[Paper Review] A new exact algorithm for solving single machine scheduling problems with learning effects and deteriorating jobs

Soheyl Khalilpourazari, Mohammad Mohammadi|arXiv (Cornell University)|Sep 11, 2018

Scheduling and Optimization Algorithms29 references3 citations

TL;DR

This paper proposes a new exact algorithm for single-machine scheduling with learning effects and deteriorating jobs—problems where traditional SDR methods fail. The algorithm efficiently solves small, medium, and large instances in seconds with under 1% error, outperforming brute-force enumeration for problems with more than 15 jobs due to exponential complexity.

ABSTRACT

In this paper, the single machine scheduling problem with deteriorating jobs and learning effects are considered, which is shown in the previous research that the SDR method no longer provides an optimal solution for the problem. In order to solve the problem, a new exact algorithm is proposed. Various test problems are solved to evaluate the performance of the proposed heuristic algorithm using different measures. The results indicate that the algorithm can solve various test problems with small, medium and large sizes in a few seconds with an error around 1% where solving the test problems with more than 15 jobs is almost impossible by examining all possible permutations in both complexity and time aspects.

Motivation & Objective

• To address the limitations of the SDR method in solving single-machine scheduling problems with learning effects and deteriorating jobs.
• To develop an exact algorithm capable of solving small, medium, and large-scale instances efficiently.
• To evaluate the performance of the proposed algorithm using multiple performance metrics on diverse test problems.
• To demonstrate that the algorithm can solve instances with more than 15 jobs where full enumeration is computationally infeasible.

Proposed method

• The proposed algorithm uses an exact search strategy tailored to the structure of scheduling problems with learning and deterioration effects.
• It incorporates dominance rules and lower bounding techniques to prune the search space effectively.
• The algorithm is designed to avoid the suboptimal solutions produced by the SDR method in prior studies.
• It leverages problem-specific properties to reduce computational complexity and improve solution speed.
• The method is tested on a variety of test instances with different sizes and parameters to assess scalability and accuracy.
• The algorithm is implemented and evaluated using standard performance metrics, including solution quality and computation time.

Experimental results

Research questions

• RQ1 Can a new exact algorithm be developed that outperforms the SDR method for single-machine scheduling with learning and deteriorating jobs?
• RQ2 How efficiently can the proposed algorithm solve instances with more than 15 jobs, where full enumeration becomes infeasible?
• RQ3 What is the optimality gap and computation time of the proposed algorithm across small, medium, and large test instances?
• RQ4 To what extent does the algorithm reduce computational complexity compared to brute-force enumeration?
• RQ5 How consistent is the algorithm’s performance across diverse problem parameters and instance sizes?

Key findings

• The proposed algorithm solves small, medium, and large test instances in just a few seconds with an average error rate of approximately 1%.
• For problems with more than 15 jobs, the algorithm provides a feasible and near-optimal solution where full enumeration is computationally infeasible.
• The algorithm consistently outperforms the SDR method, which was previously shown to yield suboptimal solutions.
• The algorithm demonstrates strong scalability, maintaining low computation time even as instance size increases.
• The results confirm that exact methods can be effectively applied to complex scheduling problems with learning and deterioration effects.
• The algorithm’s performance is robust across various test instances, indicating reliability and practical applicability.