Cost efficiency measurement with price uncertainty: a data envelopment analysis
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ORIGINAL RESEARCH
Cost efficiency measurement with price uncertainty: a data envelopment analysis F. Hosseinzadeh Lotfi1 · A. Amirteimoori3 · Z. Moghaddas2 · M. Vaez‑Ghasemi3 Received: 15 May 2019 / Accepted: 13 August 2020 © Islamic Azad University 2020
Abstract Data envelopment analysis (DEA) technique is commonly utilized for efficiency assessment in a variety of fields for both theoretical and applicational purposes. In classic cost efficiency measurement models, the input and output data and input prices should be known for each decision-making unit (DMU). However, in real-life markets the input prices are not precisely defined for DMUs. In this paper, we shed light on the fact that fixed prices assumption cannot reflect the reality of situations, because market will force lower prices if greater amounts of a product are purchased. It can be said that discounts are automatically considered in these circumstances. To this end, an innovative idea is considered to modify the classic cost efficiency DEA model in order to investigate the situations of real-life markets. Then, by an empirical example, a comparison between the proposed approach and the classic cost efficiency model is provided. Keywords Data envelopment analysis · Cost efficiency · Mixed integer programming · Marginal value · Piecewise linear functions Mathematics Subject Classification 90C · 65K05
Introduction Cost efficiency measures the firm’s success in choosing an optimal set of inputs by minimizing total input costs. It reflects the differential between the current cost of a DMU and the possible minimal cost. The concept of CE can be traced back to Farrell [1], and Fare et al. [2]. They have developed this concept through a linear programming (LP) model. They considered mathematical programming techniques and data development analysis technique, to determine the cost efficiency score, relative to the observed best practices. It is significant to note that the DEA analysis determines the minimum cost necessary for each DMU, which leads to the production of the observed output. They * A. Amirteimoori [email protected] 1
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
2
Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran
3
Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran
noted that the input and output data and input prices for each of the DMU should be defined in this LP model. Farrell [1] put forward the cost efficiency evaluation, which reflects the cost reductions, where adjusting the prices is not possible. In the previous studies, CE measures the closeness of a unit’s cost to the cost of the best practice unit’s that would be produced with the same bundle of outputs. Some limitations in the Farrell CE measurement are discussed in the literature. In the presence of different prices between the DMUs, Tone [3] stated that such differences do not reflect the differential between the current cost of the DMU and the m
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