Freight tour synthesis based on entropy maximization with fuzzy parameters including variability in transportation costs through the Markowitz model

Abstract

This research develops an optimization model to quantify and minimize the risk associated with the variability of travel costs in freight tour synthesis (FTS) transportation problems. The model integrates objectives of maximizing trip entropy to generate diverse solutions alongside minimizing costs. Demand and supply parameters are modeled using fuzzy logic to incorporate the inherent uncertainty of these data. A recent extension of the Markowitz investment model was adapted to account for cost variability. The primary goal is to equip transportation planners with a decision-making tool that incorporates uncertainty. A comparative analysis of different objectives is conducted to assess the effects of risk on outcomes. The multi-criteria TOPSIS method was utilized as a robust tool to select solutions for this multi-objective problem. Results reveal that solutions with high entropy and variability balance risk and flexibility, while those minimizing variance offer more stable solutions with lower risk. Consistently minimizing total cost resulted in the lowest costs, but at the same time, it led to the highest risk. The membership level showed that maximizing entropy and minimizing variance generated similar compliance levels, with lower variability in the case of entropy. Cost minimization resulted in lower compliance, indicating a trade-off between cost and effectiveness in the transportation network. The research demonstrates that prioritizing risk minimization enhances the average membership level compared to approaches focused on cost minimization or entropy maximization. By effectively managing and reducing uncertainty in transportation networks, the developed model serves as a tool for managing and reducing uncertainty in a transportation network, enhancing resilience. Furthermore, its adaptability offers potential applications across diverse aspects of logistics and industry, providing a framework for designing more robust, adaptive, and effective operational strategies.