Modeling and Applications in Operations Research
暫譯: 運籌學中的建模與應用

本書構想了新穎的優化方法，對現實生活中的問題產生重大影響，涵蓋從庫存控制到經濟決策等主題。內容討論了庫存控制、排隊模型、時間表排程、模糊優化以及背包問題等主題。本書的內容包括以下幾個關鍵方面：

- 提出一個基於不可靠伺服器的新模型，並使用自然啟發算法進行收斂分析
- 討論在運輸問題、時間表問題以及庫存控制中的最佳/動態定價中使用的優化技術
- 突出使用五邊形模糊數的單目標和多目標優化問題
- 說明針對不瞬時劣化物品的利潤最大化庫存模型，並考慮不精確的成本
- 展示自然啟發算法，如粒子群優化、遺傳算法、蝙蝠算法和杜鵑搜索算法

本書涵蓋多學科的實時問題，如運輸問題的模糊優化、動態定價的庫存控制、使用螞蟻群優化的時間表問題、背包問題、使用自然啟發算法的排隊建模以及多目標模糊線性規劃。它展示了對各種系統設計參數和預設成本元素組合的比較分析。本書將成為工業工程、製造工程、生產工程、機械工程和數學領域的研究生和學術研究者的理想參考書。

Jyotiranjan Nayak is a Professor in the Department of Mathematics at the Faculty of Science and Technology (IcfaiTech), IFHE, Hyderabad, India. Prior to this, he was Associate Professor at the Institute of Technical Education and Research, Siksha "O" Anusandhan University, Bhubaneswar, India, and has more than 32 years of teaching experience in undergraduate and postgraduate engineering studies. He taught the subjects like differential equations, vector analysis, complex analysis, linear algebra, numerical methods, optimization techniques, discrete mathematics, and advanced calculus at the undergraduate level. He taught postgraduate students algebra, cryptography, number theory, real analysis, topology, combinatorics, graph theory, and operations research. For Ph.D. students, he has delivered lectures on advanced computational mathematics, matrix algebra, and design of experiments at different universities, including Utkal University, Biju Patnaik University of Technology, Berhampur University, Siksha "O" Anusandhan, and ICFAI University. Besides, he has been a guest and visiting faculty at many other universities in the country. He obtained his Ph.D. degree from Utkal University in 2005. His research areas include non-convex programming, fuzzy optimization, optimal control, and topology optimization. He has published 12 research papers in leading national and international journals. He is also the former associate editor of The Journal of Orissa Mathematical Society. He was Vice-President of the Operational Research Society of India (ORSI), Bhubaneswar chapter. He is an executive member of the Orissa Mathematical Society (OMS) and a life member of the Indian Society for Technical Education (ISTE), Orissa Information Society (OITS), and Ramanujan Society of Mathematics and Mathematical Sciences (RSMSS).

Shreekant Varshney is Assistant Professor in the Department of Mathematics, School of Technology (SoT), Pandit Deendayal Energy University, Gandhinagar, Gujarat, India. Before this, he worked as Assistant Professor in the Department of Mathematics at the Faculty of Science and Technology (IcfaiTech), IFHE, Hyderabad, India. He obtained his Ph.D. degree from the Birla Institute of Technology and Science Pilani, Pilani Campus, in 2020. He is actively involved in the research areas, namely queueing theory, machine repair problem (MRP), optimal control, reliability and maintainability, stochastic modeling, sensitivity analysis, evolutionary computation, statistical analysis, fuzzy set and logic, etc. He has taught undergraduate subjects such as linear algebra, differential equations, complex analysis, advanced calculus, numerical methods, and probability and statistics. He also has experience in teaching courses like research methodology, stochastic modeling, and introduction to queueing theory for Ph.D. students. Besides attending, presenting scientific papers, and delivering invited talks in FDPs, he has organized several workshops and symposiums. He has been awarded second prize in the academic writing competition organized by SIAM journal publishing. He has 13 research articles in journals of high repute, namely, Reliability Engineering and System Safety, Journal of Computational and Applied Mathematics, Quality Technology and Quantitative Management, Arabian Journal of Science and Engineering, etc. He is also a reviewer of many reputed journals. As a professional, he has visited IIRS (ISRO), CSIR-IIP, and WIHG.

Chandra Shekhar, the Professor and Ex-HoD of the Department of Mathematics at 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 processes, evolutionary computation, statistical analysis, and fuzzy set and logic. He has expertise in the subjects of probability and statistics, differential equations, linear algebra, advanced calculus, complex variables, and statistical inference at the undergraduate level of teaching. He has taught real analysis, topology, cryptography, applied mathematics, computational mathematics, cybernetics, and many more at the post-graduation level. He has been a pioneer in evolutionary computation, Markovian and stochastic modeling, research methodology, and queueing analysis and its applications. Besides attending, presenting scientific papers, and delivering invited talks at national/international conferences and FDPs, he has organized many conferences, workshops, and symposiums as a convener and as an organizing secretary. The best research paper award has been bestowed at the international conference. He has 48 research articles in these fields in journals of high repute and has supervised two Ph.D. theses. Besides some book chapters in an edited book published by the publisher of international reputation, authorship of the textbook titled Differential Equations, Calculus of Variations and Special Functions and the edited book titled 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 a reviewer of many reputed journals, academic societies and Doctoral Research Committee, advisory board, faculty selection committee, and 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, NTPC, Bank of Maharashtra, and APS Lifetech.

