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Market risk and process uncertainty in production operations

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  • Bardia Kamrad
  • Keith Ord

Abstract

By adopting a real options framework we develop a production control model that jointly incorporates process and market uncertainties. In this model, process uncertainty is defined by random fluctuations in the outputs' yield and market risk through demand uncertainty for the output. In our approach, production outputs represent commodities or items for which financial contracts do not trade. Outputs are also functionally linked to the level of input inventories. To extend the model's applicability to a wide range of production industries, inputs are modeled to reflect either renewable or partially renewable or non‐renewable resources. Given this setting, techniques of stochastic control theory are employed to obtain value maximizing production policies in a constrained capacity environment. The rate of production is modeled as an adapted positive real‐valued process and analogously evaluated as a sequence of complex real options. Since optimal adjustments to the rate of production also functionally depend on the outputs' yield, we optimally establish “trigger boundaries” justifying controlled variations to the rate of production over time. In this context, we provide closed form analytic results and demonstrate their robustness with respect to the stochastic (including mean reverting) processes considered. Using these results, we also demonstrate that the value (net of holding costs) accrued to the producer from having an inventory of the output is equivalent to the producer's reservation price to operationally curb its process yield. These generalizations extend the scope of model applicability and provide a basis for applying the real options methodology in the operations arena. The model is explored numerically using a stylized example that allows for both output and demand uncertainty and achieves greater realism by incorporating an element of smoothing into the sequence of production decisions. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Suggested Citation

  • Bardia Kamrad & Keith Ord, 2006. "Market risk and process uncertainty in production operations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(7), pages 627-640, October.
    • Handle: RePEc:wly:navres:v:53:y:2006:i:7:p:627-640
    DOI: 10.1002/nav.20178
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    1. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    2. Arnd Huchzermeier & Morris A. Cohen, 1996. "Valuing Operational Flexibility Under Exchange Rate Risk," Operations Research, INFORMS, vol. 44(1), pages 100-113, February.
    3. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    4. Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," The Journal of Business, University of Chicago Press, vol. 58(2), pages 135-157, April.
    5. Majd, Saman & Pindyck, Robert S., 1987. "Time to build, option value, and investment decisions," Journal of Financial Economics, Elsevier, vol. 18(1), pages 7-27, March.
    6. Trigeorgis, Lenos, 1993. "The Nature of Option Interactions and the Valuation of Investments with Multiple Real Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(1), pages 1-20, March.
    7. He, Hua & Pindyck, Robert S., 1992. "Investments in flexible production capacity," Journal of Economic Dynamics and Control, Elsevier, vol. 16(3-4), pages 575-599.
    8. Candace Arai Yano & Hau L. Lee, 1995. "Lot Sizing with Random Yields: A Review," Operations Research, INFORMS, vol. 43(2), pages 311-334, April.
    9. Bardia Kamrad & Ricardo Ernst, 2001. "An Economic Model for Evaluating Mining and Manufacturing Ventures with Output Yield Uncertainty," Operations Research, INFORMS, vol. 49(5), pages 690-699, October.
    10. Chung, Kee H, 1990. "Inventory Decision under Demand Uncertainty: A Contingent Claims Approach," The Financial Review, Eastern Finance Association, vol. 25(4), pages 623-640, November.
    11. Kamrad, Bardia & Ritchken, Peter, 1994. "Valuing fixed price supply contracts," European Journal of Operational Research, Elsevier, vol. 74(1), pages 50-60, April.
    12. Kamran Moinzadeh & Hau L. Lee, 1987. "A continuous‐review inventory model with constant resupply time and defective items," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(4), pages 457-467, August.
    13. Joseph B. Mazzola & William F. McCoy & Harvey M. Wagner, 1987. "Algorithms and heuristics for variable‐yield lot sizing," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(1), pages 67-86, February.
    14. Bardia Kamrad & Akhtar Siddique, 2004. "Supply Contracts, Profit Sharing, Switching, and Reaction Options," Management Science, INFORMS, vol. 50(1), pages 64-82, January.
    15. Bardia Kamrad & Peter Ritchken, 1991. "Multinomial Approximating Models for Options with k State Variables," Management Science, INFORMS, vol. 37(12), pages 1640-1652, December.
    16. Kee H. Chung, 1990. "Output Decision Under Demand Uncertainty with Stochastic Production Function: A Contingent Claims Approach," Management Science, INFORMS, vol. 36(11), pages 1311-1328, November.
    17. Sriram Dasu & Lode Li, 1997. "Optimal Operating Policies in the Presence of Exchange Rate Variability," Management Science, INFORMS, vol. 43(5), pages 705-722, May.
    18. Constantinides, George M, 1978. "Market Risk Adjustment in Project Valuation," Journal of Finance, American Finance Association, vol. 33(2), pages 603-616, May.
    19. James E. Smith & Kevin F. McCardle, 1998. "Valuing Oil Properties: Integrating Option Pricing and Decision Analysis Approaches," Operations Research, INFORMS, vol. 46(2), pages 198-217, April.
    20. G. R. Bitran & S. Dasu, 1992. "Ordering Policies in an environment of Stochastic Yields and Substitutable Demands," Operations Research, INFORMS, vol. 40(5), pages 999-1017, October.
    21. Bruce Kogut & Nalin Kulatilaka, 1994. "Operating Flexibility, Global Manufacturing, and the Option Value of a Multinational Network," Management Science, INFORMS, vol. 40(1), pages 123-139, January.
    22. Hau L. Lee & Candace Arai Yano, 1988. "Production Control in Multistage Systems with Variable Yield Losses," Operations Research, INFORMS, vol. 36(2), pages 269-278, April.
    23. McDonald, Robert L & Siegel, Daniel R, 1985. "Investment and the Valuation of Firms When There Is an Option to Shut Down," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(2), pages 331-349, June.
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