This study develops and solves a bi-objective optimization model for an inbound assembly inventory routing problem (IRP), considering carbon emission control, stochastic supply failure risks, and uncertainty in customer demand. An assembly plant needs three different components to assemble a product based on a particular bill of materials (BOM). These components are outsourced from various geographically dispersed suppliers. A depot provides light, medium, and heavy-duty vehicles to pick up product components from these suppliers during a particular period. The first objective function of the mixed-integer nonlinear model is to minimize the total IRP network cost. The second objective function is to reduce the total carbon emission. The model also considers constraints to achieve a minimum service level in each period and avert purchasing from high-risk suppliers. The best near-optimal Pareto fronts of problem instances are obtained using a hybrid non-dominated sorting genetic algorithm-II (HNSGA-II). The best near-optimal Pareto solution is determined using multi-criteria decision-making (MCDM) techniques. The impacts of different vehicle fleet types on the inbound IRP network's performance are also investigated. Finally, the sensitivities of important time-varying parameters are reported using a full factorial-designed experiment, and several insights and recommendations are provided.