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A Model of Optimal Production Planning Based on the Hysteretic Demand Curve

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  • Mikhail E. Semenov

    (Department of Computer Science, Voronezh State University, Universitetskaya Sq. 1, 394018 Voronezh, Russia
    Department of Applied Mathematics and Mechanics, Voronezh State Technical University, XX-letiya Oktyabrya St. 84, 394006 Voronezh, Russia
    Geophysical Survey of Russia Academy of Sciences, Lenina Av. 189, 249035 Obninsk, Russia)

  • Sergei V. Borzunov

    (Department of Computer Science, Voronezh State University, Universitetskaya Sq. 1, 394018 Voronezh, Russia)

  • Peter A. Meleshenko

    (Department of Computer Science, Voronezh State University, Universitetskaya Sq. 1, 394018 Voronezh, Russia)

  • Alexey V. Lapin

    (Automatic Control Systems Department, Bauman Moscow State Technical University, 2-nd Baumanskaya St., 5, 105005 Moscow, Russia)

Abstract

The article considers a hysteretic model of consumer behaviour in mono-product markets. Demand generation with regard to an individual consumer is modeled using a non-ideal relay with inverted thresholds. Therefore, the sales rate is defined as an analogue of the Preisach converter. The article considers the problem of the optimal production, storage, and distribution of goods, taking into account the hysteretic nature of the demand curve. The problem is reduced to a non-classical optimal control problem with hysteretic non-linearities. The latter is solved using Pontryagin’s maximum principle. The adopted economic model is based on the binary relationship of consumers to the product: the product is bought or the product is not bought. Transitions between these states are determined within the framework of our model only by the price of the goods; therefore, only the operator of a non-ideal relay can accurately describe such a dependence. The article presents the results of computational experiments illustrating the theoretical assumptions.

Suggested Citation

  • Mikhail E. Semenov & Sergei V. Borzunov & Peter A. Meleshenko & Alexey V. Lapin, 2022. "A Model of Optimal Production Planning Based on the Hysteretic Demand Curve," Mathematics, MDPI, vol. 10(18), pages 1-16, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3262-:d:909777
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    References listed on IDEAS

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    1. Blanchard, Olivier & Wolfers, Justin, 2000. "The Role of Shocks and Institutions in the Rise of European Unemployment: The Aggregate Evidence," Economic Journal, Royal Economic Society, vol. 110(462), pages 1-33, March.
    2. Rod Cross, 2014. "Unemployment: natural rate epicycles or hysteresis?," European Journal of Economics and Economic Policies: Intervention, Edward Elgar Publishing, vol. 11(2), pages 136-148, September.
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    1. Petar Knežević & Aleksandar Radaković & Nikola Velimirović & Dragan Čukanović & Zoran Perović & Rada Radulović & Gordana Bogdanović, 2024. "A Preisach Model Defining Correlation Between Monotonic and Cyclic Response of Structural Mild Steel," Mathematics, MDPI, vol. 12(21), pages 1-17, October.
    2. Guangming Xue & Hongbai Bai & Tuo Li & Zhiying Ren & Xingxing Liu & Chunhong Lu, 2022. "Numerical Solving Method for Jiles-Atherton Model and Influence Analysis of the Initial Magnetic Field on Hysteresis," Mathematics, MDPI, vol. 10(23), pages 1-16, November.

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