Main motto of ship routing and scheduling is to reduce the total transportation cost of each ship or vessel without interrupting the demand and supply. In this study, we have proposed a ship routing and scheduling model for commercial ships where, to ensure unhindered demand and supply of products at various ports in a fixed time frame, the dynamic demand and supply of each port were considered under a fuzzy environment. Additionally, simultaneous loading and unloading and a fixed load factor is used to minimize port time and reduce risks, and this aspect of our work makes it realistically inclined. We also show, in our work, speed optimization to reduce fuel consumption and carbon emission. In practice, cost parameters cannot be always determined, it fluctuates at a certain range from time to time. We have treated the imprecise cost parameters as triangular fuzzy numbers. With a view to working with the developed model, a modified genetic algorithm (MGA) with a new selection technique, namely an in-vitro-fertilization-based crossover, and a generation-dependent mutation is proposed. The proposed sustainable ship routing algorithm with dynamic demand and supply in an uncertain environment gives a novelty in the literature. Another novelty is incurred through the proposed MGA in the heuristic search algorithms. This algorithm has produced numerical results superior to those of other heuristic algorithms. We have also established the efficiency of the proposed algorithm through statistical experiments.