人文学部研究年報12号.indb

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1 制御理論を用いた在庫管理モデルの一解析 * リードタイムが変動する場合 西平直史 1 [1, 2, 3, 4] [1] [2, 3, 4] [2] = +w(k) d(k) (1)

2 制御理論を用いた在庫管理モデルの一解析 西平 k w(k) d(k) L k u(k) (2) (1) 2 w(k) =u(k L) (2) = +u(k L) d(k) (3) [2] u(k) =K (4) (4) = +Kx(k L) d(k) (5) [2] L L L m > 0 L M 0 <L m L L M L L (5) d(k) =0 L m = 1, L M =3 L =1 = +K (6) [ ] = [ 1 K 1 0 ][ ] (7) L =2, 3 = = 1 0 K K (8) (9) x(k 3) 2 =0 (3) 0 0

3 (7) (9) L M =3 1 K 0 0 = x(k 3) = = 1 0 K K x(k 3) x(k 3) (10) (12) L = i L m i L M. ξ(k) = x(k i + 1) x(k i) x(k i 1). x(k L M ) (5) (10) (11) (12) ξ(k + 1) = A i ξ(k) (i = L m L M ) (13) K A i =

4 制御理論を用いた在庫管理モデルの一解析 西平 1: 3 (13) (13) [5] (13) i Lyapunov [6] K LMI P (13) A T i PA i P<0 (14) [5, 6] [7, 8] [7] A i [8] Matlab simulink 1 1 Variable Integer Delay 1 3 2

5 2: (Scpoe1) K = 1 3 K = (14) LMI 3 LMI 1 3 w(k) =0 K = K = 0.2 (14) LMI Matlab Robust Control Toolbox feasp LMI P = > K = 1 2

6 制御理論を用いた在庫管理モデルの一解析 西平 3: K = 1 (Scope) 4: K = 0.2 (Scope) K = K = 0.5 (14) LMI P 5 L =1 L =2 L =3 [8]

7 5: K = 0.5 (Scope) 4 [1] 2006 pp (2006) [2] Bullwhip 5, pp (2008) [3] 6, pp (2009) [4] 7, pp (2010)

8 制御理論を用いた在庫管理モデルの一解析 西平 [5] Vol. 23, No. 10, pp (2010) [6] (1999) [7] G. Zhai, B. Hu, A. M. Michel, L 2 Vol. 15, No. 3, pp (2002) [8] Vol. 15, No. 5, pp (2002) -55-

9 An Analysis of Inventory Management Models Using Control Theory a Case when the lead time is varied Naofumi NISHIHIRA This paper considers the problem of an analysis of inventory management models when the lead time is varied. We formulate the inventory management models as switching dynamical systems. We have shown that the stability of the entire switching systems can be reduced to simultaneously stability. Moreover, We confirmed the validity and limitations of the proposed method by some simulations. -55-

リードタイムが変動する在庫管理モデルの安定性解析 西平 w(k)= u(k-l(k)) ( 2 ) となる このモデルに対して, メモリーレスフィードバック u(k)= Kx(k) (3) を施すことを考える また, 本稿では内部安定性を考えるため, 外生信号 d(k)= 0とすると, システム (

リードタイムが変動する在庫管理モデルの安定性解析 西平 w(k)= u(k-l(k)) ( 2 ) となる このモデルに対して, メモリーレスフィードバック u(k)= Kx(k) (3) を施すことを考える また, 本稿では内部安定性を考えるため, 外生信号 d(k)= 0とすると, システム ( 山形大学人文学部研究年報第 14 号 (2017.2)125-130 研究ノートリードタイムが変動する在庫管理モデルの安定性解析 スイッチドシステムとしての考察 山形大学人文学部法経政策学科 西平直史 1. はじめに 在庫管理問題において, リードタイムの存在がしばしば問題を難しくすることがある リードタイムとは, 供給が必要になった時点と実際に供給が行われる時点との差であり, 生産活動や輸送活動などに要する時間のことである

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