فرمول EOQ کلی با استفاده از یک پارامتر جدید: ضریب جذابیت سفارش معوقه

This paper introduces and examines a generalized EOQ formula, based on the model with linear and fixed backordering costs. The new square-root formula is a combination of two well-known classical models, the basic EOQ model without stockouts and the EOQ model with backorders and linear backordering costs. Helping to combine the two is a new parameter, a fractional coefficient capturing the attractiveness of backorders. The coefficient is explained and discussed. The paper concludes with a brief discussion of generalizations in EOQ models, including EPQ.

This paper introduces and examines a possible generalization of the widely-known classical EOQ formula. It is well known that very extensive work has been done over the years on several variations of EOQ under several different assumptions. Since it is not the intention of this paper to do a large literature review, we will limit our citations mostly to those that were immediate predecessors leading to this paper. A relatively recent stream of research is the utilization of algebraic methods instead of calculus to analyze inventory models. Examples of that approach include Grubbstrom (1995), Grubbstrom and Erdem (1999), Cárdenas-Barrón, 2001 and Cárdenas-Barrón, 2010, Huang (2003), Ronald et al. (2004), Chang et al. (2005), Sphicas (2006), Minner (2007), Leung (2008). The above selected references employed mostly algebraic methods, but that should not give the impression that calculus is no longer used in the inventory literature. Some recent examples of published papers based on calculus are Yang (2007), Leung (2008), Pentico and Drake (2009), and Chung and Cárdenas-Barrón (2012). The work reported here is based on the model with linear and fixed backordering costs and is specifically motivated by the properties and results first presented in Sphicas (2006). In that paper the solution was analyzed using only algebra. Later, the same model was examined and similar results were obtained using calculus in Chung and Cárdenas-Barrón (2012), and also using a combination of analytic geometry and algebra in Cárdenas-Barrón (2011). In Section 2 the main results from Sphicas (2006) are reviewed, since they form the basis of the new development proposed here. In Section 3 the modified square-root formula and generalized EOQ is developed. Introduced and defined is a new parameter, a fractional coefficient capturing the attractiveness of backorders. The logic of that and the interpretation and significance of the coefficient are discussed in Section 4. Finally in Section 5 some discussion of generalizations in EOQ models is presented, including the case of EPQ.

The generalized EOQ formula, View the MathML sourceEOQβ=(2KD/h)(1+βr)was developed, based on the model with backorders and two backordering costs. The linear backordering cost p is part of the ratio r=h/p, while the fixed backordering cost is part of β, a new coefficient introduced here. The definition and significance of the β, a fraction representing the degree of attractiveness of backorders, were discussed, and some special cases and generalizations noted.