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

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.