اثرات تثبیت قیمت و پرتفوی موجودی

This paper presents a formal analysis of the consolidation effect in a wider perspective. While demonstrating that the stock saving structure depends on the interaction between the coefficient of variation of demand and the ratio between inventory ordering and holding costs, this research indicates that the ratio between the standard deviations of lead time at potential facilities is the key variable for consolidation. Sensitivity analyses are also performed to address common managerial issues, which can arise during the consolidation decision, such as the impact on total costs and the assumption of uncorrelated demands.

The effect of consolidating inventories into fewer locations has two distinct components: the safety stock and the cycle stock (Evers, 1995). The safety stock component corresponds to the portfolio effect. Zinn et al. (1989) initially used this term in order to describe the safety stock savings due to consolidation. Afterwards, considerable research has been conducted on the portfolio effect. Mahmoud (1992), for example, proposed the portfolio quantity effect and the portfolio cost effect models to account for the influence that consolidation may have on other functions of the logistics system. Evers and Beier (1993) extended it to the centralization of safety stocks from n to m locations (n > m). Tallon (1993) studied how centralizing stocking locations impacts on the aggregate safety stock when both demand and replenishment lead times are uncertain. Evers and Beier (1998) proposed an alternative modelling approach to the lead time demand variance and covariance. They developed a rule to determine total consolidation between two locations. Tyagi and Das (1998) extended the portfolio effect analyses to cases where the customer demands, represented by centralized locations, have unequal variances. Finally, Das and Tyagi (1999) pooled different customers into different groups via nonlinear optimization model. The authors wanted to eliminate large positive covariances and, thus, minimize aggregate safety inventories. Evers (1995) integrated the cycle stocks into the analysis of inventory consolidation and re-examined the traditional square-root formulation in light of the augmentation. The author found that, when all facilities have the same fixed cost per order, the same per-unit holding cost, and the same proportion of demand, the reduction in total inventory caused by consolidation is contingent upon other factors besides the number of centralized and decentralized locations. Ballou and Burnetas (2003) studied the consolidation effect on safety and cycle stocks under the cross filling allocation rule, where a fraction of the demand is supplied by a primary source and the remainder by secondary sources. They concluded that, while cycle stocks do not favor cross filling, safety stock levels tend to be reduced, indicating the importance to account for these countervailing inventory forces during the decision-making process. Finally, Ballou (2005) studied the consolidation effect on the aggregate cycle and safety stocks via the inventory turnover curve approximation. A comprehensive list of papers on inventory consolidation is presented in Table 1.

A review of previous work related to consolidation effect and inventory portfolio analyses, from 1976 to 2005, is presented in this paper. It expands the consolidation effect by simultaneously considering safety and cycle stocks and by relaxing the assumptions of uncorrelated demands, no lead time uncertainties, and equal inventory-related costs. This research also departs from previous work by checking the validity of the optimal allocation rule derived by Tyagi and Das (1998) for both safety and cycle stocks and by deriving the analytical expression to help in deciding between two potential facilities for consolidation. The sensitivity analyses performed via analytical expressions and simulation indicate that the consolidation decision requires an in-depth understanding of the stock saving structure, in which the lead time standard deviation ratio between two locations plays a relevant role. More precisely, the share of safety and cycle stocks on total inventory reduction basically depends on the interaction between the coefficient of variation of demand and the ratio between order processing costs and inventory holding costs. However, the magnitude of the consolidation effect depends on the lead time standard deviation ratio, the most relevant variable so far. Other relevant variables to the magnitude of the consolidation effect are the correlation coefficient, the ratio between fixed order processing costs, and the ratio between demand means at potential locations for consolidation. These sensitivity analyses also addressed other relevant issues for managerial decision-making, such as the assumption of uncorrelated demands on consolidated safety stock levels and the key variables that explain total cost savings due to consolidation. Regarding the former issue, assuming the correlation equal to zero may jeopardize the accuracy of consolidated safety stock levels, mostly if the potential locations for consolidation present different lead time means and high coefficients of variation of demand. Now, with respect to the latter issue, product inventories that result in larger savings from consolidation will provide clear opportunities for total cost reduction. However, inventories which result in lower savings from consolidation may represent pitfalls in terms of increasing total costs, particularly if these inventories present both low per-unit holding costs and fixed order processing costs. At the same time, these inventories represent opportunities to improve customer service via decentralization, with minimal increases in aggregate inventory and, eventually, with decreases in total costs. There are several possible extensions for this work that could constitute future research endeavors in this field. An immediate extension is related to the allocation rules that underlie the consolidation effect and the inventory portfolio models presented in the literature review. Should a given centralized facility supply the same fraction of demand to each decentralized location (Tyagi and Das, 1998) or should a fraction of the demand be supplied by a primary source and the remainder by secondary sources (cross filling)? The impacts of both allocation rules on total inventory levels and their implications for the consolidation decision could be explored. Another extension could be the incorporation of some of the inventory analyses developed in this research into logistics network problems, via nonlinear programming. These are, among others, some subjects of ongoing future research.