Optimizing multilevel decentralized problems with a novel application of Gabasov's adaptive method: highlighting applications in COVID-19 vaccine distribution

Abstract

This paper presents a novel algorithm for solving multilevel monoobjective decentralized linear programming problems (ML-MO-DLPPs). Our approach represents a refined adaptation of Sinha and Sinha's linear programming method, enhanced by the development of an interval reduction map, which dynamically refines the decision variable intervals based on the influence of decisions made at preceding levels. Each stage of the algorithm's construction is thoroughly analyzed. The algorithm's effectiveness is demonstrated through a comprehensive numerical example, highlighting its practical applicability to resource management problems. Particular emphasis is placed on its application to vaccination planning in long-term care facilities during the COVID-19 pandemic, addressing the optimization of resource allocation with a strong focus on the equitable distribution of COVID-19 vaccines.