Abstract
Developing a comprehensive service strategy to optimize customer satisfaction presents an ongoing challenge for effective facility provider. The essence of comprehensive systems is selecting the suitable service design, establishing an effective service delivery process, and building continuous improvement. This research analyzes a finite capacity service system incorporating several realistic customer-server dynamics: customer impatience, server’s partial breakdown, and threshold recovery policy. When the number of customers is more, the server is under pressure to increase the service rate to mitigate the service system’s load. Motivating from this fact, the concept of service pressure condition is also incorporated. For characterization, we evaluate state probabilities derived using the matrix-analytic method and henceforth several performance measures. To address the cost optimization problem involving the developed Chapman-Kolmogorov forward differential-difference equations and determine optimal operational parameters, we employ the recently devised cuckoo search (CS) optimization approach. A comparative analysis is performed with the semi-classical optimizer: quasi-Newton (QN) method, and metaheuristics technique: particle swarm optimization (PSO), to validate the efficacy of results. Lastly, several numerical illustrations are depicted in different tables and graphs to understand essential characteristics quickly.
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Authors acknowledge the sincere thanks to anonymous reviewers to improve the quality of the paper and member of editorial board for considering our manuscript for possible publication.
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The third author (MD) extends his sincere thanks to the funding agency CSIR-UGC, India, for the financial support (SRF/NET 1081/(CSIR-UGC NET DEC. 2018)).
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Shreekant Varshney is working as assistant professor in the Department of Mathematics, School of Technology (SoT) at PDEU (Formerly PDPU) since October 10, 2022. Prior joining to PDEU, he has worked for IFHE, Hyderabad. He has completed the Doctor of Philosophy (Ph.D. ) from the Department of Mathematics, BITS Pilani, Pilani Campus. Also, he has cleared CSIR JRF/NET twice with AIR 18 and 67, respectively. In the year 2017, he was appointed as a co-instructor by the Practice School Division, BITS Pilani, Pilani Campus and mentored students at IIRS (ISRO), WIHG (DST), and CSIR-IIP in Dehradun. He has published more than 16 research articles in several journal of repute with high impact factor like RESS (Elsevier), QTQM (Taylor & Francis), JCAM (Elsevier), AJSE (Springer), etc. He has presented many research papers at national and international conferences of repute. Moreover, in October 2019, he has been awarded with second prize in a technical writing competition organized by SIAM journal publishing.
Suman Kaswan received her Bachelor of Science, B.Sc. (Hons.) in Mathematics, from the University of Delhi in 2017. In 2019, she received her M.Sc. in mathematics from the Indian Institute of Technology, Patna. Currently, she is working towards a Ph.D. degree from the Birla Institute of Technology and Science, Pilani. Her research interests lie primarily in the areas of development of queueing models and reliability theory incorporating several features like retrials, vacations, impatience, service regimes, arrival control policies, etc.; implementation of optimization techniques on the cost minimization problem of the system; a matrix-analytic method for solving stationary distributions; and probability generating functions techniques. She has published two research articles in peer-reviewed journal to her credit.
Mahendra Devanda is an assistant professor in the Department of Mathematics at MSBU, Bharatpur. He has submitted his Ph.D. thesis in the Department of Mathematics at the Birla Institute of Technology and Science, Pilani. He achieved an all-India rank of 122 in the CSIRUGC NET exam (December 2018) and also qualified for the GATE exam in 2019. Dr. Devanda earned his Master of Science in mathematics from the University of Rajasthan in 2017. He has published four research articles in peer-reviewed journals and has submitted additional work to international journals. His research interests include the development of queuing models, stochastic models, and reliability theory.
Chandra Shekhar is the professor and ex-HoD in the Department of Mathematics in BITS Pilani, India, is actively involved in research and teaching in the area of queueing theory, computer and communication systems, machine repair problems, reliability and maintainability, stochastic process, evolutionary computation, statistical analysis, fuzzy set, and logic. Besides attending, presenting scientific papers, and delivering invited talks in national/ international conferences and FDPs, he has organized a number of conferences, workshops, and symposiums as convener and organizing secretary. The best research paper award has been bestowed at the international conference. He has more than 50 research articles in these fields in journals of high repute and has supervised three Ph.D. theses. Besides some book chapters in an edited book published by the publisher of international reputation, authorship of the textbook entitled Differential Equations, Calculus of Variations and Special Functions and the edited book entitled Mathematical Modeling and Computation of Real-Time Problems: An Interdisciplinary Approach is also to his credit. He is also a member of the editorial board and reviewer of many reputed journals, academic societies and doctoral research committee, advisory board, faculty selection committee, the examination board of many governments and private universities, institutions, or research labs. As a professional, he has visited IIRS (ISRO), CSIR-IIP, NIH, WIHG, CPWD, Bank of Maharashtra, APS Lifetech.
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Varshney, S., Kaswan, S., Devanda, M. et al. Finite Capacity Service System with Partial Server Breakdown and Recovery Policy: An Economic Perspective. J. Syst. Sci. Syst. Eng. (2024). https://doi.org/10.1007/s11518-024-5612-1
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DOI: https://doi.org/10.1007/s11518-024-5612-1