Estimating Marginal Rates of Substitution in Two-Stage Processes With Undesirable Factors

Document Type : Research Paper

Authors

1 Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran

2 Department of Applied Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran

Abstract

Trade-offs between production factors such as marginal rates of substitution are significant aspects for decision makers and managers. Due to the complexity of processes and the presence of undesirable measures in many real-world applications, in this study, the relative efficiency and marginal rates of substitution are calculated in two-stage structures including weakly disposable undesirable intermediate measures. Actually, an approach based on the directional distance function is provided for this purpose. Therefore, the effect of the changes of a measure in other measures such as the effect of the changes of intermediate factors on the output of the first stage and second stage is measured by maintaining efficiency, and the rate of these changes is calculated. To elaborate in details, marginal rates of substitution in two-stage processes are dealt with using the proposed two-stage data envelopment analysis (DEA) approach while undesirable intermediate components are presented. A real data set is also used to clarify the proposed method herein.

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Main Subjects


Amirteimoori, A., Fouladvand, M., & Kordrostami, S. (2017). Efficiency measurement using nonparametric production analysis in the presence of undesirable outputs. Application to power plants. Operations Research and Decisions, 27(3), 5-20.
Amirteimoori, A., Kordrostami, S., & Sarparast, M. (2006). Modeling undesirable factors in data envelopment analysis. Applied Mathematics Computation, 180(2), 444-452.
Asmild, M., Paradi, J. C., & Reese, D. N. (2006). Theoretical perspectives of trade-off analysis using DEA. Omega, 34(4), 337-343.
Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 30(9), 1078-1092.
Chambers, R. G., Chung Y., & Fare, R. (1998). Profit , directional distance functions , and Nerlovian efficiency. Journal of Optimization Theory and Applications, 98, 351-364.
Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429-444.
Cook, W. D., Zhu, J., Bi, G., & Yang F. (2010). Network DEA: Additive efficiency decomposition. European Journal of Operational Research, 207(2), 1122-1129.
Färe, R., & Grosskopf, S. (2003). Nonparametric productivity analysis with undesirable outpus: Comment. American Journal of Agricultural Economics, 85(4), 1070-1074.
Hailu, A., & Veeman TS. (2001). Non-parametric productivity analysis with undesirable outputs : An application to the Canadian pulp and paper industry. American Journal of Agricultural Economics, 83(3), 605-616.
Jahanshahloo, G., Hadi Vencheh, A., Foroughi, A., & Kazemi Matin, R. (2004). Inputs/outputs estimation in DEA when some factors are undesirable. Applied Mathematics and Computation, 156(1), 19-32.
Kao, C. (2009). Efficiency decomposition in network data envelopment analysis: A relational model. European Journal of Operational Research, 192(3), 949-962.
Khalili-Damghani, K., & Shahmir, Z. (2015). Uncertain network data envelopment analysis with undesirable outputs to evaluate the efficiency of electricity power production and distribution processes. Computers & Industrial Engineering, 88, 131-150.
Khoshandam, L., Kazemi Matin, R., & Amirteimoori, A. (2015). Marginal rates of substitution in data envelopment analysis with undesirable outputs: A directional approach. Measurement, 68, 49-57.
Kordrostami, S., & Amirteimoori, A. (2005). Undesirable factors in multi-component performance measurement. Applied Mathematics and Computation, 171(2), 721-729.
Kuosmanen, T. (2005). Weak disposability in nonparametric production analysis with undesirable outputs. American Journal of Agricultural Economics, 87(4), 1077-1082.
Kuosmanen, T., & Podinovski, V. (2009). Weak disposability in nonparametric production analysis: Reply to Färe and Grosskopf. American Journal of Agricultural Economics, 91(2), 539-545.
Liang, L., Cook, W. D., Zhu, J. (2008). DEA Models for two-stage processes : Game approach and efficiency decomposition. Naval Research Logistics, 55, 643-653.
Liu, W., Zhou, Z., Ma, C., Liu, D., & Shen, W. (2015). Two-stage DEA models with undesirable input-intermediate-outputs. Omega, 56, 74-87.
Lozano, S., Gutiérrez, E., & Moreno, P. (2013). Network DEA approach to airports performance assessment considering undesirable outputs. Applied Mathematical Modelling, 37(4), 1665-1676.
Maghbouli, M., Amirteimoori, A., & Kordrostami, S. (2014). Two-stage network structures with undesirable outputs: A DEA based approach. Measurement, 48, 109-118.
Mehdiloozad, M., & Podinovski, V. V. (2018). Nonparametric production technologies with weakly disposable inputs. European Journal of Operational Research, 266(1), 247-258.
Rosen, D., Schaffnit, C., & Paradi, J. C. (1998). Marginal rates and two-dimensional level curves in DEA. Journal of Productivity Analysis, 9(3), 205-232.
Seiford, L. M., & Zhu, J. (2002). Modeling undesirable factors in efficiency evaluation. European Journal of Operational Research, 142(1), 16-20.
436 Mahboubi et al.
Shephard, R. W. (1974). Indirect production functions (Mathematical systems in economics). Hain Meisenheim am Glan.Toloo, M., Allahyar, M., & Hanclova, J. (2018). A non-radial directional distance method on classifying inputs and outputs in DEA: Application to banking industry. Expert Systems with Applications, 92, 495-506.
Wu, J., Zhu, Q., Chu, J., & Liang L. (2015). Two-Stage network structures with undesirable intermediate outputs reused : A DEA based approach. Computational Economics, 46, 455-477.