Robust inventory-production control problem with stochastic demand

This paper deals with the inventory-production control problem where the produced items are supposed to be deteriorating with a rate that depends on the stochastic demand rate. The inventory-production control problem is formulated as a jump linear quadratic control problem. The optimal policy that solves the optimal control problem is obtained in terms of a set of coupled Riccati equations. The guaranteed cost control problem is also investigated. Copyright © 1999 John Wiley & Sons, Ltd.

[1]  P. Khargonekar,et al.  Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory , 1990 .

[2]  Kheng Joo Heng,et al.  An order-level lot-size inventory model for deteriorating items with finite replenishment rate , 1991 .

[3]  Dennis S. Bernstein,et al.  Robust stability and performance via fixed-order dynamic compensation with guaranteed cost bounds , 1990, Math. Control. Signals Syst..

[4]  K. Loparo,et al.  Stochastic stability properties of jump linear systems , 1992 .

[5]  Qing Zhang,et al.  Hierarchical Decision Making in Stochastic Manufacturing Systems , 1994 .

[6]  Hui-Ming Wee,et al.  Economic production lot size model for deteriorating items with partial back-ordering , 1993 .

[7]  El Kebir Boukas,et al.  Optimal tracker for unreliable manufacturing systems , 2000, Int. J. Syst. Sci..

[8]  D. Sworder Feedback control of a class of linear systems with jump parameters , 1969 .

[9]  G. Zames Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses , 1981 .

[10]  Lihua Xie,et al.  Output feedback H∞ control of systems with parameter uncertainty , 1996 .

[11]  Ahmed I. A. Salama,et al.  A Computational Algorithm for Solving a System of Coupled Algebraic Matrix Riccati Equations , 1974, IEEE Transactions on Computers.

[12]  El-Kébir Boukas,et al.  Manufacturing flow control and preventing maintenance: a stochastic control approach , 1988 .

[13]  E. Boukas,et al.  Necessary and Sufficient Condition for Robust Stability and Stabilizability of Continuous-Time Linear Systems with Markovian Jumps , 1998 .

[14]  François Dufour,et al.  The filtering problem for continuous-time linear systems with Markovian switching coefficients , 1994 .

[15]  H. Chizeck,et al.  Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control , 1990 .

[16]  Alan S. Willsky,et al.  A survey of design methods for failure detection in dynamic systems , 1976, Autom..

[17]  T. K. C. Peng,et al.  Adaptive Guaranteed Cost of Control of Systems with Uncertain Parameters , 1970 .

[18]  E. Boukas,et al.  H∞-Control for Markovian Jumping Linear Systems with Parametric Uncertainty , 1997 .

[19]  P. Shi Filtering on sampled-data systems with parametric uncertainty , 1998, IEEE Trans. Autom. Control..

[20]  A. Andijani,et al.  Analysis of deteriorating inventory/production systems using a linear quadratic regulator , 1998, Eur. J. Oper. Res..

[21]  I. Petersen A stabilization algorithm for a class of uncertain linear systems , 1987 .

[22]  H. Abou-Kandil,et al.  Solution and asymptotic behavior of coupled Riccati equations in jump linear systems , 1994, IEEE Trans. Autom. Control..

[23]  John R. Broussard,et al.  Application of precomputed control laws in a reconfigurable aircraft flight control system , 1989 .

[24]  El-Kébir Boukas,et al.  Optimal control of manufacturing flow and preventive maintenance , 1996 .

[25]  El-Kébir Boukas,et al.  Robust production and maintenance planning in stochastic manufacturing systems , 1995, IEEE Trans. Autom. Control..

[26]  R. Rishel Control of systems with jump Markov disturbances , 1975 .

[27]  R. Rogers,et al.  An LQ-solution to a control problem associated with a solar thermal central receiver , 1983 .

[28]  M. Mariton,et al.  Jump Linear Systems in Automatic Control , 1992 .

[29]  E. Boukas,et al.  Robust stabilizability of uncertain linear systems with Markovian jumping parameters , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[30]  Sérgio Ricardo de Souza,et al.  ℋ2 guaranteed cost control for uncertain discrete-time linear systems , 1993 .

[31]  M. Fragoso,et al.  Stability Results for Discrete-Time Linear Systems with Markovian Jumping Parameters , 1993 .

[32]  Lihua Xie,et al.  Robust Kalman filtering for uncertain systems , 1994 .

[33]  Hamid Bahari-Kashani,et al.  Replenishment Schedule for Deteriorating Items with Time-Proportional Demand , 1989 .

[34]  Lihua Xie,et al.  On designing controllers for a class of uncertain sampled-data nonlinear systems , 1993 .

[35]  Michael Athans,et al.  Command and control (C2) theory: A challenge to control science , 1986 .

[36]  Haiping Xu,et al.  An economic ordering policy model for deteriorating items with time proportional demand , 1990 .

[37]  D. McFarlane,et al.  Optimal guaranteed cost control and filtering for uncertain linear systems , 1994, IEEE Trans. Autom. Control..