Scheduling jobs with variable job processing times on unrelated parallel machines.

Guang-Qian Zhang,Ya-Jing Liu,Jian-Jun Wang

doi:10.1155/2014/242107

Guang-Qian Zhang, Ya-Jing Liu + Show 1 more

Open Access

https://doi.org/10.1155/2014/242107

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Journal: TheScientificWorldJournal	Publication Date: Jan 1, 2014
Citations: 28	License type: CC BY 3.0

Affiliation: Dalian University of Technology

Abstract

m unrelated parallel machines scheduling problems with variable job processing times are considered, where the processing time of a job is a function of its position in a sequence, its starting time, and its resource allocation. The objective is to determine the optimal resource allocation and the optimal schedule to minimize a total cost function that dependents on the total completion (waiting) time, the total machine load, the total absolute differences in completion (waiting) times on all machines, and total resource cost. If the number of machines is a given constant number, we propose a polynomial time algorithm to solve the problem.

Highlights

In classical scheduling theory, it is assumed that the job processing times are fixed and constant values
This paper extends the single machine scheduling results of Wang et al [19], by considering unrelated parallel machine scheduling problems that include the one given in Wang et al [19] as a special case
We have studied the problem of scheduling n jobs on m unrelated parallel machines with simultaneous consideration of learning effect, deteriorating jobs, and controllable processing times

Summary

Introduction

It is assumed that the job processing times are fixed and constant values. More recent papers that have considered scheduling problems with deterioration effects and/or learning effects and/or controllable processing times include Bai et al [6, 7], Cheng et al [8], Gorczyca and Janiak [9], Hsu and Yang [10], Huang and Wang [11], Lee et al [12], Leyvand et al [13], Nian and Mao [14], Shabtay and Steiner [15], Wang et al [16], J. Shabtay and Steiner [15] considered single machine scheduling with the resource allocation model in which the job processing times are pj = aj − βjuj,. Wang et al [19] considered single machine scheduling problem with effect of deterioration, learning, and resource allocation simultaneously.

Problem Formulation

Conclusions