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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Dynamic lot-size model ： ウィキペディア英語版 Dynamic lot-size model The dynamic lot-size model in inventory theory, is a generalization of the economic order quantity model that takes into account that demand for the product varies over time. The model was introduced by Harvey M. Wagner and Thomson M. Whitin in 1958.〔Harvey M. Wagner and Thomson M. Whitin, "Dynamic version of the economic lot size model," Management Science, Vol. 5, pp. 89–96, 1958〕〔Wagelmans, Albert, Stan Van Hoesel, and Antoon Kolen. "(Economic lot sizing: an O (n log n) algorithm that runs in linear time in the Wagner-Whitin case )." Operations Research 40.1-Supplement - 1 (1992): S145-S156.〕 ==Problem setup== We have available a forecast of product demand over a relevant time horizon t=1,2,...,N (for example we might know how many widgets will be needed each week for the next 52 weeks). There is a setup cost incurred for each order and there is an inventory holding cost per item per period ( and can also vary with time if desired). The problem is how many units to order now to minimize the sum of setup cost and inventory cost. Let I denote inventory: $I=I\_+\backslash sum\_^x\_-\backslash sum\_^d\_\backslash geq0$ The functional equation representing minimal cost policy is: $f\_(I)=\backslash underset\backslash geq\; d\_\}\backslash left(i\_I+H(x\_)s\_+f\_\backslash left(\; I+x\_-d\_\; \backslash right)\; \backslash right)$ Where H() is the Heaviside step function. Wagner and Whitin〔 proved the following four theorems: * There exists an optimal program such that I=0; ∀t * There exists an optimal program such that =0; ∀t or $\backslash textstyle\; \backslash sum\_^\; d\_$ is satisfied for some k (t≤k≤N) * There exists an optimal program such that if is satisfied by some , t * **, then , t=t * *+1,...,t *-1, is also satisfied by * Given that I = 0 for period t, it is optimal to consider periods 1 through t - 1 by themselves 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Dynamic lot-size model」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.