Mathematical Optimization in Innovation Productivity: A Framework and A Case Study on UAV Border Patrolling in Türkiye

Year 2024, , 283 - 304, 30.04.2024

Erdi Daşdemir

https://doi.org/10.51551/verimlilik.1322882

Abstract

Purpose: In this paper, the potential of mathematical optimization (MO) in enhancing innovation productivity is explored. Innovation is a process that converts new ideas and methods into products and services, MO can contribute to innovation management by improving productivity across all stages, from pre-innovation to post-innovation. This paper establishes a connection between MO and innovation productivity while demonstrating an application for a post-innovation phase problem of unmanned aerial vehicles (UAVs).
Methodology: A framework for incorporating MO into the design problems of innovation processes is developed. Additionally, a MO model is developed for a case study concerning UAV border patrolling in Türkiye.
Findings: Computational experiments demonstrate MO's effectiveness in optimizing UAV routes and strategies, enhancing operational efficiency, and innovation productivity. Optimal recommendations and trade-offs among different mission considerations are obtained in 18 minutes on average (with a median of 5 seconds) over 210 runs.
Originality: A link is established between MO and innovation productivity. An operations research problem is introduced for UAV operations in border patrolling in Türkiye. The codebase and data are openly provided for readers to apply the model in their research.

Keywords

Mathematical Optimization, Innovation, Productivity, Unmanned Aerial Vehicles

İnovasyon Verimliliğinde Matematiksel Optimizasyon: Bir Çerçeve ve Türkiye’de İHA Sınır Devriyesine İlişkin Bir Vaka Çalışması

Abstract

Amaç: Bu makalede, matematiksel optimizasyonun (MO) inovasyon verimliliğini artırma potansiyeli incelenmektedir. İnavasyon, yeni fikirleri ve yöntemleri ürün ve hizmetlere dönüştüren bir süreçtir. MO, inovasyon yönetimine verimliliği artırarak katkıda bulunabilir; bu, inovasyon öncesinden sonrasına kadar inovasyon sürecinin tüm aşamalarında geçerlidir. Bu makale, MO ve inovasyon verimliliği arasında bir bağlantı kurarken, insansız hava araçlarının (İHA'ların) inovasyon sonrası aşamasındaki problemlerine yönelik bir uygulama sunmaktadır.
Yöntem: İnovasyon süreçlerindeki karar problemlerine MO'nun dahil edilişi için bir çerçeve oluşturulmaktadır. Ayrıca, Türkiye'deki İHA sınır devriyesi ile ilgili bir vaka çalışması için bir MO modeli geliştirilmektedir.
Bulgular: Hesaplamalı deneyler, MO'nun İHA rotalarını ve stratejilerini optimize etme, operasyonel verimliliği ve inovasyon verimliliğini artırma konusundaki etkinliğini göstermektedir. Model, optimal tavsiyeleri ve farklı endişeler için dengeleri 210 farklı çözüm için ortalama 18 dakikada (medyan 5) bulmaktadır.
Özgünlük: MO ve inovasyon verimliliği arasında bir bağlantı kurulmuştur. Türkiye'de sınır devriyesi için İHA operasyonları için bir yöneylem araştırması problemi sunulmaktadır. Okuyucuların araştırmalarında modeli uygulayabilmeleri için kod tabanı ve veriler açık sunulmaktadır.

Keywords

Matematiksel Optimizasyon, İnovasyon, Verimlilik, İnsansız Hava Araçları.

Thanks

Buffalo Üniversitesi'ne, Hesaplama Araştırmaları Merkezi'nin yüksek performanslı bilgisayar kaynaklarında deneylerimizi gerçekleştirmeme izin verdiği için teşekkür ederim.

