Lorenz versus Pareto dominance in a single machine scheduling problem with rejection

Abstract

Scheduling problems have been studied from many years ago. Most of the papers which were published in this domain are different in one or many of issues as following: objective functions, machine environment, constraints and methodology for solving the problems. In this paper we address the problem of single machine scheduling in which due to some constraints like capacity, rejection of a set of jobs is accepted. The problem is considered as bi-objective one: minimization of the sum of weighted completion times for the accepted jobs and minimization of the sum of penalties for the rejected jobs. We find that in this problem, the solutions are not handled in a satisfactory way by general Pareto-dominance rule, so we suggest the application of Lorenz-dominance to an adapted bi-objective simulated annealing algorithm. Finally we justify the use of Lorenz-dominance as a useful refinement of Pareto-dominance by comparing the results. © 2011 Springer-Verlag.