Complexity of minimizing the total flow time with interval data and minmax regret criterion
Discrete Applied Mathematics - Special issue: International symposium on combinatorial optimization CO'02
Scheduling for stability in single-machine production systems
Journal of Scheduling
Schedule execution for two-machine flow-shop with interval processing times
Mathematical and Computer Modelling: An International Journal
Minimizing total weighted flow time of a set of jobs with interval processing times
Mathematical and Computer Modelling: An International Journal
Optimal makespan scheduling with given bounds of processing times
Mathematical and Computer Modelling: An International Journal
Minmax regret solutions for minimax optimization problems with uncertainty
Operations Research Letters
The complexity of machine scheduling for stability with a single disrupted job
Operations Research Letters
Minimizing maximal regret in the single machine sequencing problem with maximum lateness criterion
Operations Research Letters
Minimizing total weighted completion time with uncertain data: A stability approach
Automation and Remote Control
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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(n^2)-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@?1000.