The paper describes a multi-objective mathematical model for Dial a Ride Problem (DRP) and an application of Multi-Objective Simulated Annealing (MOSA) to solve it. DRP is to take over the passenger from a place of departure to a place of arrival. In the DRP, customers send transportation requests to an operator. A request consists of a specified pickup location and destination location along with a desired departure or arrival time. The ultimate aim is to offer an alternative to displacement optimized individually and collectively. The DRP is classified as NP-hard problem that’s why most research has been concentrated on the use of approximate methods to solve it. Indeed the DRP is a multi-criteria problem, the proposed solution of which aims to reduce both route duration in response to a certain quality of service provided. In this work, we offer our contribution to the study and solving the DRP in the application using the MOSA algorithm. Tests show competitive results on (Cordeau and Laporte, 2003a) benchmark datasets while improving processing times