Discussion of two motivations provided by Sphicas 2006
Abstract
We discuss two motivations proposed by Sphicas (2006). First, after Lin (2019), we provide another partition for the feasible domain to show that there are at least three partitions to point out that the first motivation of Lin (2019) is not sufficient to support his solution procedure. For the second motivation of Sphicas (2006), we provide a detailed examination from the algebraic point of view to claim that his second motivation containing severe questionable results. We suggest researchers presenting a primitive algebraic method for inventory models with fixed and linear backorder costs.
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Introduction
Sphicas[1] is the first paper to use the algebraic method to solve inventory models with fixed and linear backorder costs. Sphicas [1] applied a genuine method to partition the domain into two cases and then derived the optimal solution by algebraic methods. However, his genuine method is too sophisticated that is beyond imagined of ordinary practitioners, such that Cárdenas-Barrón[2], Chung and Cárdenas-Barrón[3], and Sphicas [4] provided further discussions for the same inventory models. Recently, Lin [5] mentioned that the algebraic approach provided by Sphicas [1] is too complicated for ordinary readers to absorb the motivation explained by Sphicas [1]. Consequently, Cárdenas-Barrón[2], Chung and Cárdenas-Barrón [3], and Sphicas [4] provided different algebraic to solve the same inventory model with linear and fixed backorder costs. Lin [5] pointed out Cárdenas-Barrón[2] containing several severe problems and then Lin [5] claimed that a primitive approach will be an interesting research topic for future researchers. In this paper, we will provide further discussion for the motivation proposed by Sphicas [1] for his algebraic method.
Conclusion
Even after Sphicas [1] provided two motivations for his algebraic approach, ordinary researchers still cannot understand the algebraic approach proposed by Sphicas [1]. Consequently, Cárdenas-Barrón[2], Chung and Cárdenas-Barrón [3], and Sphicas [4] provide further discussions for inventory models with fixed and linear backorder costs. Lin [5] discussed one motivation provided by Sphicas [1] and then we improve a typo in the discussion of Lin [5]. Moreover, we show that the second motivation proposed by Sphicas [1] containing more severe questionable results. Hence, we can claim that a primitive derivation for inventory models with fixed and linear backorder costs should be a hot research issue for academic society.