An exact algorithm for single-machine scheduling without machine idle time

Authors:
Shunji Tanaka;Shuji Fujikuma;Mituhiko Araki
Affiliations:
Graduate School of Electrical Engineering, Kyoto University, Kyoto, Japan 615-8510;Graduate School of Electrical Engineering, Kyoto University, Kyoto, Japan 615-8510;Matsue College of Technology, Matsue City, Japan 690-8518
Venue:
Journal of Scheduling
Year:
2009

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Abstract

This study proposes an exact algorithm for the general single-machine scheduling problem without machine idle time to minimize the total job completion cost. Our algorithm is based on the Successive Sublimation Dynamic Programming (SSDP) method. Its major drawback is heavy memory usage to store dynamic programming states, although unnecessary states are eliminated in the course of the algorithm. To reduce both memory usage and computational efforts, several improvements to the previous algorithm based on the SSDP method are proposed. Numerical experiments show that our algorithm can optimally solve 300 jobs instances of the total weighted tardiness problem and the total weighted earliness-tardiness problem, and that it outperforms the previous algorithms specialized for these problems.