An Efficiency Measurement Framework for Multi-stage Production Systems
We develop an efficiency measurement framework for systems composed of two subsystems arranged in series that simultaneously computes the efficiency of the aggregate system and each subsystem. Our approach expands the technology sets of each subsystem by allowing each to acquire resources from the other in exchange for delivery of the appropriate (intermediate or final) product, and to form composites from both subsystems. Managers of each subsystem will not agree to “vertical integration” initiatives unless each subsystem will be more efficient than what each can achieve by separately applying conventional efficiency analysis. A Pareto Efficient frontier characterizes the acceptable set of efficiencies of each subsystem from which the managers will negotiate to select the final outcome. Three proposals for the choice for the Pareto efficient point are discussed: the one that achieves the largest equiproportionate reduction in the classical efficiencies; the one that achieves the largest equal reduction in efficiency; and the one that maximizes the radial contraction in the aggregate consumption of resources originally employed before integration. We show how each choice for the Pareto efficient point determines a derived measure of aggregate efficiency. An extensive numerical example is used to illustrate exactly how the two subsystems can significantly improve their operational efficiencies via integration beyond what would be predicted by conventional analysis.
KeywordsMulti-stage production systems Productivity and efficiency measurement Data envelopment analysis
The authors wish to express their gratitude to the editor and two anonymous reviewers for their helpful comments.
- Charnes, A., Cooper, W. W., Golany, B., Halek, R., Klopp, G., Schmitz, E., & Thomas, D. (1986a). Two phase data envelopment analysis approaches to policy evaluation and management of army recruiting activities: Tradeoffs between joint services and army advertising. (Research Report CCS no. 532). Center for Cybernetic Studies, The University of Texas at Austin.Google Scholar
- Färe, R., Grosskopf, S., & Lovell, C. A. K. (1994). Production frontiers. New York: Cambridge University Press.Google Scholar
- Graves, S. C., Rinnoy Kan, A. H. G., & Zipkin, P. H. (1993). Logistics of production and inventory. Amsterdam: North-Holland.Google Scholar
- Hoopes, B., Triantis, K. P., & Partangel, N. (2000). The relationship between process and manufaturing plant performance: A goal programming approach. International Journal on Operations and Quantitative Management, 6, 287–310.Google Scholar
- Jehle, G. A., & Reny, P. J. (2001). Advanced microeconomic theory, (2nd ed.). New York: Addison-Wesley.Google Scholar
- Johnson, L. A., & Montgomery, D. C. (1974). Operations research in production planning, scheduling and inventory control. New York: Wiley.Google Scholar
- Shephard, R.W. (1970). Theory of cost and production functions. Princeton: Princeton University Press.Google Scholar
- Zhu, J. (2002). Quantitative models for performance evaluation and benchmarking: Data envelopment analysis with spreadsheets. Boston: Kluwer Academic.Google Scholar