عنوان مقاله [English]
In this paper, minimizing the number of tardy jobs in two-machine flowshop scheduling with deteriorating jobs and release times is discussed. In most of basic scheduling problems, the processing time of the jobs is assumed to be constant. This assumption is true in some cases, but because machines and tools depreciate and their efficiency reduces during time, this assumption cannot be true in all cases. In addition, in some industries like steel industry, jobs delay for process results in longer processing time. These kinds of jobs are introduced as deteriorating jobs, so a job is deteriorating whenever its processing time is not constant and is dependent on scheduled jobs. In this thesis, scheduling problems with deteriorating jobs are studied. A general classification of these problems is presented and literature review is studied. Then, flowshop scheduling with deteriorating jobs is discussed, and minimizing the number of tardy jobs is assumed as objective function. It is proven that the complexity of the problem is NP-hard. Therefore, a heuristic algorithm is proposed to achieve near optimum solution in a short time. Besides, an exact branch and bound algorithm, along with utilizing heuristic algorithm as upper bound, was proposed to achieve an optimal solution. Computational results demonstrate that branch and bound method solves problems with 24 jobs in the set High and 22 jobs in the set Low in a reasonable time. Results show that a high percentage of nodes are fathomed by lower bounds and dominance rules that shows the capability of the branch and bound algorithm. Also, it is shown that the average ratio of optimal solution to the heuristic one is at most 1.15 which is smaller in contrast with other studies in the related field in the literature. Finally, according to the efficiency of the presented approach, sample problems with large dimensions are generated and solved and their results are displayed.