Heterogeneous vehicle scheduling with precedence constraints

The problem of heterogeneous vehicle scheduling with precedence constraints is inspired by the transportation service in tourism areas. Tourists must take the shuttle vehicles provided by the areas because of the long distances between the scenic spots. The scheduling of vehicles in tourism areas is complicated because the transportation requests of tourists are precedence-constrained temporally and spatially. The problem optimises both the cost of using vehicles and the waiting time of tourists. A mixed-integer linear programming model is formulated according to the description of a graph. An adaptive large neighbourhood search algorithm with several specialised operators is designed to solve the problem. Experiments based on randomly generated instances validate the mathematical model and the algorithm. A real-size instance based on Qiandao Lake in China is also analysed. The results indicate that the algorithm outperforms the model. The sensitivities of key parameters are analysed with managerial insights presented.