کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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475828 | 699381 | 2012 | 19 صفحه PDF | دانلود رایگان |
We consider an uncertain single-machine scheduling problem, in which the processing time of a job can take any real value on a given closed interval. The criterion is to minimize the total weighted flow time of the n jobs, where there is a weight associated with a job. We calculate a number of minimal dominant sets of the job permutations (a minimal dominant set contains at least one optimal permutation for each possible scenario). We introduce a new stability measure of a job permutation (a stability box) and derive an exact formula for the stability box, which runs in O(n log n) time. We investigate properties of a stability box. These properties allow us to develop an O(n2)-algorithm for constructing a permutation with the largest volume of a stability box. If several permutations have the largest volume of a stability box, the developed algorithm selects one of them due to a simple heuristic. The efficiency of the constructed permutation is demonstrated on a large set of randomly generated instances with 10≤n≤100010≤n≤1000.
Journal: Computers & Operations Research - Volume 39, Issue 6, June 2012, Pages 1271–1289