A Mathematical Model of the Car Operation Problem in Multi-car Elevator Systems

The purpose of this study is to model the car operation problem in multi-car elevator systems. The multi-car elevator system is such a system that more than one car is installed in every elevator shaft. To take its full advantage, intelligent car operation is necessary so that neither collisions nor reversal occurs. In this paper we will propose a mathematical model for the car operation problem in multi-car elevator systems. First, it will be formulated as a mixed-integer linear programming problem, and next a branch-and-bound algorithm will be proposed. Then, the validity of the model and the effectiveness of the algorithm will be examined by numerical experiments.