Branch and Bound Algorithm for Parallel Machine Scheduling with Availability and Eligibility Constraints

• Main Authors: Cheng-Feng Lin, 林正峰
• Other Authors: Gwo-Ji Sheen
• Format: Others
• Language: en_US
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/34841091325039999118

碩士 === 國立中央大學 === 工業管理研究所 === 94 === In this paper we consider the problem of scheduling n non-preemptive jobs on m identical machines with machine availability and eligibility constraints when minimizing the maximum lateness. Each machine is not always available for processing and each job is only allowed to be processed on specific machines. Each job and availability interval of machines has a specific service level. Each job has to be processed at availability interval with the service level specified or higher one. We propose a branch and bound algorithm to find out the optimal solution of this problem. Firstly, network flow technique is used to formulate the scheduling problem of the preemptive jobs into a series of maximum flow problems. Then, we propose an algorithm which combines a network flow technique and a binary search procedure to find an optimal solution for the problem and use this result as our lower bound. Finally, we propose five dominance rules to increase the efficiency of the branch and bound algorithm. Computational analysis shows that the effectiveness of eliminating rules proposed is powerful and very low percentage of nodes is generated by the branch and bound algorithm. Our algorithm can get the optimal solution for the problem with up to 20 jobs and 7 machines.