دانلود رایگان مقاله برنامه ریزی موازی ماشین بدتر شدن کارها با اختلالات ماشین

abstract

We consider parallel-machine scheduling of deteriorating jobs in a disruptive environment in which some of the machines will become unavailable due to potential disruptions. This means that a disruption to some of the machines may occur at a particular time, which will last for a period of time with a certain probability. If a job is disrupted during processing by a disrupted machine and it does not need (needs) to re-start after the machine becomes available again, it is called the resumable (non-resumable) case. By deteriorating jobs, we mean that the actual processing time of a job grows when it is scheduled for processing later because the machine efficiency deteriorates over time due to machine usage and aging. However, a repaired machine will return to its original state of efficiency. We consider two cases, namely performing maintenance immediately on the disrupted machine when a disruption occurs and not performing machine maintenance. In each case, the objective is to determine the optimal schedule to minimize the expected total completion time of the jobs in both non-resumable and resumable cases. We determine the computational complexity status of various cases of the problem, and provide pseudopolynomial-time solution algorithms and fully polynomial-time approximation schemes for them, if viable.

6. Conclusions

This paper addresses parallel-machine scheduling of deteriorating jobs with potential machine disruptions. In such a case, the job processing times will deteriorate over time and some of the machines may become unavailable for some periods of time due to the potential machine disruptions. The disruption starting time is often known (should it happen) in advance, yet the disruption duration that will last for a certain duration with a certain probability is unknown until it happens. We consider the cases of performing maintenance immediately on the disrupted machines when a disruption occurs and not performing machine maintenance, where performing machine maintenance will improve the efficiency of a machine, making it return to its original state of efficiency. In each case, the objective is to find an optimal schedule to minimize the expected total completion time of the jobs for both the non-resumable and resumable cases. We summarize the major results of this paper in Table 1. It is worth noting that performing maintenance on the disrupted machines when a disruption occurs will decrease the expected total completion time of the jobs at the expense of the maintenance cost. When this cost is included in the objective function, it is not difficult to make a decision whether or not to perform machine maintenance immediately on the disrupted machines when a disruption occurs by using our algorithms.