Pareto optima for total weighted completion time and maximum lateness on a single machine

Authors:
George Steiner;Paul Stephenson
Affiliations:
McMaster University, Hamilton, Ont., Canada L8S 4M4;Acadia University, Wolfville, N.S., Canada B4P 2R6
Venue:
Discrete Applied Mathematics
Year:
2007

Citing 7
Cited 2

An improved lower bound for minimizing weighted completion times with deadlines

Operations Research
Multi-objective genetic algorithm and its applications to flowshop scheduling

Computers and Industrial Engineering
Finding the Pareto-optima for the total and maximum tardiness single machine problem

Discrete Applied Mathematics - Workshop on discrete optimization DO'99, contributions to discrete optimization
An Exact Method to Minimize the Number of Tardy Jobs in Single Machine Scheduling

Journal of Scheduling
Multicriteria Scheduling: Theory, Models and Algorithms

Multicriteria Scheduling: Theory, Models and Algorithms
Minimizing total completion time and maximum cost simultaneously is solvable in polynomial time

Operations Research Letters
An improved branch and bound algorithm for single machine scheduling with deadlines to minimize total weighted completion time

Operations Research Letters

Two robust meta-heuristics for scheduling multiple job classes on a single machine with multiple criteria

Expert Systems with Applications: An International Journal
Scheduling jobs on a single batch processing machine with incompatible job families and weighted number of tardy jobs objective

Computers and Operations Research

Quantified Score

Hi-index	0.05

Visualization

Abstract

We consider the single-machine bicriterion scheduling problem of enumerating the Pareto-optimal sequences with respect to the total weighted completion time and the maximum lateness objectives. We show that the master sequence concept originally introduced for 1|r"j|@?w"jU"j by Dauzere-Peres and Sevaux is also applicable to our problem and a large number of other sequencing problems. Our unified development is based on exploiting common order-theoretic structures present in all these problems. We also show that the master sequence implies the existence of global dominance orders for these scheduling problems. These dominance results were incorporated into a new branch and bound algorithm, which was able to enumerate all the Pareto optima for over 90% of the 1440 randomly generated problems with up to n=50 jobs. The identification of each Pareto optimum implicitly requires the optimal solution of a strongly NP-hard problem. The instances solved had hundreds of these Pareto solutions and to the best of our knowledge, this is the first algorithm capable of completely enumerating all Pareto sequences within reasonable time and space for a scheduling problem with such a large number of Pareto optima.