A mixed inventory model with variable lead time and random back-order rate

Authors:
Rómulo I. Zequeira;Alfonso Durán;Gil Gutiérrez
Affiliations:
ISTIT, Equipe Modélisation et Sûreté des Systèmes, Université de Technologie de Troyes, Troyes, France;Departmento de Ingeniería Mecánica, Área de Ingeniería de Organización, Universidad Carlos III de Madrid, Leganés, Madrid, Spain;Departmento de Ingeniería Mecánica, Área de Ingeniería de Organización, Universidad Carlos III de Madrid, Leganés, Madrid, Spain
Venue:
International Journal of Systems Science
Year:
2005

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Abstract

In this paper, we study the determination of the optimal lead time, reorder point and order quantity considering that the back-order probability of a demand made during a stock-out period depends on the interval from the moment in which the order is placed until the next replenishment. Two models are analysed for the specification of the back-order probability: exponential functions and piecewise constant functions. The distribution of the lead time demand is assumed to be Poisson. An algorithm for the determination of the optimal order quantity. reorder point and lead time is given. A numerical example is presented to illustrate the results.