Planning the departure of vacant transit vehicles to the median stops in a single line

In transit lines planning, a common issue is that transit vehicles get overcrowded as they arrive at some intermediate stops. Dispatching a portion of vacant transit vehicles to the intermediate stops may seem to be a suitable solution for this problem. This study aimed at explaining whether or not this solution can assist in enhancing the system performance in terms of the total discomfort of transit users. A mixed integer nonlinear model was proposed by adopting some simplifying assumptions. The vehicles' headway and the first boarding stop for each vehicle were the decision variables in the proposed model. The solution algorithm was a kind of hybrid algorithm consisting of a convex programming solver and a Tabu search algorithm. The results, interestingly, indicated that the total discomfort of transit users increased after dispatching vacant vehicles to the intermediate stops, although some transit users in intermediate stops may profit from dispatching vacant vehicles.