We study an inventory system in which products are ordered from outside to meet demands, and the cumulative demand is governed by a Brownian motion. Excessive demand is backlogged. We suppose that the shortage and holding costs associated with the inventory are given by a general convex function. The product ordering from outside incurs a linear ordering cost and a setup fee. There is a constant leadtime when placing an order. The optimal policy is established so as to minimize the discounted cost including the inventory cost and ordering cost.
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Supported by the National Natural Science Foundation of China (No. 11101050).
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Yao, Dc. Optimal policy for brownian inventory models with general convex inventory cost. Acta Math. Appl. Sin. Engl. Ser. 29, 187–200 (2013). https://doi.org/10.1007/s10255-013-0201-y
- stochastic inventory model
- Brownian motion
- (sS) policy
- impulse control
2000 MR Subject Classification