Single item inventory control under periodic review and a minimum order quantity

G.P. Kiesmüller, A.G. Kok, de, S. Dabia

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Abstract

In this paper we study a periodic review single item single stage inventory system with stochastic demand. In each time period the system must order none or at least as much as a minimum order quantity Qmin. Since the optimal structure of an ordering policy with a minimum order quantity is complicated, we propose an easy-to-use policy, which we call (R, S, Qmin) policy. Assuming linear holding and backorder costs we determine the optimal numerical value of the level S using a Markov Chain approach. In addition, we derive simple news-vendor-type inequalities for near-optimal policy parameters, which can easily be implemented within spreadsheet applications. In a numerical study we compare our policy with others and test the performance of the approximation for three different demand distributions: Poisson, negative binomial, and a discretized version of the gamma distribution. Given the simplicity of the policy and its cost performance as well as the excellent performance of the approximation we advocate the application of the (R, S, Qmin) policy in practice.
Original languageEnglish
Pages (from-to)280-285
Number of pages6
JournalInternational Journal of Production Economics
Volume133
Issue number1
DOIs
Publication statusPublished - 2011

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Inventory control
Poisson distribution
Spreadsheets
Markov processes
Costs
Order quantity
Periodic review

Cite this

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title = "Single item inventory control under periodic review and a minimum order quantity",
abstract = "In this paper we study a periodic review single item single stage inventory system with stochastic demand. In each time period the system must order none or at least as much as a minimum order quantity Qmin. Since the optimal structure of an ordering policy with a minimum order quantity is complicated, we propose an easy-to-use policy, which we call (R, S, Qmin) policy. Assuming linear holding and backorder costs we determine the optimal numerical value of the level S using a Markov Chain approach. In addition, we derive simple news-vendor-type inequalities for near-optimal policy parameters, which can easily be implemented within spreadsheet applications. In a numerical study we compare our policy with others and test the performance of the approximation for three different demand distributions: Poisson, negative binomial, and a discretized version of the gamma distribution. Given the simplicity of the policy and its cost performance as well as the excellent performance of the approximation we advocate the application of the (R, S, Qmin) policy in practice.",
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Single item inventory control under periodic review and a minimum order quantity. / Kiesmüller, G.P.; Kok, de, A.G.; Dabia, S.

In: International Journal of Production Economics, Vol. 133, No. 1, 2011, p. 280-285.

Research output: Contribution to journalArticleAcademicpeer-review

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