A mixed-integer linear programming approach to the optimization of event-bus schedules: a scheduling application in the tourism sector

This paper deals with “The Enchanted Journey,” which is a daily event tour booked by Bollywood-film fans. During the tour, the participants visit original sites of famous Bollywood films at various locations in Switzerland; moreover, the tour includes stops for lunch and shopping. Each day, up to five buses operate the tour. For operational reasons, however, two or more buses cannot stay at the same location simultaneously. Further operative constraints include time windows for all activities and precedence constraints between some activities. The planning problem is how to compute a feasible schedule for each bus. We implement a two-step hierarchical approach. In the first step, we minimize the total waiting time; in the second step, we minimize the total travel time of all buses. We present a basic formulation of this problem as a mixed-integer linear program. We enhance this basic formulation by symmetry-breaking constraints, which reduces the search space without loss of generality. We report on computational results obtained with the Gurobi Solver. Our numerical results show that all relevant problem instances can be solved using the basic formulation within reasonable CPU time, and that the symmetry-breaking constraints reduce that CPU time considerably.

The role of the state in investor-state arbitration

The Role of the State in Investor-State Arbitration is a collection of contributions from lawyers, arbitrators and political scientists on the development of the concept of the “State” in a field that currently presents an increasing number of controversial disputes: Investor-State Arbitration. The book analyzes the limits of the host State as a regulator, studying issues such as attribution and the role of State-Owned Enterprises and sub-State entities; the changing role of the home State in Investor-State disputes, including its direct participation in Investor-State arbitration and State to State dispute settlement; and the overall role that both home and host States can play in the improvement of Investor-State Dispute Settlement.