Solving Car Pooling Problem using DCA

Car pooling is a well known transport solution that consists in sharing a car between a driver and passengers sharing the same route, or part of it. The challenge is to minimize both the number of required cars and the additional cost in terms of time for the drivers. There are two resulting problems that are interdependent and NP-complete: assigning passengers to cars and finding the shortest path for the drivers so that the overall cost is minimized. In this paper, we present the formulate of Car pooling problem as a Mix Integer Linear Program (MILP) and then investigate a new solution method based on DC (Difference of Convex functions) programming and DCA (DC Algorithms). In order to globally solve the problem, we combine DCA with classical Branch and Bound algorithm (BBDCA). DCA is used to calculate upper bound while lower bound is calculated from a liner relaxation problem. Preliminary numerical results which obtained by DCA and BBDCA are compared with CPLEX, the best solver for MILP. They show that the proposed algorithm is an efficient algorithm for solving MILP.