fixed costs between DMUs. Using cross-efficiency method and some concepts of game theory, we propose a new fixed costs allocation approach to share costs between DMUs such that the vector of cross-efficiency scores of DMUs after allocation is Pareto. We use a real application to more illustrate the proposed method and compare it with some of the existing methods.

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