Abstract
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.
Similar content being viewed by others
References
Baumann, T., & Schiess, U. (2008). Satellitenkonto Tourismus der Schweiz, 2001 und 2005—Grundlagen, Methodik und Ergebnisse. Neuenburg: Bundesamt für Statistik.
Bektas, T. (2006). The multiple traveling salesman problem: An overview of formulations and solution procedures. Omega, 34, 209–219.
Brandimarte, P. (2013). Scheduling satellite launch missions: An MILP approach. Journal of Scheduling, 16, 29–45.
Chen, J. S. (2002). An integer programming model for the open shop scheduling problem. Journal of Far East College, 21, 211–216.
Goel, A. (2012). A mixed integer programming formulation and effective cuts for minimising schedule durations of Australian truck drivers. Journal of Scheduling, 15, 733–741.
Goel, A., & Rousseau, L. M. (2012). Truck driver scheduling in Canada. Journal of Scheduling, 15, 783–799.
Graves, S. C. (1981). A review of production scheduling. Operations Research, 29, 646–675.
Kara, I., & Bektas, T. (2006). Integer linear programming formulations of multiple salesman problems and its variations. European Journal of Operational Research, 174, 1449–1458.
Müller, H. (2001). Tourism and hospitality into the 21st Century. In A. Lockwood & S. Medlik (Eds.), Tourism and hospitality in the 21st century (pp. 61–70). Oxford: Butterworth Heinmann.
Simpson, R., & Abakarov, A. (2013). Mixed-integer linear programming models for batch sterilization of packaged-foods plants. Journal of Scheduling, 16, 59–68.
Solomon, M. M. (1987). Algorithms for the vehicle routing and scheduling problems with time window constraints. Operations Research, 35, 254–265.
Wagner, H. M. (1959). An integer linear-programming model for machine scheduling. Naval Research Logistics Quarterly, 6, 131–140.
Yu, V., Lin, S. W., & Chou, S. Y. (2010). The museum visitor routing problem. Applied Mathematics and Computation, 216, 719–729.
Yu, W., Zhaohui, L., Leiyang, W., & Fan, T. (2011). Routing open shop and flow shop scheduling problems. European Journal of Operational Research, 213, 24–36.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Brandinu, G., Trautmann, N. A mixed-integer linear programming approach to the optimization of event-bus schedules: a scheduling application in the tourism sector. J Sched 17, 621–629 (2014). https://doi.org/10.1007/s10951-014-0375-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10951-014-0375-z