Parallel Machine Scheduling with Machine Availability,Eligibility and Job Incompatible Constraints

• Main Authors: Hao-chun Hsu, 徐豪駿
• Other Authors: Gwo-ji Sheen
• Format: Others
• Language: en_US
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/24082829472579173289

碩士 === 國立中央大學 === 工業管理研究所 === 100 === In this paper we consider the problem of scheduling n preemptive jobs on m identical machines with machine availability, eligibility and incompatible job constraints when minimizing the maximum makespan. Each machine is not continuously available for processing at all time and each job is only allowed to be processed on specific machines. In the same availability interval, each job belongs to a family and only jobs from different family can be processed. Firstly, we use a network flow technique to model the scheduling problem with the job preemption into a series of maximum flow problems. Secondly, we propose an algorithm which bases on the Family With Most Job Remaining Processing Time First /Earliest Release Date First (FRPF/ERD) rule to find an upper bound. Thirdly, we use a branch and bound algorithm to deal with incompatible constraint of our problem and use six dominance rules to increase the efficiency of the branch and bound algorithm. Finally, we modify an algorithm proposed by Liao and Sheen (2008). This algorithm includes a network flow technique and a binary search procedure to find an optimal solution for the scheduling problem. Computational analysis shows that eliminating rules are effective. The percentage of nodes generated by the branch and bound algorithm is low. More than half of nodes eliminated are attributed to Proposition 5, which will become more effective when n and m increase.