Stochastic Production Planning with Regime Switching: Numerical and Sensitivity Analysis, Optimal Control, and Python Implementation
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910940974284800 |
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| author | Covei, Dragos-Patru |
| author_facet | Covei, Dragos-Patru |
| contents | This study investigates a stochastic production planning problem with regime-switching parameters, inspired by economic cycles impacting production and inventory costs. The model considers types of goods and employs a Markov chain to capture probabilistic regime transitions, coupled with a multidimensional Brownian motion representing stochastic demand dynamics. The production and inventory cost optimization problem is formulated as a quadratic cost functional, with the solution characterized by a regime-dependent system of elliptic partial differential equations (PDEs). Numerical solutions to the PDE system are computed using a monotone iteration algorithm, enabling quantitative analysis. Sensitivity analysis and model risk evaluation illustrate the effects of regime-dependent volatility, holding costs, and discount factors, revealing the conservative bias of regime-switching models when compared to static alternatives. Practical implications include optimizing production strategies under fluctuating economic conditions and exploring future extensions such as correlated Brownian dynamics, non-quadratic cost functions, and geometric inventory frameworks. This research bridges the gap between theoretical modeling and practical applications, offering a robust framework for dynamic production planning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08057 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic Production Planning with Regime Switching: Numerical and Sensitivity Analysis, Optimal Control, and Python Implementation Covei, Dragos-Patru Analysis of PDEs This study investigates a stochastic production planning problem with regime-switching parameters, inspired by economic cycles impacting production and inventory costs. The model considers types of goods and employs a Markov chain to capture probabilistic regime transitions, coupled with a multidimensional Brownian motion representing stochastic demand dynamics. The production and inventory cost optimization problem is formulated as a quadratic cost functional, with the solution characterized by a regime-dependent system of elliptic partial differential equations (PDEs). Numerical solutions to the PDE system are computed using a monotone iteration algorithm, enabling quantitative analysis. Sensitivity analysis and model risk evaluation illustrate the effects of regime-dependent volatility, holding costs, and discount factors, revealing the conservative bias of regime-switching models when compared to static alternatives. Practical implications include optimizing production strategies under fluctuating economic conditions and exploring future extensions such as correlated Brownian dynamics, non-quadratic cost functions, and geometric inventory frameworks. This research bridges the gap between theoretical modeling and practical applications, offering a robust framework for dynamic production planning. |
| title | Stochastic Production Planning with Regime Switching: Numerical and Sensitivity Analysis, Optimal Control, and Python Implementation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.08057 |