| Summary: | High turnover in the pharmaceutical industry, the location of placebos in urban spaces, and the high rate of corruption of products in this industry are the distinguishing features of the drug supply chain. Thus, to survive and maintain competitive advantages in the current business environment, managers are active in this background to implement the theoretical foundations of supply chain management. One of the influential areas in this category is integrated inventory management, inventory control, and vehicle routing. Therefore, this study mainly aims to analyze and define a routing problem, inventory in the drug supply chain with perishable products, and travel time dependence on multiple graphs with travel time dependence. The Box–Jenkins forecasting method has been utilized to meet the study’s aim and deal with demand uncertainty. This method can identify the best pattern governing the data. Finally, the mathematical model is validated, and managerial perspectives are provided. The study results demonstrated the possibility of achieving cost-saving and reducing product spoilage. Applying the solutions of this model can provide some inherent social and environmental advantages, including reducing traffic load and emissions.
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