A finite-horizon, stochastic optimal control policy for a production–inventory system with backlog-dependent lost sales

2010 ◽  
Vol 42 (12) ◽  
pp. 855-864 ◽  
Author(s):  
Gonen Singer ◽  
Eugene Khmelnitsky
Keyword(s):  
Optimal Control ◽  
Stochastic Optimal Control ◽  
Control Policy ◽  
Inventory System ◽  
Finite Horizon ◽  
Lost Sales ◽  
Production Inventory ◽  
Production Inventory System

OPTIMAL POLICY FOR A PRODUCTION–INVENTORY SYSTEM WITH SETUP COST AND AVERAGE COST CRITERION

2012 ◽  
Vol 26 (4) ◽  
pp. 457-481 ◽  
Author(s):  
Xiuli Chao ◽  
Yifan Xu ◽  
Baimei Yang
Keyword(s):  
Optimal Control ◽  
Optimal Policy ◽  
Production Capacity ◽  
Control Policy ◽  
Inventory System ◽  
Setup Cost ◽  
Inventory Theory ◽  
Cost Rate ◽  
Production Inventory ◽  
Production Inventory System

One of the most fundamental results in inventory theory is the optimality of (s, S) policy for inventory systems with setup cost. This result is established under a key assumption of infinite ordering/production capacity. Several studies have shown that, when the ordering/production capacity is finite, the optimal policy for the inventory system with setup cost is very complicated and indeed, only partial characterization for the optimal policy is possible. In this paper, we consider a continuous review production/inventory system with finite capacity and setup cost. The demand follows a Poisson process and a demand that cannot be satisfied upon arrival is backlogged. We show that the optimal control policy has a very simple structure when the holding/shortage cost rate is quasi-convex. We also develop efficient algorithms to compute the optimal control parameters.

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