Complexity of minimizing the total flow time with interval data and minmax regret criterion

Authors:
Vasilij Lebedev;Igor Averbakh
Affiliations:
Department of Mathematics, Volgograd State University, Volgograd, Russia;Division of Management, University of Toronto at Scarborough, Scarborough, Ont. Canada
Venue:
Discrete Applied Mathematics - Special issue: International symposium on combinatorial optimization CO'02
Year:
2006

Citing 4
Cited 7

Robust scheduling to hedge against processing time uncertainty in single-stage production

Management Science
Scheduling Algorithms

Scheduling Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
Sensitivity Analysis for Scheduling Problems

Journal of Scheduling

Improved polynomial algorithms for robust bottleneck problems with interval data

Computers and Operations Research
Scheduling with uncertainties on new computing platforms

Computational Optimization and Applications
Minimizing total weighted flow time under uncertainty using dominance and a stability box

Computers and Operations Research
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
A 2-approximation algorithm for interval data minmax regret sequencing problems with the total flow time criterion

Operations Research Letters
Computing and minimizing the relative regret in combinatorial optimization with interval data

Discrete Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider the minmax regret (robust) version of the problem of scheduling n jobs on a machine to minimize the total flow time, where the processing times of the jobs are uncertain and can take on any values from the corresponding intervals of uncertainty. We prove that the problem in NP-hard. For the case where all intervals of uncertainty have the same center, we show that the problem can be solved in O(n log n) time if the number of jobs is even, and is NP-hard if the number of jobs is odd. We study structural properties of the problem and discuss some polynomially solvable cases.