ISSN:
1573-2878
Keywords:
Flexible manufacturing systems
;
controlled Markov processes
;
production planning
;
repair rate control
;
maintenance scheduling
;
Hamilton-Jacobi-Bellman equation
;
viscosity solution
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In this paper, we consider a periodic preventive maintenance, repair, and production model of a flexible manufacturing system with failure-prone machines, where the control variables are the repair rate and production rate. We use periodic preventive maintenance to reduce the machine failure rates and improve the productivity of the system. One of the distinct features of the model is that the repair rate is adjustable. Our objective is to choose a control process that minimizes the total cost of inventory/shortage, production, repair, and maintenance. Under suitable conditions, we show that the value function is locally Lipschitz and satisfies an Hamilton-Jacobi-Bellman equation. A sufficient condition for optimal control is obtained. Since analytic solutions are rarely available, we design an algorithm to approximate the optimal control problem. To demonstrate the performance of the numerical method, an example is presented.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02190100
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