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

• Main Authors: Yi-hsiang Lai, 賴以翔
• Other Authors: 沈國基
• Format: Others
• Language: en_US
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/55577676941553418505

碩士 === 國立中央大學 === 工業管理研究所 === 95 === In this paper we consider the problem of scheduling n non-preemptive jobs on m identical machines with machine availability, eligibility and incompatible job constraints when minimizing the maximum lateness. Each machine is not continuously available at all time and each job is only allowed to be processed on specific machines. Each job has to be processed at an availability interval with the same service level or higher. Some job belongs to a family and only jobs from different family may be processed in the same availability interval. We propose a branch and bound algorithm to find out the optimal solution. Firstly, we propose an algorithm which bases on the Most Remaining Jobs Family First/Earliest Due Date First (MJF/EDD) rule to find an upper bound. Then, we use a network flow technique to model the scheduling problem with the job preemption into a series of maximum flow problems. We propose an algorithm which extends from the work of Lin (2006). Our algorithm combines a network flow technique and a binary search procedure to find an optimal solution for the scheduling problem with the job preemption and use the result as the lower bound. Finally, we use four dominance rules to increase the efficiency of the branch and bound algorithm. Computational analysis shows that eliminating rules proposed is effective and very low percentage of nodes is generated by the branch and bound algorithm. Among those eliminating rules, we find the percentage of nodes eliminated by job incompatible restriction increases as the probability in generating jobs with a family type increases or number of families decreases. Our algorithm can get the optimal solution for the problem with up to 15 jobs, 7 machines and 3 families.