An optimal replenishment policy for items with inventory-level-dependent demand and fixed lifetime under the LIFO policy
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An optimal replenishment policy for items with inventory-level-dependent demand and fixed lifetime under the LIFO policy Y-W Zhou1* and S-L Yang2 1 Hefei University of Technology, Hefei, People’s Republic of China; and 2Hefei University of Technology, Hefei, People’s Republic of China
In a recent paper, Hwang and Hahn considered inventory replenishment problems for an item with an inventory-leveldependent demand rate and a fixed lifetime. They developed an EQQ model under the situation of considering the firstin–first-out (FIFO) issuing policy. First, this paper reconsiders Hwang and Hann’s problem by employing the last-in– first-out (LIFO) issuing policy, which is more practical in the retail industry. An inventory model is developed. Secondly, the concavity of the objective function is proved. Thirdly, this paper presents conditions where the present model has a unique optimal solution and a method for finding the global optimal solution. A simple solution procedure and sensitivity analyses of parameters are also provided. Journal of the Operational Research Society (2003) 54, 585–593. doi:10.1057/palgrave.jors.2601482 Keywords: inventory; inventory-level-dependent demand rate; fixed product lifetime
Introduction During the past three decades, many marketing researchers have observed that in some retailer systems such as a supermarket, the demand of goods may be influenced by the on-hand inventory. For example, Levin et al1 pointed out: ‘At times, the presence of inventory has a motivational effect on the people around it. It is a common belief that a large pile of goods displayed in a supermarket will lead the customer to buy more.’ Silver and Peterson2 also noted that sales of the goods tend to be proportional to inventory displayed. These basic observations imply that a retailer running a supermarket probably obtains the potential profits from a high demand rate associated with a high inventory level, although the high inventory level will also yield high holding costs and high deterioration cost if items are perishable. Therefore, a common problem faced by the retailer is: What should be the size of the replenishment and the length of the replenishment cycle? In this paper, this problem is modeled for a situation selling an item with a fixed lifetime in a supermarket. The early existing models3–6 dealing with the stockdependent demand rate provided retailers with some answers. However, these models failed to consider the deterioration phenomenon. In real life, however, deterioration of items is a common phenomenon. Perishable items *Correspondence: Y-W Zhou, Department of Mathematics, Hefei University of Technology, Hefei, Anhui 230009, People’s Republic of China. E-mail: [email protected]
can usually be divided into two categories. Category l is made up of those items that have unlimited lifetime with an amount of decrease over time due to deterioration, such as petrol, alcohol and radioactive matters.
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