- Published 2003

Lower bounds are typically used to evaluate the performance of heuristics for solving combinatorial minimization problems. In the absence of tight analytical lower bounds, optimal objective-function values may be estimated statistically. In this paper, extreme value theory is used to construct confidence-interval estimates of the minimum makespan achievable when scheduling nonsimilar groups of jobs on a two-stage flow line. Experimental results based on randomly sampled solutions to each of 180 randomly generated test problems revealed that (i) least-squares parameter estimators outperformed standard analytical estimators for the Weibull approximation to the distribution of the sample minimum makespan; (ii) to evaluate each Weibull fit reliably, both the Anderson-Darling and Kolmogorov-Smirnov goodness-of-fit tests should be used; and (iii) applying a local improvement procedure to a large sample of randomly generated initial solutions improved the probability that the resulting Weibull fit yielded a confidence interval covering the minimum makespan.

Showing 1-10 of 27 references

Highly Influential

7 Excerpts

Highly Influential

9 Excerpts

Highly Influential

5 Excerpts

Highly Influential

4 Excerpts

Highly Influential

5 Excerpts

Highly Influential

14 Excerpts

Highly Influential

5 Excerpts

Highly Influential

6 Excerpts

Highly Influential

4 Excerpts

Highly Influential

3 Excerpts

@inproceedings{Wilson2003ToAE,
title={To appear, European Journal of Operational Research. Case Study on Statistically Estimating Minimum Makespan for Flow Line Scheduling Problems},
author={Amy D. Wilson and Russell E. King and James R. Wilson},
year={2003}
}