Optimization of Multi-depot Semi-open Cold-Chain Logistics Paths Under Time-Dependent Road Networks

To address the inefficiencies and high loss rates in urban cold-chain logistics, this study investigates a complex distribution scenario characterized by a multi-depot semi-open structure, time-dependent road networks, and simultaneous pickup and delivery. A comprehensive mathematical model is developed to minimize total costs, incorporating cold-chain product deterioration, vehicle energy consumption, and customer time windows. To solve this combinatorial optimization problem effectively, a hybrid metaheuristic algorithm (FA–LNS) is proposed, which integrates the global exploration capability of the Firefly Algorithm (FA) with the local refinement strength of Large Neighborhood Search (LNS). The FA component is adapted with a discrete position update strategy, while LNS performs solution-space intensification through targeted destruction and repair operations. Extensive experiments, including benchmark comparisons with exact methods and existing heuristics, demonstrate the superior performance of FA–LNS in terms of solution quality and computational efficiency. Furthermore, sensitivity analyses are conducted on key logistics parameters—vehicle departure times, dynamic driving speeds, and return strategies—highlighting the importance of modeling time-varying congestion, semi-open routing flexibility, and departure-time optimization. The findings offer actionable managerial insights to support strategic decision-making in cold-chain logistics.