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Scheduling reclaimers serving a stock pad at a coal terminal

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Abstract

We study a variant of an abstract scheduling problem inspired by the management of reclaimers in the stockyard of a coal export terminal. We prove NP-completeness of the problem and formulate it as a mixed-integer program. We show that for a given reclaiming sequence, the problem can be solved in pseudo-polynomial time. In addition, we provide simple, constant-factor approximation algorithms as well as exact branch-and-bound algorithms. An extensive computational study analyzes the performance of the algorithms.

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Author information

Authors and Affiliations

  1. University of Newcastle, Newcastle, Australia

    Thomas Kalinowski & Reena Kapoor

  2. Georgia Institute of Technology, Atlanta, USA

    Martin W. P. Savelsbergh

Authors
  1. Thomas Kalinowski
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  2. Reena Kapoor
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  3. Martin W. P. Savelsbergh
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Corresponding author

Correspondence to Thomas Kalinowski.

Appendix: Computational results with \(s = 5\)

Appendix: Computational results with \(s = 5\)

1.1 Exact solution

The results can be found in Tables 4 and 5, in which we report the number of instances solved to optimality, the solution times, and the number of nodes explored.

Table 4 Solve time in seconds with a time limit of 3600 s
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Table 5 Number of nodes explored with a time limit of 3600 s
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Figures 9 and 10 compare the runtime of CPLEX, BB1, and BB2 for instances in Class 1 and Class 2, respectively.

Fig. 9
figure 9

Percentage of Class 1 instances solved within a given time

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Fig. 10
figure 10

Percentage of Class 2 instances solved within a given time

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1.2 Approximation algorithms

As in Sect. 8.3, we compare the objective function value of the solutions they produce to the value of the objective function of the best solution produced by BB1 in 3600 s. The results can be found in Figs. 11 and 12, where we plot the fraction of instances with a relative gap less than or equal to x, i.e., \((z(\mathbf BB1 ) - z(A))/z(\mathbf BB1 ) \leqslant x\). We also analyze the performance of the three algorithms by comparing them against each other. More specifically, we compare the objective function value of the solutions they produce to \(z(\mathbf best )\), the value of the objective function of the best solution produced for the instance by any of the three algorithms. We plot the fraction of instances with a relative gap less than or equal to x, i.e., \((z(\mathbf best ) - z(A))/z(\mathbf best ) \leqslant x\), in Figs. 13 and 14.

Fig. 11
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Performance of the three approximation algorithms relative to BB1 (Class 1 instances)

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Fig. 12
figure 12

Performance of the three approximation algorithms relative to BB1 (Class 2 instances)

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Fig. 13
figure 13

Comparison of the three approximation algorithms (Class 1 instances)

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Fig. 14
figure 14

Comparison of the three approximation algorithms (Class 2 instances)

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Kalinowski, T., Kapoor, R. & Savelsbergh, M.W.P. Scheduling reclaimers serving a stock pad at a coal terminal. J Sched 20, 85–101 (2017). https://doi.org/10.1007/s10951-016-0495-8

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  • DOI: https://doi.org/10.1007/s10951-016-0495-8

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