New Properties for Solving the Single- Machine Scheduling Problem with Early/Tardy Jobs
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Date
2016-07-12
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Université de M'sila
Abstract
This paper presents a mathematically enhanced genetic algorithm (MEGA) using the mathematical
properties of the single-machine scheduling of multiple jobs with a common due date. The objective of the
problem is to minimize the sum of earliness and tardiness penalty costs in order to encourage the completion
time of each job as close as possible to the common due date. The importance of the problem is derived from
its NP-hardness and its ideal modeling of just-in-time concept. This philosophy becomes very significant in
modern manufacturing and service systems, where policy makers emphasize that a job should be completed
as close as possible to its due date. That is to avoid inventory costs and loss of customer’s goodwill. Five mathematical
properties are identified and integrated into a genetic algorithm search process to avoid premature
convergence, reduce computational effort, and produce high-quality solutions. The computational results
demonstrate the significant impact of the introduced properties on the efficiency and effectiveness of MEGA
and its competitiveness to state-of-the-art approaches.
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Keywords
Genetic algorithm, single machine scheduling, early/tardy jobs, common due date, mathematical properties.