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Applications to Production and Inventory

In: Optimal Control Theory

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  • Suresh P. Sethi

    (University of Texas at Dallas)

Abstract

Many manufacturing enterprises use a production-inventory system to manage fluctuations in consumer demand for their products. In Sect. 6.1, a model similar to the classic HMMS model is formulated as an optimal control problem that must balance the benefits of production smoothing versus the costs of holding inventory theory to minimize the total discounted system cost. The problem is completely solved using the maximum principle. The turnpike solution is also obtained when the horizon is infinite. Section 6.2 introduces a wheat trading model in which a wheat speculator must buy and sell wheat in an optimal way to take advantage of changes in the price of wheat over time. In Sects. 6.2.1–6.2.3, we solve the model when the short-selling of wheat is allowed. In Sect. 6.3, we introduce a warehousing constraint, i.e., an upper bound on the amount of wheat that can be stored. In addition to being realistic, the introduction of the warehousing constraint helps us to illustrate the concepts of decision and forecast horizons through examples. This section is expository and theoretical developments of these ideas are available in the literature. There are many exercises at the end of the chapter.

Suggested Citation

  • Suresh P. Sethi, 2021. "Applications to Production and Inventory," Springer Texts in Business and Economics, in: Optimal Control Theory, edition 4, chapter 6, pages 175-206, Springer.
    • Handle: RePEc:spr:sptchp:978-3-030-91745-6_6
    DOI: 10.1007/978-3-030-91745-6_6
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