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In this study, we consider infinite supply of raw materials and backlogged demands as give two boundary conditions. And we need not make any specific any specific assumptions about the inter-arrival of external demand and service time distributions. Under these situations, the ultimate objective of this study is to prove the variability propagation principle in a pull serial line and is to measure it to measure it in terms of the first two moments of the inter-departure process subject to number of cards in each cell. Two preparations are required to achieve this objective: the one is to derive a true lower bound of variance of the inter-departure process. The other is to establish a constrained discrete mini-max problem for the no backorder (backlogging) probabilities in each cell. We may get some fundamental results necessary to a completion for the proof through the necessary and sufficient conditions for existence of optimal solution of a constrained discrete minimax problem and the implicit function theorem. Finally, we propose a numeric model to measure the variability propagation principle. Numeric examples show the validity and applicability of our study.
Keyword: LOWER Bound of Variance, Constrained Discrete Minimax Problem
Keyword: LOWER Bound of Variance, Constrained Discrete Minimax Problem
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