Lead time and ordering cost reductions in continuous review inventory systems with partial backorders
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Lead time and ordering cost reductions in continuous review inventory systems with partial backorders L-Y Ouyang, C-K Chen and H-C Chang Tamkang University, Taiwan This paper investigates the impact of ordering cost reduction on the modi®ed continuous review inventory systems involving variable lead time with a mixture of backorders and lost sales. The objective is to simultaneously optimise the order quantity, ordering cost, reorder point and lead time. We ®rst assume the lead time demand follows a normal distribution, then relax this assumption to consider the distribution free case where only the mean and variance of lead time demands are known. An algorithm procedure of ®nding the optimal solution is developed, and two numerical examples are given to illustrate the results. Keywords: inventory; ordering cost reduction; distribution free lead time
Introduction In traditional economic order quantity (EOQ) and economic production quantity (EPQ) models, set-up (or ordering) cost is treated as a constant. However, in practical situations, set-up cost can be controlled and reduced through various efforts such as worker training, procedural changes, and specialised equipment acquisition. For an example, according to Silver et al1, the implementation of electronic data interchange (EDI) may reduce the ®xed setup=ordering cost and result in new replenishment policy and the corresponding lower cost. Also, through the Japanese successful experiences of using Just-In-Time (JIT) production, the advantages and bene®ts associated with efforts to reduce set-up cost can be clearly perceived. The ultimate goal of JIT from an inventory standpoint is to produce small lot sizes with good quality products. In order to achieve this goal, investing capital in reducing set-up cost is regarded as one of the effective ways. Moreover, accompanying the smaller lot sizes from lower set-up cost, bene®ts such as greater ¯exibility in scheduling, lower storage space and lower investment in inventory can also be obtained. Recognising these principles, many authors have investigated the effects of investing in reducing setup cost on economic lot sizes models. Initially, Porteus2 introduced the concept and developed a framework of investing in reducing set-up cost on EOQ models. Porteus3 extended Porteus2 to consider the discounted effects on the EOQ Correspondence: Dr L-Y Ouyang, Department of Management Sciences, Tamkang University, 151 Ying-Chuan Road, Tamsui, Taipei Hsian, Taiwan 25137, R.O.C. E-mail: [email protected]
model with setup cost reduction. Billington4 considered the EPQ model without backorders and included the setup cost as a function of capital expenditure. Nasri et al 5 investigated the effects of setup cost reduction on the EOQ model with stochastic lead time. Kim et al 6 presented several classes of set-up cost reduction functions and described a general solution procedure on the EPQ model. Paknejad
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