Optimal Control of Production-Inventory Systems with Constant and Compound Poisson Demand
In this paper, we study a production-inventory systems with finite production capacity and fixed setup costs. The demand process is modeled as a mixture of a compound Poisson process and a constant demand rate. For the backlog model we establish conditions on the holding and backlogging costs such that the average-cost optimal policy is of (s, S)-type. The method of proof is based on the reduction of the production-inventory problem to an appropriate optimal stopping problem and the analysis of the associated free-boundary problem. We show that our approach can also be applied to lost-sales models and that inventory models with un onstrained order capacity can be obtained as a limiting case of our model. This allows us to analyze a large class of single-item inventory models, including many of the classical cases, and compute in a numerical efficient way optimal policies for these models, whether these optimal policies are of (s, S)-type or not.
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- Grunow, M. & Gunther, H.-O. & Westinner, R., 2007. "Supply optimization for the production of raw sugar," International Journal of Production Economics, Elsevier, vol. 110(1-2), pages 224-239, October.
- Pool, Arnout & Wijngaard, Jacob & van der Zee, Durk-Jouke, 2011. "Lean planning in the semi-process industry, a case study," International Journal of Production Economics, Elsevier, vol. 131(1), pages 194-203, May.
- R. G. Vickson, 1986. "A Single Product Cycling Problem Under Brownian Motion Demand," Management Science, INFORMS, vol. 32(10), pages 1336-1345, October.
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