### 2010-17

**Measures of Problem Uncertainty for Total Weighted Flow Time Scheduling on a Single Machine**

by Sotskov, Y.N.; Werner, F.; Lai, T.-C.; Egorova, N.G..

**Series:** 2010-17, Preprints

- MSC:
- 90B35 Scheduling theory, deterministic
- 49K40 Sensitivity, stability, well-posedness

**Abstract:**

A single-machine scheduling problem is investigated under the assumption that the processing time of a job can take any real value from a given closed interval. The criterion is to minimize the total weighted completion time for a set of given jobs. As a measure of uncertainty for such a scheduling problem, it is reasonable to consider the cardinality of a minimal dominant set of job permutations containing an optimal permutation for each possible realization of the job processing times. We show that a minimal dominant set may be uniquely determined and demonstrate how to select a suitable solution method for the individual problem using the value of an uncertainty measure.

**Keywords:**

Single-machine scheduling; Total weighted flow time; Uncertain processing times; Measure of uncertainty