Peccati. Borgonovo and Peccati propose a new approach to calculate the differences between different inventory policies determined by several risk aversion attitudes using different risk measures.
Another research direction is to perform a good sensitivity analysis of inventory models. For example, cardenasBarron made a sensitivity analysis for the EOQ and EPQ inventory models considering two without/with backorders backorder costs (linear and fixed). On the other hand. it is important to point out that another type of sensitivity analysis to the ECQEPQ inventory models with backorders can be done in line of the works of Borgonovo and Peccati Borgonovo , and Borgonovo and Peccati just to name a few.
As we was mentioned before, there are several researchers have developed the basic EOQ/EPQ inventory models with linear and fixed backorder costs using alternative solution procedures. See for example the works of Hadley and Whitin , . Johnson and Montgomery . Sphicas. Omar et al. and Cardenas-Barron . Just to name a few. However,their solution procedures to locate and guarantee the optimal solution are not of all complete.
Perhaps, Hadley and Whitin , and Johnson and Montgomery were the first researchers to models with two backorder costs. a linear and a fixed cost per unit. Their solution procedure is treat the EOQ/EPQ inventory based on calculus and solved the system equations resulting from the first-order conditions. Recently. Sphicas indicates that Johnson and Montgomery 's arguments to locate the optimal solutions are not complete. Therefore, Sphicas adopts an algebraic approach to demonstrate how a relatively complex model can be fully analyzed without derivatives and obtained the explicit identification of the models. E0Q/EPQ inventory models.
In this respect,our research work basically improves Johnson and Montgomery 12Jand Sphicas works to adopt an analytic approach based on calculus to locate and ensure the optimal solutions of the models. The main EOQ/EPQ inventory results of this paper are fourfold