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Mixture distributions for modelling demand during lead time

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  • B R Cobb

    (Virginia Military Institute, Lexington, VA, USA)

Abstract

A mixture distribution approach to modelling demand during lead time in a continuous-review inventory model is described. Using this approach, both lead time and demand per unit time can follow state-dependent distributions. By using mixtures of truncated exponentials functions to approximate these distributions, mixture distributions that can be easily manipulated in closed form can be constructed as the marginal distributions for lead time and demand per unit time. These are then used to approximate the mixture of compound distributions for demand during lead time. The technique is illustrated by first applying it to a ‘normal-gamma’ inventory problem, then by modelling a problem with empirical distributions for lead time and demand per unit time.

Suggested Citation

  • B R Cobb, 2013. "Mixture distributions for modelling demand during lead time," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 64(2), pages 217-228, February.
    • Handle: RePEc:pal:jorsoc:v:64:y:2013:i:2:p:217-228
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    Cited by:

    1. Cobb, Barry R. & Johnson, Alan W. & Rumí, Rafael & Salmerón, Antonio, 2015. "Accurate lead time demand modeling and optimal inventory policies in continuous review systems," International Journal of Production Economics, Elsevier, vol. 163(C), pages 124-136.
    2. John P. Saldanha & Bradley S. Price & Douglas J. Thomas, 2023. "A nonparametric approach for setting safety stock levels," Production and Operations Management, Production and Operations Management Society, vol. 32(4), pages 1150-1168, April.
    3. Minken, Harald & Johansen, Bjørn Gjerde, 2019. "A logistics cost function with explicit transport costs," Economics of Transportation, Elsevier, vol. 19(C), pages 1-1.
    4. Sarkar, Biswajit & Moon, Ilkyeong, 2014. "Improved quality, setup cost reduction, and variable backorder costs in an imperfect production process," International Journal of Production Economics, Elsevier, vol. 155(C), pages 204-213.
    5. Wanke, Peter & Pestana Barros, Carlos & Chen, Zhongfei, 2015. "An analysis of Asian airlines efficiency with two-stage TOPSIS and MCMC generalized linear mixed models," International Journal of Production Economics, Elsevier, vol. 169(C), pages 110-126.

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