In the recent era, the rapidly increasing trend of e-commerce business creates opportunities for logistics service providers to grow globally. With this growth, the concern regarding the implementation of sustainability in logistic networks has received attention in recent years. Thus, in this work, we have focused on the vehicle routing problem (VRP) to deliver the products in a lesser time horizon with driver safety concern considerations in business (B2B) e-commerce platforms. We proposed a sustainable logistics network that captures the complexities of suppliers, retailers, and logistics service providers. A mixed-integer nonlinear programming (MINLP) approach is applied to formulate a model to minimize total time associated with order processing, handling, packaging, shipping, and vehicle maintenance. Branch-and-bound algorithms in the LINGO optimization tool and genetic algorithm (GA) are used to solve the formulated mathematical model. The computational experiments are performed in eight different case scenarios (small-sized problem to large-sized problem) to validate the model.