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Optimal Production Management When Demand Depends on the Business Cycle

Author

Listed:
  • Abel Cadenillas

    (Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada; and Graduate School of Financial Engineering, Ajou University, Suwon 443-749, South Korea)

  • Peter Lakner

    (Department of Information, Operations and Management Sciences, Stern School of Business, New York University, New York, New York 10012)

  • Michael Pinedo

    (Department of Information, Operations and Management Sciences, Stern School of Business, New York University, New York, New York 10012)

Abstract

We assume that the cumulative consumer demand for an item follows a Brownian motion, with both the drift and the variance parameters modulated by a continuous-time Markov chain that represents the regime of the economy. The management of the company would like to maintain the inventory level as close as possible to a target inventory level and would also like to produce at a rate that is as close as possible to a target production rate. The company is penalized for deviations from the target levels, and the objective is to minimize the total discounted penalty costs. We consider two models. In the first model the management of the company knows the state of the economy, whereas in the second model the management does not know it. We solve both problems and obtain the optimal production policy and the minimal total expected discounted cost. Furthermore, we compare the total expected discounted costs of the two models and determine the value of knowing the regime of the economy. We also solve the above problems in the case when the consumer demand rate follows a geometric Brownian motion modulated by a continuous-time Markov chain that represents the regime of the economy.

Suggested Citation

  • Abel Cadenillas & Peter Lakner & Michael Pinedo, 2013. "Optimal Production Management When Demand Depends on the Business Cycle," Operations Research, INFORMS, vol. 61(4), pages 1046-1062, August.
    • Handle: RePEc:inm:oropre:v:61:y:2013:i:4:p:1046-1062
    DOI: 10.1287/opre.2013.1181
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    References listed on IDEAS

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    1. Luz Rocío Sotomayor & Abel Cadenillas, 2009. "Explicit Solutions Of Consumption‐Investment Problems In Financial Markets With Regime Switching," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 251-279, April.
    2. Sotomayor, Luz R. & Cadenillas, Abel, 2011. "Classical and singular stochastic control for the optimal dividend policy when there is regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 344-354, May.
    3. Abel Cadenillas & Peter Lakner & Michael Pinedo, 2010. "Optimal Control of a Mean-Reverting Inventory," Operations Research, INFORMS, vol. 58(6), pages 1697-1710, December.
    4. Eugene Khmelnitsky & Ernst Presman & Suresh Sethi, 2011. "Optimal production control of a failure-prone machine," Annals of Operations Research, Springer, vol. 182(1), pages 67-86, January.
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    Cited by:

    1. Chi Seng Pun, 2022. "Robust classical-impulse stochastic control problems in an infinite horizon," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(2), pages 291-312, October.
    2. Abel Cadenillas & Ricardo Huamán-Aguilar, 2016. "Explicit formula for the optimal government debt ceiling," Annals of Operations Research, Springer, vol. 247(2), pages 415-449, December.
    3. Dragos-Patru Covei, 2023. "Exact Solution for the Production Planning Problem with Several Regimes Switching over an Infinite Horizon Time," Mathematics, MDPI, vol. 11(20), pages 1-13, October.
    4. Jianmin Shi, 2020. "Optimal control of multiple Markov switching stochastic system with application to portfolio decision," Papers 2010.16102, arXiv.org.
    5. Tunay I. Tunca & Weiming Zhu, 2018. "Buyer Intermediation in Supplier Finance," Management Science, INFORMS, vol. 64(12), pages 5631-5650, December.
    6. Ricardo Huamán-Aguilar & Abel Cadenillas, 2015. "Government Debt Control: Optimal Currency Portfolio and Payments," Operations Research, INFORMS, vol. 63(5), pages 1044-1057, October.

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