Stochastic production planning: optimal control and analytical insights
Abstract
This study investigates a stochastic production planning problem with a running cost composed of quadratic production costs and inventory-dependent costs. The objective is to minimize the expected cost until production stops when inventory reaches a specified level, subject to a boundary condition. Using probability space and Brownian motion, the Hamilton-Jacobi-Bellman (HJB) equation is derived, and optimal feedback control is obtained. The solution demonstrates desirable monotonicity and convexity properties under specific assumptions. An illustrative example further confirms these results with explicit function properties and a practical application.
Fields of Study & Subjects
Risk and Portfolio Optimization
Stochastic processes and financial applications
Supply Chain and Inventory Management
Publication details
- Journal / source
- Journal of Management Analytics
- Publisher
- Informa UK Limited
- Volume
- 13
- Issue
- 3
- Pages
- 576–600
- Publication date
- 29 June 2026
- Language
- EN