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Approximate Approach to Deal with the Uncertainty in Integrated Production Scheduling and Maintenance Planning

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Abstract

This paper deals with the integration problem between production scheduling and maintenance planning in a single machine, where the impact of failure uncertainty is considered. The objective is to minimize the weighted sum of quality robustness and solution robustness, which is determined by the jobs’ sequence, preventive maintenances’ position and buffer time in the schedule. Then, a three-stage algorithm is devised to solve the problem, where the gradient descent algorithm based on an effective surrogate measure is developed in the second stage. The numerical experiments show that the deviation of the approximate approach is very small, as compared with the exact solution obtained by CPLEX. The balance between quality robustness and solution robustness and the distribution of buffer time in different scenarios are shown in a case study. It validates the necessity and effectiveness of the consideration of robustness in the industrial practice.

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Abbreviations

b [i] :

The buffer time immediately before job j[i]

B :

The buffer time list

C r [i],w :

The real finish time of j[i] in the scenario w

d r [i]w :

The delay of the start time of j[i] in w

D 1,[i] :

The first measure approximating E(dr[i], w)

D 2, [i] :

The second measure approximating E(dr[i], w)

E, E w :

The expectation

j [i] :

The job processed in the ith position for a jobs’ sequence

J :

A set of jobs, J = j1, …, ji, …, jn

n :

The number of jobs

N [i],w :

The number of breakdowns when processing j[i] in the scenario w

p [i] :

The processing time of the job ji

p [i] :

The processing time of j[i]

P r [j] :

The probability of breakdowns when processing the job j[j]

t p :

The maintenance time of PM

t r :

The maintenance time of minimal repair

t a [i] :

The machine’s age immediately after j[i]

t b [i] :

The machine’s age immediately before j[i]

t e [j] :

The expected breakdown time during j[j] when the breakdown occurs in j[j]

w :

The symbol indicating the scenario of breakdowns

x [i] :

The index of job j[i]

X :

The jobs’ sequence

y [i] :

The PM variable immediately before j[i]

Y :

The PMs’ position list

β :

The shape parameter of Weibull distribution

θ :

The scale parameter of Weibull distribution

ρ 1 :

The weight of the solution robustness

ρ 2 :

The weight of the quality robustness

τ i :

The planned start time of ji

τ [i],w :

The planned start time of j[i]

τ r [i],w :

The real start time of j[i] in the scenario w

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Authors and Affiliations

  1. School of Management, Shanghai University, Shanghai, 200444, China

    Weiwei Cui  (崔维伟)

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  1. Weiwei Cui  (崔维伟)
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Correspondence to Weiwei Cui  (崔维伟).

Additional information

Foundation item: the National Natural Science Foundation of China (No. 71801147), and the Shanghai Pujiang Program

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Cui, W. Approximate Approach to Deal with the Uncertainty in Integrated Production Scheduling and Maintenance Planning. J. Shanghai Jiaotong Univ. (Sci.) 25, 106–117 (2020). https://doi.org/10.1007/s12204-019-2086-2

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  • DOI: https://doi.org/10.1007/s12204-019-2086-2

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