Abstract

In this paper we give a survey of the most important results on multicriteria scheduling that have appeared in the literature or are to appear. We provide an extensive introduction including two example problems and then discuss the relevant literature. Here we pay special attention to the area of earliness-tardiness scheduling, scheduling with controllable processing times, simultaneous approximation, and new models.

Keywords: Machine scheduling; Multicriteria; Pareto optimal; Earliness-tardiness; Controllable processing times; Simultaneous approximation

Article Outline

1. Introduction

2. Basic concepts and notation

2.1. Basic scheduling concepts

2.2. Basic concepts of multicriteria scheduling

3. Two example problems

3.1. The 1F(L_max,∑_jC_j) problem

3.2. Producing glass bottles

4. Earliness–tardiness scheduling

4.1. General due dates

4.1.1. Minimizing maximum earliness and maximum tardiness

4.1.2. Minimizing a function of total earliness and total tardiness

4.1.2.1. Finding the optimal starting times

4.1.2.2. Finding the optimal sequence of jobs

4.2. Common due date scheduling

4.2.1. Equal job weights, d large

4.2.2.Individual job weights, d large

4.2.3. Results for a small common due date

5. Controllable processing times

5.1. Other models

6. Other single-machine bicriteria results

6.1. Lexicografical optimization

6.2. Minimizing a linear composite objective function

6.3. Minimizing a general composite objective function

7. Results for multiple machines

7.1. Parallel machine scheduling

7.2. Shop models

7.2.1. The flow shop

7.2.2. The open shop

8. Simultaneous bicriteria approximation

9. New developments

9.1. Interfering job sets

9.2. Scheduling with rejection

9.3. Rescheduling for new orders

Acknowledgements

References