A 2-approximation algorithm for interval data minmax regret sequencing problems with the total flow time criterion
Section snippets
Preliminaries
We are given a set of jobs to be processed on a single machine. For the sake of simplicity, we will identify every job with its index . A schedule is a permutation of jobs. The set of jobs may be partially ordered by some precedence constraints, namely if , then job must be processed after job . A schedule is feasible if it satisfies all the precedence constraints. We denote by the set of all feasible schedules. Consider the case in which the processing
The main result
Let us denote by the position occupying by job in schedule . For any two schedules , and scenario the following equality is true: Using (2) and the definition of the maximal regret (1) one can easily prove that for any two feasible schedules and the following inequality holds: We now show that any feasible schedules and satisfy the inequality:
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