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] 1 1 3 2 [2] = +w(k) d(k) (1) 2014 12 1 1
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 1 0 0 0 1 0 1 0 0 K 1 0 0 0 0 1 0 0 0 0 1 0 (8) (9) x(k 3) 2 =0 (3) 0 0
(7) (9) L M =3 1 K 0 0 = 1 0 0 0 0 1 0 0 0 0 1 0 x(k 3) = = 1 0 K 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 K 1 0 0 0 0 1 0 0 0 0 1 0 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) 1 0 0 K 0 0 1 0 0 0.................. A i =................................. 0 0 1 0
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
2: (Scpoe1) 2 3 5 K = 1 3 K = 1 4 5 5 (14) LMI 3 LMI 1 3 w(k) =0 K = 0.2 4 K = 0.2 (14) LMI Matlab Robust Control Toolbox feasp LMI P = 1.7034 0.8918 0.3141 0.0859 0.8918 1.3909 0.2840 0.0701 0.3141 0.2840 0.8966 0.1522 0.0859 0.0701 0.1522 0.4598 > 0 3 4 K = 1 2
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 = 0.5 5 K = 0.5 (14) LMI P 5 L =1 L =2 L =3 [8]
5: K = 0.5 (Scope) 4 [1] 2006 pp. 66 67 (2006) [2] Bullwhip 5, pp. 205 214 (2008) [3] 6, pp. 157 162 (2009) [4] 7, pp. 105 109 (2010)
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. 243 245 (2010) [6] (1999) [7] G. Zhai, B. Hu, A. M. Michel, L 2 Vol. 15, No. 3, pp. 117-125 (2002) [8] Vol. 15, No. 5, pp. 232-237 (2002) -55-
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-