2015 A note on single-machine scheduling with sum-of-processing-time-based learning and forgetting effects

Research Overview

This research note investigates single-machine scheduling problems where both learning and forgetting effects are present, with a novel model based on sum-of-processing-time rather than traditional position-based approaches. The proposed model includes several existing models as special cases, providing a comprehensive framework for scheduling optimization.

Key Contributions

Theoretical Framework:

• Develops a sum-of-processing-time-based model for learning and forgetting effects that generalizes existing approaches
• Provides mathematical formulations that capture realistic learning and forgetting patterns in manufacturing environments
• Establishes the theoretical foundation for optimal scheduling under dual learning-forgetting dynamics

Optimal Solutions:

• Derives optimal solutions for various single-machine scheduling problems under the proposed model
• Addresses multiple objective functions including:
  • Makespan minimization
  • Total completion time optimization
  • Total weighted completion time minimization
  • Total tardiness reduction
  • Maximum lateness minimization

Mathematical Analysis:

• Provides several helpful lemmas to prove optimality conditions for different objective functions
• Demonstrates the computational tractability of the proposed model
• Shows how the sum-of-processing-time approach offers more realistic modeling of human learning behavior

Impact and Significance

Published in Applied Mathematical Modelling (Volume 39, Issue 2, Pages 415-424), this work extends the theoretical understanding of scheduling problems with human factor considerations. The sum-of-processing-time-based approach provides a more realistic representation of how workers learn and forget in industrial settings compared to position-based models.

The collaborative research with Chia-Huang Wu and Wen-Chiung Lee demonstrates the importance of incorporating both learning and forgetting effects in scheduling theory, contributing to more accurate production planning and workforce management strategies.

Recommended citation: Chia-Huang Wu, Peng-Jen Lai and Wen-Chiung Lee. (2015). "A note on single-machine scheduling with sum-of-processing-time-based learning and forgetting effects." Applied Mathematical Modelling. Volume 39, Issue 2, Pages 415-424.
Download Paper