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

https://doi.org/10.1016/j.orl.2007.11.004Get rights and content

Abstract

In this paper we discuss a minmax regret version of the single-machine scheduling problem with the total flow time criterion. Uncertain processing times are modeled by closed intervals. We show that if the deterministic problem is polynomially solvable, then its minmax regret version is approximable within 2.

Section snippets

Preliminaries

We are given a set of jobs J={J1,,Jn} to be processed on a single machine. For the sake of simplicity, we will identify every job Ji with its index i. A schedule is a permutation π=(π(1),,π(n)) of jobs. The set of jobs may be partially ordered by some precedence constraints, namely if ij, then job j must be processed after job i. A schedule π is feasible if it satisfies all the precedence constraints. We denote by Π the set of all feasible schedules. Consider the case in which the processing

The main result

Let us denote by iπ the position occupying by job i in schedule π. For any two schedules π, σ and scenario SΓ the following equality is true: F(π,S)F(σ,S)=iJ(iσiπ)piS. Using (2) and the definition of the maximal regret (1) one can easily prove that for any two feasible schedules π and σ the following inequality holds: Z(π){i:iσ>iπ}(iσiπ)p¯i+{i:iσ<iπ}(iσiπ)p¯i. We now show that any feasible schedules π and σ satisfy the inequality: Z(σ)Z(π)+{i:iπ>iσ}(iπiσ)p¯i+{i:iπ<iσ}(iπiσ)p¯i.

References (9)

There are more references available in the full text version of this article.

Cited by (0)

View full text