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Transfer lines with multi-machine stages and non-deterministic processing time: transient performance analysis and control

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Abstract

Serial transfer lines with parallel machines in each stage are now a fairly common manufacturing system. However, its analysis and predictive-reactive control during transients remains mostly unexplored. This manufacturing system consists of a series of stages where in each stage a finite number of machines work concurrently. A two multi-state stage transfer line is studied in this paper. To describe the probability of one part being completed from the several machines in a stage, an equivalent multi-state, perfectly reliable machine is proposed. This multi-state model enables variance in the processing time between job completions to be captured stochastically. Based on historic data or engineering experience, an equivalent multi-state machine is simulated from the cumulative distribution function of the aggregated behavior of the parallel machines. In this paper, a serial production line with two equivalent, multi-state machines is used to analyze transient performance. Analytical closed-form expressions are derived to evaluate system transient behaviors. This system is also used with a controller to implement practical production control. Using model predictive control, system control parameter values provide decision support for managers to control short-term production. The proposed methodology can be applied to improve resource efficiency in other operation management problems.

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Acknowledgment

The authors gratefully acknowledge the support of the National Science and Engineering Research Council of Canada and the University of Calgary for this work.

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Authors and Affiliations

  1. Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, AB, Canada

    Zhigang Zeng & Robert William Brennan

  2. Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA

    Theodor Freiheit

Authors
  1. Zhigang Zeng
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  2. Robert William Brennan
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  3. Theodor Freiheit
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Correspondence to Zhigang Zeng.

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Zeng, Z., Brennan, R. & Freiheit, T. Transfer lines with multi-machine stages and non-deterministic processing time: transient performance analysis and control. Oper Res Int J 22, 2489–2528 (2022). https://doi.org/10.1007/s12351-020-00617-y

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  • DOI: https://doi.org/10.1007/s12351-020-00617-y

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