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Job Shop Scheduling with Petri Nets

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Handbook of Combinatorial Optimization

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Abstract

In job shop scheduling problem (JSSP), deadlock-free design and scheduling optimization are important issues, which are difficult to tackle in the JSSP having multiple shared resources. To deal with these issues, this chapter introduces a modular-based system design method for modeling and optimizing JSSP. Several operators are presented for handling the combination of JSSP modules and resource sharing. For handling deadlock issues with multi-resources sharing, the conditions on “dead transitions” and “circular waiting” are considered. Based on a transitive matrix, deadlock detection and deadlock recovery algorithms are developed in order to get a deadlock-free system. For each operator, the partial schedule and makespan of each module are obtained. The optimal scheduling of JSSP can be derived from these theoretical results step by step. With the modular-based system design method, one cannot only design a correct system model which is live, bounded, reversible, and deadlock-free and terminate properly but also find the optimal scheduling of JSSP in a formal way. For handling large-scale JSSP, the traditional optimization technologies such as genetic algorithm, branch and bound method, hybrid methods, and rule-based methods can be applied together with the modular-based approach in this chapter. Based on the Petri net model, a genetic algorithm is also introduced here.

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Author information

Authors and Affiliations

  1. Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, People’s Republic of China

    Hejiao Huang

  2. Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, People’s Republic of China

    Hongwei Du

  3. Information Technology, University of Central Punjab, Lahore, Pakistan

    Farooq Ahmad

Authors
  1. Hejiao Huang
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  2. Hongwei Du
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  3. Farooq Ahmad
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Corresponding author

Correspondence to Hejiao Huang .

Editor information

Editors and Affiliations

  1. Department of Industrial and Systems Eng, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  2. Department of Computer Science, University of Texas, Dallas, Richardson, Texas, USA

    Ding-Zhu Du

  3. Dept. Comp. Sci. & Engineering, University of California, San Diego, La Jolla, California, USA

    Ronald L. Graham

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Huang, H., Du, H., Ahmad, F. (2013). Job Shop Scheduling with Petri Nets. In: Pardalos, P., Du, DZ., Graham, R. (eds) Handbook of Combinatorial Optimization. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7997-1_51

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