Researchers have used analytic methods (calculus) to solve inventory models with fixed and linear backorder costs. They have found conditions to partition the feasible domain into two parts. For one part, the system of the first partial derivatives has a solution. For the other part, the inventory model degenerates to the inventory model without shortages. A scholar tried to use the algebraic method to solve this kind of model. The scholar mentioned the partition of the feasible domain. However, other researchers cannot understand why the partition appears, even though the scholar provided two motivations for his derivations. After two other researchers provided their derivations by algebraic methods, the scholar showed a generalized solution to combine inventory models with and without shortages together. In this paper, we will point out that this generalized solution approach not only did not provide explanations for his previous partition but also contained twelve questionable results. Recently, an expert indicated questionable findings from two other researchers. Hence, we can claim that solving inventory models with fixed and linear backorder costs is still an open problem for future researchers.
Solution Procedure for Inventory Models with Linear and Fixed Backorder Costs
