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

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 dyna...

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Bibliographic Details
Published in:Journal of Scheduling Vol. 12; no. 6; pp. 575 - 593
Main Authors: Tanaka, Shunji, Fujikuma, Shuji, Araki, Mituhiko
Format: Journal Article
Language:English
Published: Boston Springer Science and Business Media LLC 01.12.2009
Springer US
Springer Nature B.V
Subjects:
Algorithms
Artificial Intelligence
Business and Management
Calculus of Variations and Optimal Control; Optimization
Dynamic programming
Experiments
Integer programming
Operations Research/Decision Theory
Optimization
Production scheduling
Scheduling
Studies
Supply Chain Management
Single-machine scheduling
Successive sublimation dynamic programming method
Time-indexed formulation
Exact algorithm
Lagrangian relaxation
ISSN:1094-6136, 1099-1425
Online Access:Get full text
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Summary: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.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:1094-6136
1099-1425
DOI:10.1007/s10951-008-0093-5