Scientia Iranica

Scientia Iranica

Stepwise pricing in evaluating revenue efficiency in data envelopment analysis: A case study of power plants

Document Type : Research Article

Authors
Z. Moghaddas 1
M. Vaez-Ghasemi 2
F. Hosseinzadeh Lotfi 3
R. Farzipoor Saen 4
1 Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran
2 Department of Mathematics, Rasht Branch, Islamic Azad University, Gilan, Iran
3 Department of Mathematics, Science and Research, Islamic Azad University, Tehran, Iran
4 Faculty of Business, Sohar University, Sohar, Oman
10.24200/sci.2020.55350.4184
Abstract
Data envelopment analysis (DEA) technique is widely applied for performance assessment of decision making units (DMUs). The revenue efficiency (RE) evaluation is one of the controversial subject matters that can be performed through DEA context. The amount of productions and its prices are crucial factors in the RE. The classical DEA models consider the prices to be fixed and known which are not the case in real world. Also, the classical DEA models considers linear pricing in revenue assessment. However, most of real world problems deal with nonlinear prices. This paper evaluates the RE given the piecewise linear theory in non-competitive situations. In doing so, a stepwise pricing function is introduced which lets the prices to be changed in relation to the amount of the production. As an innovative idea, a more accurate mathematical modeling for the RE is proposed. We define a dynamic weights’ function in maximum revenue optimization model which no longer considers fixed prices. A case study validates our proposed model.
Keywords
Data envelopment analysis (DEA)
Revenue efficiency
Stepwise pricing
Mixed integer programming
Big M
Malmquist productivity index (MPI)
Piecewise linear functions

  1. References:

    1. Farell, M.J. "The measurement of productive efficiency", J. R. Statist. Soc., 120(3), pp. 253–281 (1957).
    2. Charnes, A., Cooper, W.W., Rhodes E. "Measuring the efficiency of decision-making units" Eur. J. Oper. Res., 2(6), pp. 429-444 (1978).
    3. Kuosmanen, T., Post, T., (2001). "Measuring economic efficiency with incomplete price information: With an application to European commercial banks", Eur. J. of Oper. Res., 134, 43-58.
    4. Kuosmanen, T., Post, T. "Measuring economic efficiency with incomplete price information", Eur. J. of Oper. Res. 144(2), pp. 454-457 (2003).
    5. Mostafaee, A., Saljooghi, F. "Cost efficiency measures in data envelopment analysis with data uncertainty", Eur. J. of Oper. Res., 202(2), pp. 595-603 (2010).
    6. Chakraborty, T., Chauhan, S.S., Awasthi, A. Chameeva, T.B. "Two-period pricing and ordering policy with price sensitive uncertain demand", J. of Oper. Res. Soci., 70(3), pp. 377-394 (2018).
    7. Fang, L., Li, H. "A comment on cost efficiency in data envelopment analysis with data uncertainty" Eur. J. of Oper. Res., 220(2), pp. 588-590 (2012).
    8. Mozaffari, M., Kamyab, P., Joblonsky, J., Gerami, J. "Cost and revenue efficiency in DEA-R models", Comp. Indus. Eng. 78, pp. 188-194 (2014).
    9. Ghiyasi, M. "Inverse DEA based on cost and revenue efficiency", Comp. & Indus. Engin., 114, pp. 258-264 (2017).
    10. Fang, L., Hecheng, Li. "Duality and efficiency computations in the cost efficiency model with price uncertainty" Comp. & Oper. Res., 40(2), pp. 594-602 (2013).
    11. Aparicio, J., Borras, F., Pastor J.T., Vidal, F. "Accounting for slacks to measure and decompose revenue efficiency in Spanish Designation of Origin Wines with DEA", Eur. J. Oper. Res. 231(2), pp. 443-451 (2013).
    12. Sahoo, B.K, Mehdillozad, M., Tone, K. "Cost, revenue, and profit efficiency measurement in DEA", Eur. J. Oper. Res. 237(3), pp. 921-931 (2014).
    13. Aparicio, J., Borras, F, Pastor, J.T., Vidal, F. "Measuring and decomposing firm’s revenue and cost efficiency: The Russell measures revisited", Int. J. Production Economics. 165, pp. 19-28 (2015).
    14. Cook, D.W., Zhu, J. "Piecewise linear output measure in DEA", Eur. J. Oper. Res., pp. 197(1), 312-319 (2009).
    15. Hosseinzadeh Lotfi, F.H., Rostamy-Malkhalifeh, M., Moghaddas, Z. "Modified piecewise linear DEA model", Eur. J. Oper. Res., 205(3), pp. 729-733 (2010).
    16. Konara, P., Tan, Y., Johnes, J. "FDI and heterogeneity in bank efficiency: Evidence from emerging markets", Res. Int. Bus. Finance, 49(c), pp. 100-113 (2019).
    17. Deng, Y., Veiga, H., Wiper, M.P. "Efficiency evaluation of hotel chains: a Spanish case study", SERIEs, 10(2), pp. 115–139 (2019).
    18. Cao, Y., Zhang, W., Ren, J. "Efficiency analysis of the input for water-saving agriculture in China", Water, 12(1), pp. 207 (2020).
    19. Aroche-Reyes, F. "Endogenous Prices for Input/Output Models: A Note", Economic Systems Research, 5(4), pp. 365-376 (2006).
    20. Johnson, A.L., Ruggiero, J. "Allocative Efficiency Measurement with Endogenous Prices", Econ.Letters, 111(1), pp. 81-83 (2011),
    21. Moura, A. "Investment shocks, sticky prices, and the endogenous relative price of investment", Rev. of Econ. Dynam., 27, pp. 48-63 (2018).
    22. Din, H., Sun, C.H. "Welfare improving licensing with endogenous choice of prices versus quantities", North Amer. J. of Econ. and Fina., 51(c), pp. 100859 (2020).
    23. Cellini, R., Siciliani, L., RuneStraume, O. "A dynamic model of quality competition with endogenous prices", J. of Econ. Dynam. and Contr., 94(c), pp. 190-206 (2018).
    24. Cooper, W.W., Seiford, L.M., Tone, K. "Data envelopment analysis, A Comprehensive Text with Models, Applications, References and DEA-Solver Software", Second edition, Springer (2007).
    25. Wang, C.G., Fare, R., Seavert, C.F. "Revenue Capacity Efficiency of Pear Trees and its Decomposition", J. Amer. Soci. for Horticultural Sci., 131(1), pp.32-40 (2006).
    26. Caves, D.W., Christensen, L.R., Diewert, W.E. "The economic theory of index numbers and the measurement of input, output and productivity", J. Econometrica, 50(6), pp. 1393-1414 (1982).
    27. Tavanir Management Organization (2015). "Electric Power Industry in Iran 1997–2004".
Scientia Iranica
Volume 29, Issue 2
Transactions on Industrial Engineering (E)
March and April 2022
Pages 915-928

  • Receive Date 30 January 2020
  • Revise Date 04 May 2020
  • Accept Date 08 June 2020