本論文主要在探討具有最大時間區間與最小時間區間限制特性的零工式生產( job-shop)排程問題，此限制類型的問題常見於工業環境中，例如:半導體產業的蝕刻製程，化學產業的鍍鎳製程等等，當一工件從前一工作站完工後，需要等待一段時間才能進入至下一工作站進行加工，該工件都至少必須等待一定的最小時間，同時等待不能超過一定的最大時間，因此最小與最大等候時間區制須要考慮每個工件能開始加工的時間。針對此問題我們將發展一結合 Carlier and Pinson (1989)，Sheen and Liao (2007) and Pinedo (2008)提出的演算法，利用開始時間與最大最小完工時間的限制減少需要展開的時間與節點數量，並求得最佳解。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.
