2013, the classical EOQ formula Will have a century of its discovery by Harris 1913, Later the EPQ formula was developed by Taft in 1918. Perhaps the first book in inventory management was written by Raymond in 1931. Since then, many extensions of the EOQ and EPO inventory models have been developed by researcher and academicians. Some extensions cover deterministic and stochastic inventory models. Moreover, the researchers and academicians have shown methods to derive the EOQ, EPQ and some extensions of them with a huge interest in developing alternative optimization pedagogical value It is worth mentioning that some optimization methods are very simple and others are too complex. For an up to date review of different optimization methods in inventory field, see 14]. However, some of the optimization methods lack the mathematical rigor and some of them are based on intuitive arguments. Furthermore, some of them do not have the mathematical proof needed. In addition, all optimization methods that develop the Foo and EPO inventory models with two classical backorders costs (linear and fixed) available until today are deficient or incomplete. Therefore, we find that in both inventory models, there exists the need for developing a complete solution procedure for determining the optimal lot size and backorders level
Recently, an increasing interest in analyzing inventory models considering risk coherent inventories has been found in the inventory literature. In this direction. see for example the research works of Ahmed et al. and Borgonovo and