MATHEMATICAL FOUNDATIONS OF THE EXPEDITIONARY ACTIVITIES OF TRANSPORT COMPANIES FOR THE OPTIMIZATION OF REVERSE LOGISTICS MANAGEMENT

Abstract

An extensive analysis of existing economic-mathematical instruments and their practical applications in solving transportation problems within expeditionary activities – illustrated by research conducted by Ukrainian scholars – has revealed several significant limitations in optimizing reverse logistics management, particularly in the context of returning transport vehicles. Key challenges include limited access to current data, an insufficiently comprehensive statistical base, a high sensitivity of the models to changes in input parameters, and a lack of adaptability to the real-world operating conditions of transport companies. These challenges have motivated the primary objective of the present study: to enhance the mathematical foundations underpinning the expeditionary activities of transport enterprises by developing innovative approaches for optimizing reverse logistics management with the goal of minimizing operational costs. To achieve this, the research integrates advanced optimization techniques. This approach enables a thorough comparative cost analysis among competing transport companies and facilitates the formulation of optimal freight transportation plans that consider both fixed and variable cost components. Consequently, the model not only ensures cost-effective delivery of goods but also systematically addresses the return routing of transport vehicles, thereby achieving a dual-level optimization of logistics operations. The proposed integrated mathematical model is designed to adapt to dynamic operational conditions and variable real-time data, providing a robust decision-support tool for logistics managers. By incorporating detailed cost factors such as fuel consumption, labor expenses, vehicle depreciation, and loading/unloading charges, the model assists in identifying the most economically viable routing strategies for both forward and reverse logistics. The novelty of this work lies in its comprehensive treatment of reverse logistics within the expeditionary transport framework – a domain that has traditionally received limited attention. By addressing the entire cycle of transportation, including the often-overlooked return phase, this study offers a methodological advancement that bridges the gap between theoretical optimization models and practical logistics management. Future research will focus on developing an information support system to automate computations and provide real-time decision-making assistance, further enhancing the applicability and impact of the proposed approach.