Fuzzy modeling and cost optimization for machine repair problem with retrial under admission control F-policy and feedback

• Published in: Mathematics and computers in simulation Vol. 211; pp. 214 - 240
• Main Authors: Sanga, Sudeep Singh, Charan, Gannamaneni Sai
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-09-2023
• Subjects: Cost; F-policy; Feedback; Fuzzy; Harmony search method; Machining repair; Retrial; F-policy; Retrial; Feedback; Fuzzy; Harmony search method; Cost; Machining repair
• ISSN: 0378-4754; 1872-7166
• DOI: 10.1016/j.matcom.2023.03.036

In the present paper, the machine repair problem (MRP) with real-life scenarios is investigated, which plays a significant role in the manufacturing process, industries, production lines, etc. An M∖M∖1∖K machine repair problem with retrial attempts under admission control policy F-policy and machine’s feedback is considered in which a single repairman is available to repair the failed machines. The recursive technique is applied to solve the mathematical model and establish the probability distributions for different states, which are further used to develop the performance indices. The parametric non-linear programming (P-NLP) technique is employed to develop the MRP with F-policy in a fuzzy environment using the trapezoidal and sigmoidal fuzzy numbers. Zadeh’s extension principle and parametric non-linear programming technique help us to find the α-cuts of the developed performance predictors of MRP. We frame and minimize the total cost of the system. The harmony search method (HSM) and quasi-Newton method are implemented to achieve the total minimum cost of the system corresponding to the optimal repair rate, which helps the system managers in the formulation of business policies in industries, including the automobile sector. A numerical example is also given, which produces several tables and graphs that show the validity of the model.