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The paper describes a multi-objective mathematical model for the Dial a Ride Problem (DRP) and an application of the Multi-Objective Simulated Annealing (MOSA) to solve the dynamic DRP. Indeed, different versions of the dynamic Dial a Ride Problem are found in every day practice; transportation of people in low-density areas, transportation of the handicapped and elderly persons and parcel pick-up and delivery service in urban areas. The problem is to affect every new passenger request to one of the vehicles and to design a new route and schedule for this vehicle. This affectation must be done in real time. In this work, we offer our contribution to the study and solving the dynamic DRP in the application using the MOSA algorithm. Numerical results show the benefits of this algorithm in a real-time context.