Purpose: Spurred by the high turnover in the pharmaceutical industry, locating pharmacies inside urban areas along with the high product perishability in this industry, the pharmaceutical supply chain management has recently gained increasing attention. Accordingly, this paper unveils an inventory-routing problem for designing a pharmaceutical supply chain with perishable products and time-dependent travel time in an uncertain environment. Design/methodology/approach: In this study, mathematical programming is employed to formulate a multi-graph network affected by the traffic volume in order to adapt to real-world situations. Likewise, by transforming the travel speed function to the travel time function using a step-by-step algorithm, the first-in-first-out property is warranted. Moreover, the Box–Jenkins forecasting method is employed to diminish the demand uncertainty. Findings: An appealing result is that the delivery horizon constraint in the under-study multi-graph network may eventuate in selecting a longer path. Our analysis also indicates that the customers located in the busy places in the city are not predominantly visited in the initial and last delivery horizon, which are the rush times. Moreover, it is concluded that integrating disruption management, routing planning and inventory management in the studied network leads to a reduction of costs in the long term. Originality/value: Applying the time-dependent travel time with a heterogeneous fleet of vehicles on the multi-graph network, considering perishability in the products for reducing inventory costs, considering multiple trips of transfer fleet, considering disruption impacts on supply chain components and utilizing the Box–Jenkins method to reduce uncertainty are the contributions of the present study.

In the dynamic and intricate domain of social networks, precise identification and ranking of influential nodes are essential for effective information dissemination, strategic decision making, and optimal resource allocation. Conventional centrality metrics frequently yield unstable outcomes due to their limited capacity to capture the multidimensional nature of influence. To address this challenge, a novel hybrid data-driven framework is introduced, comprising three integrated stages. Initially, sophisticated machine learning algorithms, namely Random Forest, XGBoost, and CatBoost, are applied to determine objective weights for six centrality metrics: The following centrality measures are examined: degree centrality, betweenness centrality, closeness centrality, eigenvector centrality, PageRank, and the global clustering coefficient-dependent degree centrality. These weights are derived from real-world data, guided by the Susceptible Infected Recovered diffusion model. In the subsequent stage, the TOPSIS method consolidates these weighted metrics to generate preliminary node rankings, thereby establishing training labels for subsequent modeling. In the final stage, a Multi Layer Perceptron neural network predicts influence scores with enhanced autonomy and precision. This network leverages structural features to rank nodes without requiring repeated TOPSIS execution. The validation of the proposed framework was conducted on four benchmark datasets: Zachary's Karate Club, American College Football, Dolphin Social Network and Bitcoin-OTC. The findings indicate that the proposed framework demonstrates superior accuracy, robustness to structural noise, and generalizability across both unsigned and signed graphs when compared to traditional single metric approaches. The outcomes underscore the framework's adaptability across diverse network structures, offering a robust instrument for advancing network science research and applications.