**Jyotiranjan Nayak** 是印度海得拉巴 IFHE 科技與科學學院 (IcfaiTech) 數學系的教授。在此之前，他曾擔任印度布巴內斯瓦爾 Siksha 'O' Anusandhan 大學技術教育與研究所的副教授，並擁有超過 32 年的本科及研究生工程學科教學經驗。他在本科階段教授微分方程、向量分析、複變函數、線性代數、數值方法、優化技術、離散數學和高等微積分等科目。在研究生階段，他教授代數、密碼學、數論、實分析、拓撲學、組合學、圖論和運籌學等課程。對於博士生，他在不同大學（包括烏塔卡爾大學、比朱·帕特奈克科技大學、貝漢普爾大學、Siksha 'O' Anusandhan 和 ICFAI 大學）講授高級計算數學、矩陣代數和實驗設計等課程。此外，他還曾在國內多所大學擔任客座教授和訪問教授。他於 2005 年獲得烏塔卡爾大學的博士學位。他的研究領域包括非凸規劃、模糊優化、最優控制和拓撲優化。他在國內外知名期刊上發表了 12 篇研究論文。他也是《奧里薩數學學會期刊》的前副編輯，曾擔任印度運籌學會 (ORSI) 布巴內斯瓦爾分會的副會長。他是奧里薩數學學會 (OMS) 的執行委員會成員，並且是印度技術教育學會 (ISTE)、奧里薩信息學會 (OITS) 和拉馬努金數學與數學科學學會 (RSMSS) 的終身會員。

**Shreekant Varshney** 是印度古吉拉特邦甘地納格爾的潘迪特·丁達亞爾能源大學 (Pandit Deendayal Energy University) 科技學院 (SoT) 數學系的助理教授。在此之前，他曾在印度海得拉巴 IFHE 科技與科學學院 (IcfaiTech) 數學系擔任助理教授。他於 2020 年在比爾拉科技與科學學院 (Birla Institute of Technology and Science) 獲得博士學位。他積極參與的研究領域包括排隊理論、機器維修問題 (MRP)、最優控制、可靠性與可維護性、隨機建模、敏感度分析、進化計算、統計分析、模糊集合與邏輯等。他教授過本科課程，如線性代數、微分方程、複變函數、高等微積分、數值方法以及機率與統計。他還有教授研究方法論、隨機建模和排隊理論入門等博士生課程的經驗。除了參加、發表科學論文和在 FDP 中進行邀請演講外，他還組織了多個研討會和座談會。他在 SIAM 期刊出版的學術寫作比賽中獲得第二名。他在多個知名期刊上發表了 13 篇研究文章，包括《可靠性工程與系統安全》、《計算與應用數學期刊》、《質量技術與定量管理》、《阿拉伯科學與工程期刊》等。他也是多個知名期刊的審稿人。作為專業人士，他曾訪問 IIRS (ISRO)、CSIR-IIP 和 WIHG。

**Chandra Shekhar** 是印度比爾拉科技學院 (BITS Pilani) 數學系的教授及前系主任，積極參與排隊理論、計算機與通信系統、機器維修問題、可靠性與可維護性、隨機過程、進化計算、統計分析以及模糊集合與邏輯等領域的研究與教學。他在本科教學中專精於機率與統計、微分方程、線性代數、高等微積分、複變數和統計推斷等科目。他在研究生階段教授實分析、拓撲學、密碼學、應用數學、計算數學、控制論等多個課程。他在進化計算、馬可夫與隨機建模、研究方法論以及排隊分析及其應用方面是先驅。除了參加、發表科學論文和在國際/國內會議及 FDP 中進行邀請演講外，他還作為召集人和組織秘書組織了多個會議、研討會和座談會。他在國際會議上獲得最佳研究論文獎。他在這些領域的高知名度期刊上發表了 48 篇研究文章，並指導了兩篇博士論文。除了在國際知名出版社出版的編輯書籍中的一些章節外，他還著有《微分方程、變分法與特殊函數》一書，以及編輯書籍《實時問題的數學建模與計算：跨學科方法》。他還是多個知名期刊的編輯委員會成員和審稿人，並在多所政府和私立大學、機構或研究實驗室的學術社團、博士研究委員會、顧問委員會、教職選拔委員會和考試委員會中擔任成員。作為專業人士，他曾訪問 IIRS (ISRO)、CSIR-IIP、NIH、WIHG、CPWD、NTPC、馬哈拉施特拉銀行和 APS Lifetech。