EOQ و EPQ با هزینه های خطی و هزینه های ثابت سفارش معوقه: دو مورد شناسایی و مدل های تجزیه و تحلیل بدون حساب دیفرانسیل و انتگرال

The EOQ and EPQ models with linear and fixed backorder costs are newly analyzed and all formulae are proven using only algebra. Two cases are identified, where backorders should and should not be allowed. The results are shown to include several known special cases.

Two recent papers in this journal, Grubbström and Erdem (1999) and Cárdenas-Barrón (2001) used an algebraic approach to prove the formulae for the EOQ and economic production quantity (EPQ) with a single cost of backordering, only linear (time dependent). Here we extend the approach to the more general models of EOQ and EPQ with two backorder costs, a linear and a fixed cost per unit. The only treatment of these models we could find was in Johnson and Montgomery (1974, pp. 26–33). In their analysis they used calculus and solved the system of equations resulting from the first-order conditions. They did not explicitly identify the two distinct cases we examine here. Our analysis is based entirely on an algebraic approach. In addition to the fact that it is of interest to demonstrate how a relatively complex model can be fully analyzed without derivatives, we obtain the explicit identification of the two cases, a result that does not appear as easy to do by using calculus.

This paper used an algebraic approach to examine the EOQ model with two backorder costs. The analysis identified two cases: when the size of the fixed backorder cost is relatively large (View the MathML sourceπ⩾2kh/rD), there should optimally be no backordering, and the basic EOQ applies. When ππ is smaller than View the MathML source2kh/rD, there should optimally be some backorders. The linear backorder p cost plays no role in this dichotomy: that component is never too large itself to make backordering too expensive. The optimal values of all variables were obtained without calculus, and some new results developed and some special cases considered. It was also shown that the EPQ model is basically similar and the results and formulae for that were obtained.