Bounding the Pareto set for a bicriteria single machine scheduling problem

Federico Della Croce (1) , Fabio Salassa (2) , Vincent t'Kindt (3)

1 DAUIN - Department of Computer Engineering
2 DAUIN - Dipartimento di Automatica e Informatica [Torino]
3 LIFAT - Laboratoire d'Informatique Fondamentale et Appliquée de Tours

Consider n jobs that have to be scheduled on a single machine without preemption. Each job i is defined by a processing time pi and a due date di. The aim is to determine a schedule which minimizes the total completion time, referred to as\sum_i Ci, and the maximum earliness, referred to as Emax. We denote by Ci the completion time of job i in a given schedule and by E_i its earliness, defined by E_i=\max(0;d_i-C_i). This bicriteria problem is NP-hard and can be referred to as 1|d_i|Emax,\sum_i Ci. We focus on the problem of approximating strict Pareto optima.

Domaines: Complexité [cs.CC]; Recherche opérationnelle [math.OC]

Federico Della Croce, Fabio Salassa, Vincent t'Kindt. Bounding the Pareto set for a bicriteria single machine scheduling problem. 10th International Conference on Multiple Objective Programming and Goal Programming, Jun 2012, Niagara Falls, Canada. ⟨hal-01025828⟩