Quality & Quantity 36: 311–323, 2002.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
A Note on Minimax Mixture of Distributions Free
Procedure for Inventory Model with Variable Lead
, WEN-CHUAN LEE
and HUI-YIN TSAI
Department of Statistics, Tamkang University, Tamsui, Taipei, Taiwan, R.O.C.;
Business Administration, Ming Chuan University, Taipei, Taiwan, R.O.C.;
Graduate Institute of
Management Science, Ming Chuan University, Taipei, Taiwan, R.O.C.
Abstract. In recent papers, Moon and Choi (1998) and Hariga and Ben-Daya (1999) considered
a continuous review inventory model with a mixture of backorders and lost sales in which the lead
time, the order quantity, and the reorder point are decision variables was studied. Moreover, they
also develop a minimax distribution free procedure for the problem. While the demands of different
customers are not identical in the lead time, then we can’t only use a single distribution (such as
Moon & Choi (1998) and Hariga & Ben-Daya (1999)) to describe the demand of the lead time.
Hence, we correct and extend the model of Moon and Choi (1998) and Hariga and Ben-Daya (1999)
by considering the lead time demand with the mixture of distributions. In addition, we also apply
the minimax mixture of distributions free approach to the model by simultaneously optimizing the
order quantity, the reorder point, and the lead time to devise a practical procedure which can be used
without speciﬁc information on demand distribution.
Key words: crashing cost, inventory model, lead time, minimax, mixture of distributions, order
quantity, reorder point
1. 1. Introduction
Most of the literatures (such as Azoury & Brill (1994), Chiu (1995), Foote et al.
(1988), Kim & Park (1985), Liberatore (1977), Magson (1979), Naddor (1966), and
Silver & Peterson (1985), etc.) have been used deterministic or probabilistic models
to deal with inventory problems, the lead time is viewed as a prescribed constant or
a stochastic variable, which is therefore not subject to control. In practice, Tersine
(1982) thought that the lead time usually consists of the following components:
order preparation, order transit, supplier the lead time, delivery time, and setup
Corresponding author: Jong-Wuu Wu, Department of Statistics, Tamkang University, Tam-
sui, Taipei, Taiwan 25137, R.O.C. Tel: (886)-2-26215656-2677; Fax: (886)-2-26209732; E-mail: