This paper discusses the development of a robust optimization model of vehicle routing problems carried out from multiple depots to meet consumer requirements for simultaneous delivery and pickup of products from customer locations as implemented in closed-loop logistics. In this proposed optimization model, we considered the uncertainty of travel time and service time at each consumer location. The proposed robust optimization model aims to generate travel routes and vehicle scheduling from multi-depot by anticipating travel time uncertainty between locations and the uncertainty of the number of products delivered and picked up, resulting in uncertainty of service time needed at each consumer location. In this research, the uncertainty of travel times and service times are expressed in discrete scenarios with certain probabilities. The objective function of the developed robust optimization model of multi-depot vehicle routing problem with simultaneous deliveries and pickups (MDVRPSDP) is to minimize the expected total costs of fixed costs of using the vehicles and the expected variable costs of vehicle trips from all depots. The method for solving this robust optimization model applied two-stage methods, namely clustering the consumer locations served by each depot by using the set partitioning model. Furthermore, the vehicle routing and scheduling optimization were applied to each customer clustering of each depot and solved by using Gurobi-Python optimization. Numerical experiments have been conducted to evaluate the robust optimization model and the proposed solution method. The experimental results pointed out the effectiveness of the optimization model and the efficiency of the computational time of the proposed solution method for medium-scale problems. This proposed robust optimization model for MDVRPSDP can be applied in practical applications of closed-loop logistics such as distribution systems of fuel, blood, consumable products, etc.