Approximation Algorithm for Scheduling Parallel Machines with Machine Eligibility Restrictions and special jobs
DOI: 10.23977/jemm.2016.11005 | Downloads: 61 | Views: 4712
Zhan Yong 1, Zhong Yuguang 1
1 College of Mechanical and Electrical, Harbin Engineering University, Harbin, 150001, China
Corresponding AuthorZhan Yong
This paper addresses the scheduling problem of parallel machines with machine eligibility restrictions and special jobs with the objective of minimizing the makespan. Each job can only be assigned to a specific subset of the machines. And the processing times of jobs are restricted to one of two values, 1 andε. A semi-matching model G=[J∪M,E,W] is presented to formulate this scheduling problem. We propose an approximation algorithm, which is composed of two steps, that is, initial solution construction and initial solution improvement. The initial solution construction algorithm is developed to build a feasible solution by performing a simple greedy heuristic method. The initial solution is used as a starting point by the improvement algorithm. The main idea of the improvement algorithm is to construct alternating tree, then to find the optimal alternating path for each vertex in M iteratively. In order to improve efficiency, the length of each path in alternating tree is limited to 4 at most.
KEYWORDSparallel machine, machine eligibility restrictions, approximation algorithm
CITE THIS PAPER
Yong, Z. and Yuguang, Z. (2016) Approximation Algorithm for Scheduling Parallel Machines with Machine Eligibility Restrictions and special jobs. Journal of Engineering Mechanics and Machinery (2016) 1: 28-33.
 PURUSHOTHAMAN D, MARIO C V: Expert Systems with Applications Vol. 39(1) (2012), p.1451
 WANG W L, WANG H Y, ZHAO Y W , ZHANG L P, XU X L: Computers & Operations Research Vol.40(5) (2013), p.1196
 TAN Z Y, CHEN Y, ZHANG A: International Journal of Production Economics Vol.146(1) (2013), p.293
 LIU M, ZHENG F F, WANG S J, XU Y F: Theoretical Computer Science Vol.497(29) (2013), p.108
 LOW C P: Information Processing LettersVol.100(4) (2006), p.154
 DORATHA E D, STEFAN H: Lecture Notes in Computer Science Vol.2647 (2003), p.107.