Critical fractile

CR = cj(c + cj = 0.571. The issue now is to translate this critical ratio into a critical fractile of the demand distribution. Recall from the preceding text that D N(10,000,3,121). Thus, another table look-up (or Excel computation) gives us Q = 10,558, the value that accumulates a total probability of 0.571 under the normal distribution pdf with mean 10,000 and standard deviation 3,121. 

The approximation developed by Shang and Song (2003) uses echelon holding costs, as defined earlier, and starts from the optimal echelon N base-stock level, which—by the authors reference to Chen and Zheng (1994)— is given by computing the critical fractile... 

When there is a tradeoff between the holding cost and the penalty cost for failing to immediately satisfy uncerfain demand, we should employ a "critical fractile-based" solution to exploit this tradeoff. 

A more rigorous derivation of the previously mentioned formula is provided in Appendix 13A. The optimal CSL has also been referred to as the critical fractile. The resulting optimal order quantity maximizes the firm s profit. If demand during the season is normally distributed, with a mean of jx and a standard deviation of a-, the optimal order quantity is given by... 

The Critical-Fractile Method for Inventory Planning. Harvard Business School Note 9-191-132,1991. 

The comparsion with the critical value k = Ff,oD,i.a-fractil (dependent on the significance level a) decides on the acceptance of Ho... 

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