This article presents a study on the job shop problem, a combinatorial optimization problem that models scheduling and resource allocation in industrial settings. The article aims to investigate the relationship between optimality gap and required computational resources, considering various optimality gap levels that are applicable in real-life situations. The study uses a Monte Carlo simulation to analyze the behavior of solvers in solving different sizes of random-generated scheduling problems. The findings of the study offer insights into the worthiness of reaching an optimal solution versus implementing a near-optimal solution and starting the work. The codes used in the study are accessible on the author's GitHub account.
In secure networks, the authentication process, which verifies a user's identity, is a sensitive operation. Balancing the authentication process's security and usability while keeping operating costs low is a major challenge. We investigate this process in a secure system that has multiple authentication methods available. The goal is to find a fast and easy‐to‐implement approach to assign incoming requests to authentication methods in a way that balances cost, usability, and security. We model the system as a continuous‐time, infinite‐horizon Markov Decision Process. Then, we propose a new, fast heuristic approach to solve the problem, as the curse of dimensionality limits the effectiveness of exact methods. The proposed heuristic uses closed‐form approximations to define threshold policies that are easily implementable. Numerical experiments show that our approach yields robust, near‐optimal solutions, with high accuracy, for a wide range of problem instances.
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