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Exact Solution for the Production Planning Problem with Several Regimes Switching over an Infinite Horizon Time

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  • Dragos-Patru Covei

    (Department of Applied Mathematics, The Bucharest University of Economic Studies, Piata Romana, 1st District, 010374 București, Romania)

Abstract

We consider a stochastic production planning problem with regime switching. There are k ≥ 1 regimes corresponding to different economic cycles. The problem is to minimize the production costs and analyze the problem by the value function approach. Our main contribution is to show that the optimal production is characterized by an exact solution of an elliptic system of partial differential equations. A verification result is given for the determined solution.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4307-:d:1260753
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    References listed on IDEAS

    as
    1. 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.
    2. Petrović, Milena J., 2015. "An Accelerated Double Step Size model in unconstrained optimization," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 309-319.
    3. Predrag S. Stanimirović & Gradimir V. Milovanović & Milena J. Petrović & Nataša Z. Kontrec, 2015. "A Transformation of Accelerated Double Step Size Method for Unconstrained Optimization," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-8, April.
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