Mathematical programming models to tackle the COVID-19 pandemic: operations research perspective

¹ Department of Industrial Engineering, Tokat Gaziosmanpaşa University, Tokat, Türkiye
² Department of Industrial Engineering, Istinye University, Istanbul, Türkiye
³ Department of Industrial Engineering and Management, Yuan Ze University, Taoyuan, Taiwan

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 24 October 2024
Accepted: 6 February 2026

Abstract

The novel coronavirus pandemic (COVID-19) massively disrupted daily life globally and locally, resulting in many issues. Since the pandemic started, Operations Research (OR) scholars have conducted research and published studies on various issues raised by COVID-19. They developed various mathematical programming models (MPMs) to optimize and plan for the problems caused by the pandemic. This work aims to provide researchers with a starting point for MPMs in the management and planning of the COVID-19 pandemic. First, a bibliometric analysis of the previous studies is performed, wherein the models are proposed to tackle the COVID-19 pandemic. Then, it systematically reviewed the deterministic MPMs used in the fight against COVID-19 and analyzed the current trends in the literature, the types of models used, OR application areas, objective functions, constraint structures, and solution methods. These studies are classified in the OR literature into the following approaches: linear programming (LP), mixed-integer linear programming (MILP), multi-objective programming (MOP), goal programming (GP), and bi-level programming (BLP). The findings show that MPMs provide significant benefits in tackling the pandemic in various areas such as healthcare systems, supply chain management, vehicle routing, scheduling, and assignment. Moreover, the research challenges, trends, and outlook for future studies are discussed, which will guide researchers and practitioners to conduct more applicable and efficient research and determine optimal policies, respectively.