Comments on Two Models for Operating Two-Warehouse Inventory Systems with Deteriorating Items and Inflationary Effects

Comments on Two Models for Operating Two-Warehouse Inventory Systems with Deteriorating Items and Inflationary Effects

Huachun Xiong (Tsinghua University, China), Jinxing Xie (Tsinghua University, China) and Bo Niu (China Railway Express Co., China)
DOI: 10.4018/978-1-4666-2925-7.ch018

Abstract

This paper deals with the two-warehouse partial backlogging inventory problems under inflation for a deteriorating product with a constant demand rate over an infinite horizon. In contrast to the traditional model in which each replenishment cycle starts with an instant replenishment and ends with shortages, an alternative model is proposed in recent literature in which each cycle starts with shortages. It is proven to be less expensive to operate than the traditional model in terms of the present value of the cost per unit time. The present paper points out that the criteria of minimizing the cost per unit time is unreasonable when the inflationary effect is taken into consideration, and instead, the criteria of minimizing the present value of the total cost over the whole infinite planning horizon should be used. The objective functions of these two models are changed and proved that the model with shortages at the start of the cycle is less expensive to operate than the traditional model in terms of the present value of the total cost, but the optimal solutions of the models minimizing the cost per unit time indicate significantly higher total costs.
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Introduction

The inventory problem for deteriorating items with deterministic demand rates has been studied extensively in the literature. Nahmias (1982), and Goyal and Giri (2001) provided excellent reviews for research works in this field before 1980s and 2000s respectively. The problem attracts growing interests from researchers thereafter (Dye et al., 2007a & 2007b; Shah et al., 2009; Teng et al., 2002). In contrast to the studies that assume an organization owns only a single warehouse with unlimited capacity, the last decade sees an explosive number of studies focusing on two warehouses, i.e., an owned warehouse (OW) with limited capacity and a rented warehouse (RW) which is assumed to be available with abundant capacity. An early discussion on the effect of two warehouses can be traced back to Hartely (1976), and recently the two-warehouse inventory models have been considered by many other researchers (Chung et al., 2009; Dey et al., 2007b, 2008; Gayen & Pal, 2009; Hsieh et al., 2008; Lee & Hsu, 2009; Niu & Xie, 2008; Rong et al., 2008; Wee et al., 2005; Yang, 2004, 2006; Zhou, 2003; Zhou & Yang, 2005).

In traditional inventory models, it is generally assumed that each replenishment cycle starts with an instant replenishment and ends with shortages. In a recent paper, Yang (2004) considered the two-warehouse inventory problem for deteriorating items with shortages under inflation, and proposed an alternative model in which each cycle begins with shortages and ends without shortages. Under some assumptions, he proved that the model with shortages at the start of the cycle is less expensive to operate than the traditional models under the objective of minimizing the cost per unit time. More recently, Yang (2006) extended the completely backlogging model to incorporate partial backlogging.

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