An EOQ model for deteriorating items with time varying demand and partial backlogging
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An EOQ model for deteriorating items with time varying demand and partial backlogging H-J Chang* and C-Y Dye Tamkang University, Taiwan In the classical economic order quantity model, it is often assumed that the shortages are either completely backlogged or completely lost. However, in some inventory systems, it is more reasonable to assume that the backlogging rate is dependent on the length of the waiting time for the next replenishment. The longer the waiting time is, the smaller the backlogging rate would be. In this paper, we focus on the effect of the backlogging rate on the economic order quantity decision. Numerical examples are presented to illustrate the model. Keywords: ®nite time horizon; deteriorating items; time-varying demand; partial backlogging; inventory control
Introduction In the last two decades, the models for inventory replenishment policies involving time-varying demand patterns have received the attention of several researchers. The fundamental result in the development of economic order quantity model with time-varying demand patterns is that of Donaldson1 who established the classical no-shortage inventory model with a linear trend in demand over a known and ®nite horizon. However, his procedure was too complex and tedious in computing. The complexity of Donaldson's approach has led to the development of heuristic methods. Silver,2 Phelps,3 Ritchie,4 and Teng,5 derived simple heuristic procedures for Donaldson's problem. Dave and Patel6 ®rst considered the inventory model for deteriorating items with time-varying demand. They considered a linear increasing demand rate over a ®nite horizon and a constant deterioration rate. Sachan7 extended Dave and Patel's model to allow for shortages. Datta and Pal8 presented an EOQ model for items with variable deterioration rate and power demand pattern. Researchers including Mudeshwar,9 Goswami and Chaudhuri,10 Goyal et al,11 Hariga,12 Chakrabarti and Chaudhuri,13 Benkherouf,14 and Hariga and Alyan15 developed economic order quantity models that focused on deteriorating items with time-varying demand and shortages. In practice, some customers would like to wait for backlogging during the shortage period, but the others would not. Consequently, the opportunity cost due to lost sales should be considered in the modeling. Many *Correspondence: Dr H-J Chang, Graduate Institute of Management Sciences, Tamkang University, Tamsui, Taipei, Taiwan 25173, ROC. E-mail: [email protected]
researchers9±16 assumed that shortages are completely backlogged. A recent article17 in the ®eld of deteriorating items with shortages has revealed the economic order quantity with a known market demand rate. In this paper, the backlogging rate was assumed to be a ®xed fraction of demand rate during the shortage period. However, in some inventory system, for many stock such as fashionable commodities, the length of the waiting time for the next replenishment
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