Ridesharing problem attempts to decrease traffic congestion and environmental concerns by matching passengers to drivers with empty seats in their cars. In this work, we model the dynamic ridesharing problem as an optimization problem while both the pick-up and drop off locations of passengers is on the original route of the driver, but either the origin or the destination of passengers is not on the way. Therefore, passengers must walk to reach the pick-up locations or destinations (partial ridesharing). In the other words, in this type of Ridesharing, drivers do not deviate from the original route to satisfy the request of passengers.

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