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

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.

Bus Route Design Problem for Rural Tourism Objectives: A Multiobjective Approach

“…An attractive bus network for rural tourism development can facilitate access opportunities for visitors without cars, attracting new market segments and visitor spending. To promote sustainable transport development in rural destinations, many studies have been implemented from diferent view-angles, such as understanding sustainable transport in rural tourism [15], modeling the sustainable accessibility of rural tourist attractions [16], organizing a public transport route network for tourists, optimizing touring bus schedules [17,18], and regulating the tourist buses [19]. Te design and optimization of a rural tourism bus route network are some of the basic and most efective ways to strengthen sustainable transport services at the early stage of rural tourism destination development and tourist source cultivation.…”

Optimal route planning for day tours in Marinduque, Philippines

“…Route optimization is part of a more general spectrum of problems under spatial optimization where different approaches are used to solve the problems [6]. In spatial optimization, integer programming (IP) and heuristics are often used for route optimization problems [7][8][9][10][11]. In particular, IP is used for the traveling salesman problem (TSP) that aims to find the shortest route given a set of locations that requires the tour to start and end at the same location [10].…”

“…In particular, IP is used for the traveling salesman problem (TSP) that aims to find the shortest route given a set of locations that requires the tour to start and end at the same location [10]. Some applications of integer programming related to route optimization are in mass and personal transportation [9], and tour planning [7,8,11]. Neto et al (2012) formulated an IP model to determine an optimal route in visiting several tourist sites such that the distance traveled is minimized [7].…”

“…The model was formulated as a TSP and an economic insertion technique called 2-Opt route to improve the solution in every iteration [7]. Brandinu and Trautmann (2014) addressed a planning problem for a multi-bus tour using a mixed IP formulation such that no two buses can stay in one location at the same time. The authors introduced symmetry breaking constraints to improve the computation time and followed a two-step methodology: minimize waiting time first then minimize the total travel time of all buses [8].…”

“…Brandinu and Trautmann (2014) addressed a planning problem for a multi-bus tour using a mixed IP formulation such that no two buses can stay in one location at the same time. The authors introduced symmetry breaking constraints to improve the computation time and followed a two-step methodology: minimize waiting time first then minimize the total travel time of all buses [8]. Hasuike et al (2013) proposed a personal tour planning methodology where tour routes and tourists' satisfaction are considered.…”