Supply chain design has garnered significant attention in recent years, as integrated management of the supply chain can mitigate the spread of disruptions across the network and substantially influence the profitability of its stakeholders. Uncertainties, particularly in demand and associated costs, are often inherent in such systems. Traditional approaches typically model these uncertainties as random variables, relying on probability theory for analysis. In this study, we introduce a fuzzy mathematical programming framework tailored for a supply chain that incorporates multiple depots, vehicles, products, customers, and time periods. Unlike conventional models, this approach treats not only demand and costs but also decision variables as fuzzy entities. Two ranking functions are employed to solve the model, which aims to optimize depot selection from potential candidates, allocate orders to depots and vehicles, and assign returning vehicles to depots, all with the objective of minimizing total costs. The model’s validity is demonstrated through numerical experiments and sensitivity analysis. Additionally, a regression model is utilized to evaluate the effectiveness of the applied fuzzy ranking methods.