Geodesic
Optimal Control Policy of an Inventory System with Postponed Demand
Chitra Devi, P.1 ; Sivakumar, B.2 ; Krishnamoorthy, A.3
1 Department of Mathematics, G.T.N. Arts College, Dindigul, 624005 Tamilnadu, India
2 Department of Applied Mathematics and Statistics, Madurai Kamaraj Univesity Madurai, 625021 Tamilnadu, India.
3 Department of Mathematics, Cochin University of Science & Technology, 682022 Kerala, India
RAIRO - Operations Research - Recherche Opérationnelle, Tome 50 (2016) no. 1, pp. 145-155

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This paper deals with the problem of controlling the selection rates of the pooled customer of a single commodity inventory system with postponed demands. The demands arrive according to a Poisson process. The maximum inventory level is fixed at S. The ordering policy is (s,S) policy that is as and when the inventory level drops to s an order for Q(=S-s) items is placed. The ordered items are received after a random time, which is distributed as exponential. We assume that the demands that occur during stock out period either enter a pool of finite size or leave the system according to a Bernoulli distribution. Whenever the on-hand inventory level is positive, customers are selected one-by-one and the selection rate can be chosen from a given set. The problem is to determine a decision rule that specifies the rate of these selections as a function of the on-hand inventory level and the number of customers waiting in the pool at each instant of time to minimise the long-run total expected cost rate. The problem is modelled as a semi-Markov decision problem. The optimal policy is computed using Linear Programming algorithm and the results are illustrated numerically.

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DOI : 10.1051/ro/2015021
Classification : 90B05, 90C40
Keywords: Inventory control, semi-Markov decision process, Postponed demands

Chitra Devi, P. 1 ; Sivakumar, B. 2 ; Krishnamoorthy, A. 3

1 Department of Mathematics, G.T.N. Arts College, Dindigul, 624005 Tamilnadu, India
2 Department of Applied Mathematics and Statistics, Madurai Kamaraj Univesity Madurai, 625021 Tamilnadu, India.
3 Department of Mathematics, Cochin University of Science & Technology, 682022 Kerala, India 
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     title = {Optimal {Control} {Policy} of an {Inventory} {System} with {Postponed} {Demand}},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
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Chitra Devi, P.; Sivakumar, B.; Krishnamoorthy, A. Optimal Control Policy of an Inventory System with Postponed Demand. RAIRO - Operations Research - Recherche Opérationnelle, Tome 50 (2016) no. 1, pp. 145-155. doi: 10.1051/ro/2015021

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