References

• Ackoff, R.L. (1979). "The Future of Operational Research is Past", The Journal of the Operational Research Society, 30(2), 93-104.
• Arf, C. (1959). "Makine Düşünebilir Mi ve Nasıl Düşünebilir?", Atatürk Üniversitesi – Üniversite Çalışmalarını Muhite Yayma ve Halk Eğitimi Yayınları Konferanslar Serisi, 1, 91-103.
• Baykar (2023). "Bayraktar Akinci" https://baykartech.com/tr/uav/bayraktar-akinci/ (Access date: 29.03.2024). Braekers, K., Ramaekers, K. and Van Nieuwenhuyse, I. (2016). "The Vehicle Routing Problem: State of the Art Classification and Review", Computers & Industrial Engineering, 99, 300-313.
• Camm, J.D., Cochran, J.J., Fry, M.J. and Ohlmann, J.W. (2020). "Business Analytics", Cengage Learning, Boston.
• Cantner, U., Dettmann, E., Giebler, A., Guenther, J. and Kristalova, M. (2019). "The Impact of Innovation and Innovation Subsidies on Economic Development in German Regions", Regional Studies, 53(9), 1284-1295.
• Carayannis, E. and Grigoroudis, E. (2014). "Linking Innovation, Productivity, and Competitiveness: Implications for Policy and Practice", The Journal of Technology Transfer, 39(2), 199-218.
• CCR (University at Buffalo), (2024). “The Center for Computational Research”, http://hdl.handle.net/10477/79221, (Erişim tarihi: 29.03.2024)
• Cockburn, I.M., Henderson, R. and Stern, S. (2019). "The Impact of Artificial Intelligence on Innovation: An Exploratory Analysis ", In: Agrawal, A., Gans, J. and Goldfarb, A. (eds.) The economics of artificial intelligence : an agenda. Chicago ; London : The University of Chicago Press.
• Coutinho, W.P., Battarra, M. and Fliege, J. (2018). "The Unmanned Aerial Vehicle Routing and Trajectory Optimisation Problem, A Taxonomic Review", Computers & Industrial Engineering, 120, 116-128.
• Dasdemir, E., Batta, R., Köksalan, M. and Tezcaner Öztürk, D. (2022). "UAV Routing for Reconnaissance Mission: A Multi-Objective Orienteering Problem with Time-dependent Prizes and Multiple Connections", Computers & Operations Research, 145, 105882.
• Dasdemir, E., Köksalan, M. and Tezcaner Öztürk, D. (2020). "A Flexible Reference Point-Based Multi-Objective Evolutionary Algorithm: An Application to the UAV Route Planning Problem", Computers & Operations Research, 114, 104811.
• Elmokadem, T. and Savkin, A.V. (2021). “Towards Fully Autonomous UAVs: A Survey”. Sensors, 21.
• Evers, L., Barros, A. I., Monsuur, H. and Wagelmans, A. (2015). "UAV Mission Planning: From Robust to Agile", Military Logistics: Research Advances and Future Trends, (Editors: Zeimpekis, V., Kaimakamis, G. and Daras, N.J), . Springer International Publishing, Cham.
• Garud, R., Tuertscher, P. and Van de Ven, A.H. (2013). "Perspectives on Innovation Processes", Academy of Management Annals, 7(1), 775-819.
• Guerriero, F., Surace, R., Loscri, V. and Natalizio, E. (2014). "A Multi-Objective Approach for Unmanned Aerial Vehicle Routing Problem with Soft Time-Windows Constraints", Applied Mathematical Modelling, 38(3), 839-852.
• Gunawan, A., Lau, H.C. and Vansteenwegen, P. (2016). "Orienteering Problem: A Survey of Recent Variants, Solution Approaches and Applications", European Journal of Operational Research, 255(2), 315-332.
• Gurobi Optimization, LLC. 2024. Gurobi Optimizer Reference Manual.
• Haefner, N., Wincent, J., Parida, V. and Gassmann, O. (2021). "Artificial Intelligence and Innovation Management: A Review, Framework, and Research Agenda", Technological Forecasting and Social Change, 162, 120392.
• Haenlein, M. and Kaplan, A. (2019). "A Brief History of Artificial Intelligence: On the Past, Present, and Future of Artificial Intelligence", California Management Review, 61(4), 5-14.
• Hall, J.R. and Hess, S.W. (1978). "OR/MS: Dead or Dying? RX for Survival", Interfaces, 8, 42-44.
