Retailer Ordering Policy for Deteriorating Items with Initial Inspection and Allowable Shortage Under the Condition of Permissible Delay in Payments

Retailer Ordering Policy for Deteriorating Items with Initial Inspection and Allowable Shortage Under the Condition of Permissible Delay in Payments

Chandra K. Jaggi (University of Delhi, India) and Mandeep Mittal (Amity School of Engineering & Technology, India)
Copyright: © 2012 |Pages: 16
DOI: 10.4018/ijaie.2012010106
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While developing the inventory model with shortages under permissible delay in payments, it has been observed in the literature, the researchers have not considered the fact that the retailer can earn interest on the revenue generated after fulfilling the outstanding demand as soon as he receives the new consignment at the start of the cycle. Owing to this fact, the present paper investigates the impact of interest earned from revenue generated after fulfilling the stock out at the start of the cycle on a single commodity inventory model with shortages for deteriorating item, in which the whole lot goes through an inspection on arrival before entering into inventory system, under the conditions of permissible delay in payments. The results have been demonstrated with the help of a numerical example using the tools of Matlab7.0.1.
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1. Introduction

Usually in all public and private sector organization, the quantity received is always subject to inspection because by and large all concern are likely to produce some defective items, although numbers may be small. The inspected items may be classified into two categories viz., non-defective and defective. Now, the non-defective items enter into the inventory system. However, when the nature of the item is deteriorating then inspection of the lot becomes more meaningful.

The deterioration is now a well-established fact, which may take place in the form of gradual decay, damage or perishability and the process is affected by extraneous and invisible factors. Moreover, the deterioration may also happen due to weather conditions, insufficient and unscientific storage structure etc. This situation occurs particularly in case of foodstuffs, which are damaged due to insects, spoilage, and rodents, where as in other commodities deterioration may occur during normal storage facilities. Ghare and Schrader (1963) proposed an economic order quantity (EOQ) model for items with an exponentially decaying inventory. Covert (1973) introduced variable rate of deterioration in Ghare (1963) model. A further improvement was introduced by Shah (1977) considering a model allowing complete backlogging of the unsatisfied demand. A good amount of work has been done by different researchers to explore the effect of deterioration on EOQ model under different circumstances (Dave & Patel, 1981; Mak, 1982; Hollier & Mak, 1983; Heng et al., 1991; Raafat, 1991).

Moreover, while developing a mathematical model in inventory control, it is assumed that the payment will be made to the suppliers for the goods immediately after receiving the consignment. However, in the day-to-day dealing, supplier does allow a certain fixed period to settle the account, during which the supplier charges no interest, but beyond this period interest is charged by the supplier under the terms and conditions agreed upon. Now, in case debt financing, it is often a short-term financing. Thus, interest paid here is nothing but the cost of capital or opportunity cost. Also, short-term loans can be thought of as having been taken from the suppliers on the expiry of the credit period. However, before the account has to be settled, the customer can sell the goods and continues to accumulate revenue and earn interest instead of paying the overdraft that is necessary if the supplier requires settlement of the account after replenishment. Therefore, it makes economic sense for the customer to delay the settlement of the replenishment account up to the last day of the credit period allowed by the supplier.

Goyal (1985) presented the model by introducing permissible delay in payments for fixed time period and Aggarwal and Jaggi (1995) extended his work for deteriorating items. Furthermore, Jamal et al. (1997) allowed shortages in the Aggarwal and Jaggi (1995) model, since then, many articles have been appeared under different situations (Raafat, 1991; Shah 2000, 2000; Goyal & Giri, 2001). The primary benefit of taking trade credit is that one can have saving in purchase cost and opportunity cost, which becomes quite relevant for deteriorating items, because in such cases, one has to procure more units than required in the given cycle to account for the deteriorating effect. In particular, when the unit purchase cost is high and decay is continuous, the saving due to delayed payment appears to be more significant.

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