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  • Flexible manufacturing systems  (3)
  • hierarchical control  (2)
  • 1
    Electronic Resource
    Electronic Resource
    Hierarchical Production Control in Dynamic Stochastic Jobshops with Long-Run Average Cost (2000)
    Springer
    Journal of optimization theory and applications 106 (2000), S. 231-264 
    Details
    ISSN: 1573-2878
    Keywords: hierarchical control ; manufacturing systems ; stochastic dynamic programming ; optimal control ; long-run average cost
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a production planning problem for a dynamic jobshop producing a number of products and subject to breakdown and repair of machines. The machine capacities are assumed to be finite-state Markov chains. As the rates of change of the machine states approach infinity, an asymptotic analysis of this stochastic manufacturing systems is given. The analysis results in a limiting problem in which the stochastic machine availability is replaced by its equilibrium mean availability. The long-run average cost for the original problem is shown to converge to the long-run average cost of the limiting problem. The convergence rate of the long-run average cost for the original problem to that of the limiting problem together with an error estimate for the constructed asymptotic optimal control is established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004667028547
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Hierarchical controls in stochastic manufacturing systems with convex costs (1994)
    Springer
    Journal of optimization theory and applications 80 (1994), S. 299-317 
    Details
    ISSN: 1573-2878
    Keywords: Stochastic manufacturing systems ; convex production planning ; hierarchical control ; dynamic programming ; viscosity solutions ; convergence rates ; error bounds
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper presents an extension of earlier research on heirarchical control of stochastic manufacturing systems with linear production costs. A new method is introduced to construct asymptotically optimal open-loop and feedback controls for manufacturing systems in which the rates of machine breakdown and repair are much larger than the rate of fluctuation in demand and rate of discounting of cost. This new approach allows us to carry out an asymptotic analysis on manufacturing systems with convex inventory/backlog and production costs as well as obtain error bound estimates for constructed open loop controls. Under appropriate conditions, an asymptotically optimal Lipschitz feedback control law is obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02192938
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Piecewise deterministic Markov process model for flexible manufacturing systems with preventive maintenance (1994)
    Springer
    Journal of optimization theory and applications 81 (1994), S. 259-275 
    Details
    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
    URL: http://dx.doi.org/10.1007/BF02191664
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Periodic maintenance and repair rate control in stochastic manufacturing systems (1996)
    Springer
    Journal of optimization theory and applications 91 (1996), S. 347-361 
    Details
    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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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Minimax production planning in failure-prone manufacturing systems (1995)
    Springer
    Journal of optimization theory and applications 87 (1995), S. 269-286 
    Details
    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
    URL: http://dx.doi.org/10.1007/BF02192564
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    Paper (German National Licenses)
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