Title: Sample median approximation on stochastic data envelopment analysis

Authors: Marah Doly Nasution; Herman Mawengkang; Anton Abdulbasah Kamil; Syahril Efendi; Sutarman

Addresses: Graduate School of Mathematics, Universitas Sumatera Utara, Padang Bulan 20155, Medan, Indonesia ' Faculty of Mathematics and Natural Sciences, Department of Mathematics, Universitas Sumatera Utara, Padang Bulan 20155, Medan, Indonesia ' Faculty of Economics, Administrative and Social Sciences, Istanbul Gelisim University, Istanbul 34310, Turkey ' Faculty of Mathematics and natural Sciences, Department of Mathematics, Universitas Sumatera Utara, Padang Bulan 20155, Medan, Indonesia ' Faculty of Mathematics and natural Sciences, Department of Mathematics, Universitas Sumatera Utara, Padang Bulan 20155, Medan, Indonesia

Abstract: This paper study a new approximation model to solving stochastic data envelopment analysis (SDEA) problem. The proposed approach is based on problems that might occur in everyday life. This paper discusses the approach in determining the efficiency and super efficiency ratings of a decision making unit (DMU) in the DEA model with stochastic data. In determining efficiency, SDEA is first transformed into an equivalent deterministic DEA by changing its chance constraints in such a way that the SDEA problem can be solved easily. The author proposes an approach technique called a sample median approximation (SMA) to change the chance constraints so that it will be easy to get the optimal solution in determining the efficiency of DMUs. In the process, the data to be processed first is determined by the median average which will later be considered to represent the actual sample average. As a numerical example, the author resolves the vendor selection problem as presented by Wu and Olson (2006) in their paper. By taking the same parameter value (α = 0.2 and beta = 0.9), the efficiency score and super efficiency of the problem are obtained.

Keywords: data envelopment analysis; SDEA; stochastic data envelopment analysis; deterministic data envelopment analysis; SMA; sample median approximation; decision making unit; efficiency; super efficiency; Banker, Charnes and Cooper model; level of risk; level of aspiration.

DOI: 10.1504/IJASM.2020.109242

International Journal of Agile Systems and Management, 2020 Vol.13 No.3, pp.279 - 295

Received: 24 Jul 2019
Accepted: 04 Jan 2020
Published online: 02 Sep 2020 *

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