• Jacques, B., Eric, H., Sree, R., Chui, M. , Allas, T., Dahlstrom, P., Henke, N. and Trench, M. (2017). "Artificial Intelligence: The Next Digital Frontier?", McKinsey and Company Global Institute, 47.3.6,
• Mariani, M.M., Machado, Isa, M.V. and Dwivedi, Y.K. (2023). "Artificial Intelligence in Innovation Research: A Systematic Review, Conceptual Framework, and Future Research Directions", Technovation, 122, 102623.
• McCloskey, J.F. (1987). "The Beginnings of Operations Research: 1934-1941", Operations Research, 35(1), 143-152.
• Minford, L. and Meenagh, D. (2019). "Testing a Model of UK Growth: A Role for R&D Subsidies", Economic Modelling, 82, 152-167.
• Mittal, S. and Deb, K. (2007), “Three-Dimensional Offline Path Planning for UAVs Using Multiobjective Evolutionary Algorithms”, 2007 IEEE Congress on Evolutionary Computation, Singappre, 3195-3202.
• Mittelmann, H.D. (2020). "Benchmarking Optimization Software - A (Hi)Story", SN Operations Research Forum, 1(1), 2.
• Moskal, M.D. and Batta, R. (2017). "A Macrogrid Approach for Routing UAVs in Support of Information Gathering", Military Operations Research, 22(4), 35-54.
• Moskal, M.D., Dasdemir, E.and Batta, R. (2023). "Unmanned Aerial Vehicle Information Collection Missions with Uncertain Characteristics", INFORMS Journal on Computing, 35(1), 120-137.
• Moustakas, K., Loizidou, M., Rehan, M. and Nizami, A. S. (2020). "A Review of Recent Developments in Renewable and Sustainable Energy Systems: Key Challenges and Future Perspective", Renewable & Sustainable Energy Reviews, 119
• Pfeiffer, B., Batta, R., Klamroth, K. and Nagi, R. (2009). "Path Planning for UAVs in the Presence of Threat Zones Using Probabilistic Modelling", Handbook of Military Industrial Engineering, (Editors: Badiru, A. B. and Thomas, M. U.), CRC Press, USA.
• Picchi, A. (2023). “College Majors Have A Big Impact on Income. Here Are the Highest- and Lowest-Earning Fields”, https://www.cbsnews.com/news/college-major-top-and-lowest-earning-majors-impact-on-income-pay/, (Access Date: 29.03.2024)
• Rojas V., Daniela, Solano-Charris, E.L., Muñoz-Villamizar, A. and Montoya-Torres, J.R. (2021). "Unmanned Aerial Vehicles/Drones in Vehicle Routing Problems: A Literature Review", International Transactions in Operational Research, 28(4), 1626-1657.
• Rothberg, E. (Forbes), (2021). “Operations Research Analyst: The Fastest-Growing Job You've Never Heard of”. https://www.forbes.com(Access Date: 29.03.2024)
• Sabuncuoğlu, İ. and Dengiz, B. (2022). "Türkiye’de Endüstri Mühendisliğine Bir Bakış: Geçmişi, Bugünü Ve Geleceği", Verimlilik Dergisi, 3, 559-568.
• Stavropoulou, F., Repoussis, P.P. and Tarantilis, C.D. (2019). "The Vehicle Routing Problem with Profits and consistency constraints", European Journal of Operational Research, 274(1), 340-356.
• Teece, D.J. (2018). "Tesla and the Reshaping of the Auto Industry", Management and Organization Review, 14(3), 501-512.
• Tezcaner, D. and Köksalan, M. (2011). "An Interactive Algorithm for Multi-objective Route Planning", Journal of Optimization Theory and Applications, 150(2), 379-394.
• Tezcaner Öztürk, D. and Köksalan, M. (2023). "Biobjective Route Planning of An Unmanned Air Vehicle in Continuous Space", Transportation Research Part B: Methodological, 168, 151-169.
• Verganti, R., Vendraminelli, L. and Iansiti, M. (2020). "Innovation and Design in the Age of Artificial Intelligence", Journal of Product Innovation Management, 37(3), 212-227.
• Xia, Y., Batta, R. and Nagi, R. (2017). "Controlling a Fleet of Unmanned Aerial Vehicles to Collect Uncertain Information in a Threat Environment", Operations Research, 65(3), 674-692.
• Zheng, Z. B., Xie, S.A., Dai, H.N., Chen, X.P. and Wang, H.M. (2018). "Blockchain Challenges and Opportunities: A Survey", International Journal of Web and Grid Services, 14(4), 352-375.