Title :
Flow control in a failure-prone multi-machine manufacturing system
Author :
Abou-Kandkil, H. ; Smet, O. De ; Freiling, G. ; Jank, G.
Author_Institution :
Ecole Normale Superieure de Cachan, France
Abstract :
The problem of computing optimal production rates for a multimachine multiproduct manufacturing system subject to machine failure is considered. The inventory balance equation is represented by a discrete-time flow model with Markovian jumps to take into account machine breakdown. When defining quadratic cost functions, the associated optimal control problem leads to a set of strongly coupled Riccati-like equations. A necessary and sufficient condition for the existence of a positive semidefinite solution for such equations is given. By verifying a simple matrix inequality, it is shown that such solution exists and can be obtained as a limit of a monotonic sequence. This leads to a straightforward numerical algorithm for the computation of the solution. In this way the optimal production rates for each product type can be determined. An example involving 9 machines and 6 product types is given to illustrate the proposed approach
Keywords :
Markov processes; Riccati equations; discrete time systems; matrix algebra; optimal control; production control; reliability theory; Markovian jumps; discrete-time flow model; failure-prone multimachine manufacturing system; inventory balance equation; machine breakdown; monotonic sequence limit; multiproduct manufacturing system; necessary and sufficient condition; optimal control problem; optimal production rates; positive semidefinite solution; production flow control; quadratic cost functions; simple matrix inequality; strongly coupled Riccati-like equations; Computer aided manufacturing; Control systems; Cost function; Electric breakdown; Linear matrix inequalities; Manufacturing systems; Optimal control; Production systems; Riccati equations; Sufficient conditions;
Conference_Titel :
Emerging Technologies and Factory Automation, 1995. ETFA '95, Proceedings., 1995 INRIA/IEEE Symposium on
Conference_Location :
Paris
Print_ISBN :
0-7803-2535-4
DOI :
10.1109/ETFA.1995.496697