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In this article, we proposed a programming linear model in integer numbers(PLIN) for the optimal allocation of the time slots in the international Leopold Sedar Senghor airport of Dakar (L.S.S). The slots are specific allocated periods which allow an aircraft to land or take off in a saturated airport. Their attribution depends on the configuration of the airport, more particularly on its capacity. We maximize the confirmed demand in each slot and take the number of aircrafts and the number of manageable passengers with an optimal quality service into account. We used the CPLEX software so that to test the effectiveness of the linear model. Firstly, in the proposed model linear in integer numbers, any unmet demand was isolated. Secondly, the rejected demands by introducing a model and an algorithm of resolution based on the dynamic programming.

The Dynamic Vehicle Routing Problem (DVRP) is a more complex problem than the traditional Vehicle Routing Problem (VRP) in the combinatorial optimization of operations research. With more degrees of freedom, DVRP introduces new challenges while judging the merit of a given route plan. This thesis utilized the time slice strategy to solve dynamic and deterministic routing problems. Based on Group Role Assignment (GRA) and two different routing methods (Modified Insertion heuristic routing and Modified Composite Pairing Or-opt routing), a new ridesharing system has been designed to provide services in the real world. Simulation results are presented in this thesis. A qualitative comparison has been made to outline the advantages and performance of our solution framework. From the numerical results, the proposed method has a great potential to put into operation in the real world and provides a new transit option for the public.