Optimizing waiting measures in flow-shops

Melinda Dalrymple McGurer, University of Rhode Island


The Wait Between Machines Flow-shop n:m: F:W BM and its permutation variant n: m:P:W BM are defined and proven to be non-regular and strongly NP-complete for m ≥ 3. The computational complexity of the two-machine problems is undetermined although it is suspected that they are NP-hard. The permutation variants 7:2:P:W BM and 20:20:P:W BM were selected for computational analysis. Seventeen data sets of one hundred problems each were created for each variant using discrete Uniform distributions to generate random, independent, constant processing times. ^ The existing heuristics of Nawaz, Enscore, and Ham [1] and Rajendran and Ziegler [2] were programmed to solve the WBM flow-shop problem. Two new heuristics, WBMn and WBMr, were developed by creating a new WBM starting sequence to work with the existing insertion procedures of NEH and RZ. An exhaustive search to find the optimal solution was also employed for the m2 n7 problem. The solution methods were also applied to the makespan, minsum, idle between, and total idle optimization functions. ^ A regression analysis conducted on the m2n7 WBM problem revealed, in individual 95% confidence tests, that the mean and standard deviation of the absolute heuristic error linearly increase as the processing time range increases. According to these measures with 90% combined confidence, the performance of NEH degrades faster than that of RZ as the processing time range increases. ^ For each optimization function, it is concluded with 95% confidence that all heuristics do not perform the same. In most cases, the RZ heuristic variants provide better results than the NEH variants. Individually, thirty of the thirty-six pairwise comparisons between NEH variants and RZ variants statistically concluded with 99% confidence that the RZ variant provided better results. The results of the WBM heuristic variants in comparison to their respective original heuristics are mixed and generally not statistically significant. ^ Of particular note is that the RZ heuristic, designed for the minsum problem, performs better for makespan than NEH which has long been touted as the best constructive heuristic for makespan since it was published in 1983 [1,3–5]. ^

Subject Area

Engineering, Industrial|Operations Research

Recommended Citation

Melinda Dalrymple McGurer, "Optimizing waiting measures in flow-shops" (2007). Dissertations and Master's Theses (Campus Access). Paper AAI3276996.