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An Exact Algorithm for the Single-Machine Earliness–Tardiness Scheduling Problem

  • Shunji TanakaEmail author
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 60)

Abstract

This paper introduces our exact algorithm for the single-machine total weighted earliness–tardiness scheduling problem, which is based on the Successive Sublimation Dynamic Programming (SSDP) method. This algorithm starts from a Lagrangian relaxation of the original problem and then constraints are successively added to it until the gap between lower and upper bounds becomes zero. The relaxations are solved by dynamic programming, and unnecessary dynamic programming states are eliminated in the course of the algorithm to suppress the increase of states caused by the addition of constraints. This paper explains the methods employed in our algorithm to construct the Lagrangian relaxations, to eliminate states and to compute an upper bound together with some other improvements. Then, numerical results for known benchmark instances are given to show the effectiveness of our algorithm.

Notes

Acknowledgements

This work is partially supported by Grant-in-Aid for Young Scientists (B) 19760273, from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) Japan.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Electrical EngineeringKyoto UniversityNishikyo-kuJapan

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