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2013 Brownian inventory models with convex holding cost, Part 2: Discount-optimal controls
J. G. Dai, Dacheng Yao
Stoch. Syst. 3(2): 500-573 (2013). DOI: 10.1214/11-SSY046


We consider an inventory system in which inventory level fluctuates as a Brownian motion in the absence of control. The inventory continuously accumulates cost at a rate that is a general convex function of the inventory level, which can be negative when there is a backlog. At any time, the inventory level can be adjusted by a positive or negative amount, which incurs a fixed positive cost and a proportional cost. The challenge is to find an adjustment policy that balances the inventory cost and adjustment cost to minimize the expected total discounted cost. We provide a tutorial on using a three-step lower-bound approach to solving the optimal control problem under a discounted cost criterion. In addition, we prove that a four-parameter control band policy is optimal among all feasible policies. A key step is the constructive proof of the existence of a unique solution to the free boundary problem. The proof leads naturally to an algorithm to compute the four parameters of the optimal control band policy.


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J. G. Dai. Dacheng Yao. "Brownian inventory models with convex holding cost, Part 2: Discount-optimal controls." Stoch. Syst. 3 (2) 500 - 573, 2013.


Published: 2013
First available in Project Euclid: 11 February 2014

zbMATH: 1298.60084
MathSciNet: MR3353210
Digital Object Identifier: 10.1214/11-SSY046

Primary: 60J70, 90B05, 93E20

Rights: Copyright © 2013 INFORMS Applied Probability Society


Vol.3 • No. 2 • 2013
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