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Stochastic Production Planning: Optimal Control and Analytical Insights
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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.
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Cited by 1 Pith paper
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Stochastic Production Planning in Manufacturing Systems
The paper extends a quadratic-cost stochastic production planning model to general convex domains and derives an elliptic PDE for the value function, but the concavity and martingale verification claims are not rigoro...
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