| Summary: | 碩士 === 國立中央大學 === 工業管理研究所 === 100 === We consider the job shop scheduling problem with minimum and maximum time lags while minimizing the makespan. This problem is common in a manufacturing environment where the next job has to be carried out within a specific time range after the completion of the immediately preceding job. Each operation in job shop system must be waiting for the lower bound of waiting time but do not exceed the upper bound of waiting time to perform the next operation. Besides, minimum and maximum time lags constraints on the starting time of each operation are also considered.
We describe a branch and bound algorithm, based on the input and output of a clique and relevant propositions, for finding the optimal waiting times. There are n jobs have to be processed on m machines in order to minimize makespan. We incorporate the concept of head and tail which proposed from Carlier and Pinson (1989) and the branch and bound algorithm proposed by Sheen and Liao (2007) to solve the job-shop scheduling with minimum and maximum time lags problem. With the proposed branch and bound algorithm, we can either find an optimal schedule or establish the infeasibility within an acceptable run time.
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