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Optimal control of hybrid manufacturing systems by log-exponential smoothing aggregation

  • * Corresponding author: Jianxing Li and Honglei Xu

    * Corresponding author: Jianxing Li and Honglei Xu 
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  • This paper studies new optimal control policies for solving complex decision-making problems encountered in industrial hybrid systems in a manufacturing setting where critical jobs exist in a busy structure. In such setting, different dynamical systems interlink each other and share common functions for smooth task execution. Entities arriving at shared resources compete for service. The interactions of industrial hybrid systems become more and more complex and need a suitable controller to achieve the best performance and to obtain the best possible service for each of the entities arriving at the system. To solve these challenges, we propose an optimal control policy to minimize the operational cost for the manufacturing system. Furthermore, we develop a hybrid model and a new smoothing algorithm for the cost balancing between the quality and the job tardiness by finding optimal service time of each job in the system.

    Mathematics Subject Classification: Primary: 37C75, 93C10; Secondary: 34D20.

    Citation:

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  • Table 1.  Job arrival $ 0.4\le r_i \le 1.5 $

    $ F_1 \, | \, \text{no-wait, seq-dependent}\, | \, x_{\max} $ $ F_1 \, | \, \text{wait, seq-dependent}\, | \, x_{\max} $
    Job Arrival time Control input Completion time Processing cost Control input Completion time Processing cost
    0.4 0.3162 0.5000 2.4500 0.4404 0.5940 1.4872
    0.5 0.4472 0.7000 1.5900 0.4404 0.7950 1.7664
    0.7 0.4472 0.9000 1.9100 0.4404 0.9959 2.1262
    0.9 0.5300 1.1809 2.1777 0.5132 1.2593 2.4211
    1.3 0.4472 1.5000 3.3500 0.447214 1.5000 3.3500
    1.5 0.4423 1.6956 3.9998 0.4423 1.6956 3.9998
    Total cost: 15.4775 Total cost: 15.1507
     | Show Table
    DownLoad: CSV

    Table 2.  Job arrival $ 1.1\le r_i \le 2.3 $

    $ F_1 \, | \, \text{no-wait, seq-dependent}\, | \, x_{\max} $ $ F_1 \, | \, \text{wait, seq-dependent}\, | \, x_{\max} $
    Job Arrival time Control input Completion time Processing cost Control input Completion time Processing cost
    1.1 0.4963 1.3463 2.7057 0.4963 1.3463 2.7057
    1.4 0.4472 1.6000 3.6600 0.4472 1.6000 3.6600
    1.6 0.3162 1.7000 5.0900 0.4310 1.7857 4.3733
    1.7 0.4204 1.8767 4.7668 0.4121 1.9530 5.1098
    2.2 0.3162 2.3000 7.4900 0.3652 2.3393 7.2480
    2.3 0.3690 2.4361 7.5503 0.3633 2.4713 7.9814
    Total cost: 31.2628 Total cost: 31.0782
     | Show Table
    DownLoad: CSV
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