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
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
Minimizing total weighted flow time under uncertainty using dominance and a stability box
Computers and Operations Research
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We consider a single-machine scheduling problem with each job having an uncertain processing time which can take any real value within each corresponding closed interval before completing the job. The scheduling objective is to minimize the total weighted flow time of all n jobs, where there is a weight associated with each job. We establish the necessary and sufficient condition for the existence of a job permutation which remains optimal for any possible realizations of these n uncertain processing times. We also establish the necessary and sufficient condition for another extreme case that for each of the n! job permutations there exists a possible realization of the uncertain processing times that this permutation is uniquely optimal. Testing each of the conditions takes polynomial time in terms of the number n of jobs. We develop precedence-dominance relations among the n jobs in dealing with the general case of this uncertain scheduling problem. In case there exist no precedence-dominance relations among a subset of n jobs, a heuristic procedure to minimize the maximal absolute or relative regret is used for sequencing such a job subset. Computational experiments for randomly generated instances with n jobs (5@?n@?1000) show that the established precedence-dominance relations are quite useful in reducing the total weighted flow time.