Optimal control policy for a standing order inventory system

In this paper we consider an inventory system with increasing concave ordering cost and average cost optimization criterion. The demand process is modeled as a Brownian motion. Porteus (1971) studied a discrete-time version of this problem and under the strong condition that the demand distribution belongs to the class of densities that are finite convolutions of uniform and/or exponential densities (note that normal density does not belong to this class), an optimal control policy is a generalized (s, S) policy consisting of a sequence of (si, Si). Using a lower bound approach, we show that an optimal control policy for the Brownian inventory model is determined by a single pair (s, S).

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Optimal Control Policy of an Inventory System with Postponed Demand

RAIRO - Operations Research ◽

10.1051/ro/2015021 ◽

2016 ◽

Vol 50 (1) ◽

pp. 145-155 ◽

Cited By ~ 3

Author(s):

P. Chitra Devi ◽

B. Sivakumar ◽

A. Krishnamoorthy

Keyword(s):

Optimal Control ◽

Control Policy ◽

Inventory System

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

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964812000149 ◽

2012 ◽

Vol 26 (4) ◽

pp. 457-481 ◽

Cited By ~ 3

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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Optimal control policy for a Brownian inventory system with concave ordering cost

Journal of Applied Probability ◽

10.1017/s0021900200112987 ◽

2015 ◽

Vol 52 (04) ◽

pp. 909-925 ◽

Cited By ~ 2

Author(s):

Dacheng Yao ◽

Xiuli Chao ◽

Jingchen Wu

Keyword(s):

Optimal Control ◽

Brownian Motion ◽

Cost Optimization ◽

Control Policy ◽

Optimization Criterion ◽

Inventory System ◽

Single Pair ◽

Normal Density ◽

Strong Condition ◽

Demand Distribution

In this paper we consider an inventory system with increasing concave ordering cost and average cost optimization criterion. The demand process is modeled as a Brownian motion. Porteus (1971) studied a discrete-time version of this problem and under the strong condition that the demand distribution belongs to the class of densities that are finite convolutions of uniform and/or exponential densities (note that normal density does not belong to this class), an optimal control policy is a generalized (s, S) policy consisting of a sequence of (si , Si ). Using a lower bound approach, we show that an optimal control policy for the Brownian inventory model is determined by a single pair (s, S).

Download Full-text