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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 87 (1995), S. 269-286 
    ISSN: 1573-2878
    Keywords: Flexible manufacturing systems ; minimax production planning ; Hamilton-Jacobi-Isaacs equation ; viscosity solutions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider a minimax production planning model of a flexible manufacturing system with machines that are subject to random breakdown and repair. The objective is to choose the rate of production that minimizes the related minimax cost of production and inventory/shortage. The value function is shown to be the unique viscosity solution to the associated Hamilton-Jacobi-Isaacs equation. Under certain conditions, it is shown that the value function is continuously differentiable. A verification theorem is given to provide a sufficient condition for optimal control. Finally, two examples are solved explicitly.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 91 (1996), S. 347-361 
    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
    Library Location Call Number Volume/Issue/Year Availability
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 81 (1994), S. 259-275 
    ISSN: 1573-2878
    Keywords: Flexible manufacturing systems ; controlled piecewise deterministic Markov process ; maintenance and production planning
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider a maintenance and production model of a flexible manufacturing system. The maintenance activity involves lubrication, routine adjustments, etc., which reduce the machine failure rates and therefore reduce the aging of the machines. The objective of the problem is to choose the rate of maintenance and the rate of production that minimize the overall costs of inventory/shortage, production, and maintenance. It is shown that the value function is locally Lipschitz. Then, the existence of the optimal control policy is shown, and necessary and sufficient conditions for optimality are obtained.
    Type of Medium: Electronic Resource
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