Stochastic Production Planning with Regime Switching: Numerical and Sensitivity Analysis, Optimal Control, and Python Implementation

TL;DR

This paper develops a regime-switching stochastic production planning model using PDEs, providing numerical solutions and sensitivity analysis to optimize production strategies under economic fluctuations.

Contribution

It introduces a novel regime-dependent PDE framework for stochastic production planning with numerical methods and sensitivity analysis, bridging theory and practical application.

Findings

Regime-switching models show conservative bias compared to static models.

Numerical solutions enable quantitative analysis of production strategies.

Sensitivity analysis highlights impact of volatility and costs on optimal policies.

Abstract

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.