On Minimizing Average Weighted Completion Time A PTAS for the Job Shop Problem with Release Dates 1st edition by Aleksei Fishkin, Klaus Jansen, Monaldo Mastrolilli ISBN 3540206958 9783540206958

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ISBN 10:       3540206958
ISBN 13: 978-3540206958
Author:         Aleksei V. Fishkin, Klaus Jansen, Monaldo Mastrolilli 
 We consider the non-preemptive job shop scheduling problem with release dates and the average weighted completion time objective. We propose here a polynomial-time approximation scheme (PTAS) for the case when the number of machines is constant and each job consists of at most a constant number of operations. This substantially improves on previous results [4], adds to a number of techniques [1,2,6,10,22], and gives some answers to the questions mentioned in [20,23].

On Minimizing Average Weighted Completion Time A PTAS for the Job Shop Problem with Release Dates 1st Table of contents:

• Introduction

  • 1.1 Overview of the Job Shop Scheduling Problem
  • 1.2 The Problem with Release Dates
  • 1.3 Motivation for Minimizing Average Weighted Completion Time
  • 1.4 Importance of Polynomial Time Approximation Schemes (PTAS)
  • 1.5 Structure of the Paper

• Background and Related Work

  • 2.1 Classical Job Shop Problem: Definitions and Challenges
  • 2.2 Job Shop Problem with Release Dates: Generalized Models
  • 2.3 Scheduling Problems and the Weighted Completion Time Objective
  • 2.4 Polynomial Time Approximation Schemes (PTAS): Concepts and History
  • 2.5 Previous Work on Approximation for Job Shop Scheduling

• Mathematical Formulation and Problem Definition

  • 3.1 Formal Definition of the Job Shop Problem with Release Dates
  • 3.2 Weighted Completion Time Objective Function
  • 3.3 Assumptions and Constraints
  • 3.4 Notations and Terminology

• Approximation Algorithms for Job Shop Problems

  • 4.1 Overview of Approximation Algorithms for Scheduling Problems
  • 4.2 PTAS in Scheduling: Basic Principles and Applications
  • 4.3 Challenges in Designing Approximation Schemes for Job Shop Problems

• Main Contribution: PTAS for Job Shop Scheduling with Release Dates

  • 5.1 Key Ideas and Intuition Behind the PTAS
  • 5.2 Detailed Algorithm Description
  • 5.3 Algorithmic Framework and Steps
  • 5.4 Theoretical Analysis of the PTAS
  • 5.5 Performance Bound and Approximation Ratio

• Implementation and Complexity Analysis

  • 6.1 Time Complexity of the Proposed PTAS
  • 6.2 Space Complexity Considerations
  • 6.3 Comparison with Exact Algorithms
  • 6.4 Experimental Evaluation of the PTAS

• Practical Applications and Case Studies

  • 7.1 Manufacturing and Production Scheduling
  • 7.2 Resource Allocation in Real-World Job Shops
  • 7.3 Impact of Release Dates in Practice
  • 7.4 Case Study: Application in a Specific Industry

• Extensions and Generalizations

  • 8.1 Extending the PTAS to Other Scheduling Models
  • 8.2 Handling Variations in Release Dates and Job Types
  • 8.3 Incorporating Additional Constraints (e.g., Precedence Constraints)
  • 8.4 Generalizing to Parallel Machines or Multimachine Environments

• Open Problems and Future Directions

  • 9.1 Open Problems in Job Shop Scheduling with Release Dates
  • 9.2 Potential Improvements to the PTAS
  • 9.3 Directions for Future Research in Scheduling and Approximation Algorithms

• Conclusion

  • 10.1 Summary of Contributions
  • 10.2 Impact on Scheduling Theory and Practice
  • 10.3 Final Thoughts and Outlook

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