A car pooling model and solution method with stochastic vehicle travel times

Carpooling is one method that can be easily instituted and can help resolve a variety of problems that continue to plague urban areas, ranging from energy demands and traffic congestion to environmental pollution. However, most carpooling organizations currently use a trial-and-error process, in accordance with the projected vehicle travel times, for carpooling, which is neither effective nor efficient. In other words, stochastic disturbances arising from variations in vehicle travel times in actual operations are neglected. In the worst case scenario, where vehicle travel times fluctuate wildly during operations, the planned schedule could be disturbed enough to lose its optimality. Therefore, we constructed a stochastic carpooling model that considers the influence of stochastic travel times. The model is formulated as an integer multiple commodity network flow problem. Since real problem sizes can be large, it could be difficult to find optimal solutions within a reasonable period of time. Therefore, we develop a solution algorithm to solve the model. To test how well the model and the solution algorithm can be applied to the real world, we also developed a simulation-based evaluation method. To test the model and the solution algorithm, a case study is performed based upon data reported from a past study carried out in northern Taiwan. The results show that the model and solution algorithm are good and could be useful for carpooling practices.