Note on a Single-Machine Scheduling Problem with Sum of Processing Times Based Learning and Ready Times

Shang-Chia Liu,Chin-Chia Wu,Wei-Ling Hung

doi:10.1155/2015/452602

Shang-Chia Liu, Chin-Chia Wu + Show 1 more

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https://doi.org/10.1155/2015/452602

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Abstract

In the recent 20 years, scheduling with learning effect has received considerable attention. However, considering the learning effect along with release time is limited. In light of these observations, in this paper, we investigate a single-machine problem with sum of processing times based learning and ready times where the objective is to minimize the makespan. For solving this problem, we build a branch-and-bound algorithm and a heuristic algorithm for the optimal solution and near-optimal solution, respectively. The computational experiments indicate that the branch-and-bound algorithm can perform well the problem instances up to 24 jobs in terms of CPU time and node numbers, and the average error percentage of the proposed heuristic algorithm is less than 0.5%.

Highlights

In the classical scheduling models, most researchers consider that the job processing times are all constant numbers
Following Reeves [40] setting, we generated the job processing time from a uniform distribution U(1, 20) and generated job ready times from another uniform distribution U(0, 20nλ), where λ is taken as the values 1/n, 0.25, 0.5, 0.75, and 1
We reported the mean and the maximum error percentages

Summary

Introduction

In the classical scheduling models, most researchers consider that the job processing times are all constant numbers It can be seen in many real situations that a production time can be shortened if it is operated later due to the fact that the efficiency of the production facility (e.g., a machine or a worker) continuously improves with time. This situation is named as the “learning effect” in the research community [1, 2]. For more recent problems with time-dependent processing times on single-machine settings, we refer readers to Cheng et al [4], Eren and Guner [5, 6], Eren [7], Janaik and Rudek [8], Toksarı et al [9], Toksari and Guner [10], Wang and Liu [11], Wang et al [12], Yin et al [13], Yin et al [14,15,16,17], Wu et al [18,19,20], Wang et al [21,22,23], Bai et al [24], VahediNouri et al [25], Lu et al [26], and so forth

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