Abstract
The paper describes a multi-objective mathematical model for the 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, passengers send transportation requests to an operator. 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 which aims to reduce both route duration in response to a certain quality of service provided. Actually, during the system of transport on demand (TOD) there are many problems can inhibit the proper functioning of the system, such as failure of the car and bottling etc. We propose a resolution of the dynamic DRP using a service of TOD called TOD with Simulated Annealing (TOD-SA). The solution proposed in this paper enables both a reduction of travel time also the distance traveled.