Two-Machine No-wait Total Tardiness Flowshop Scheduling Problem

• Main Authors: Sheng-Fa Yang, 楊盛發
• Other Authors: Ching-Fang Liaw
• Format: Others
• Language: zh-TW
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/ugkp89

碩士 === 朝陽科技大學 === 工業工程與管理系碩士班 === 94 === Abstract The flowshop scheduling problem can be stated as follows. There are n independent jobs and m different machines. There is a common restriction on the order in which the operations of a job are to be performed. Each machine can process at most one job at a time and each job can be processed on one machine at a time. Flowshop scheduling is often encountered in mass production systems. Scheduling problems with no-wait constraints occur in many industries. For instance, in hot metal rolling industries , where the heated metal has to undergo a series of operations at continuously high temperatures before it is cooled in order to prevent defects. Similarly , in the plastic molding and silverware production industries, a series of operations must be performed to immediately follow one another to prevent degradation. We consider the performance measure of total tardinesss in a two-machine no-wait flow shop environment. In our research, we present a heuristic solution method for solving large-scaled problems. We also develop a branch and bound algorithm. We use an upper bound based on the heuristic algorithm developed, and propose some dominance rules to help pruning unpromising nodes in the branch-and-bound search tree. Finally, computational experiments are conducted to evaluate the performances of the proposed algorithms. As the result, branch-and-bound algorithm can only solve to the optimum solution small-scaled problems. When the number of jobs equals to 25, the average error of heuristic solution is 6%. The average error of lower bound is about 11%. The developed dominance rules help reducing 16%~20% nodes in the branch-and-bound search tree. Besides, our research examines two special cases of bottleneck-machine. It is showed that both heuristic solution and lower bound coincide with the optimum solution in great majority problems with bottleneck-machine. Therefore, problems with bottleneck-machine become easier to solve.