Last-Train Timetabling under Transfer Demand Uncertainty: Mean-Variance Model and Heuristic Solution

Abstract

Traditional models of timetable generation for last trains do not account for the fact that decision-maker (DM) often incorporates transfer demand variability within his/her decision-making process. This study aims to develop such a model with particular consideration of the decision-makers' risk preferences in subway systems under uncertainty. First, we formulate an optimization model for last-train timetabling based on mean-variance (MV) theory that explicitly considers two significant factors including the number of successful transfer passengers and the running time of last trains. Then, we add the mean-variance risk measure into the model to generate timetables by adjusting the last trains' departure times and running times for each line. Furthermore, we normalize two heterogeneous terms of the risk measure to provide assistance in getting reasonable results. Due to the complexity of MV model, we design a tabu search (TS) algorithm with specifically designed operators to solve the proposed timetabling problem. Through computational experiments involving the Beijing subway system, we demonstrate the computational efficiency of the proposed MV model and the heuristic approach.

Optimal Coordination of Last Trains for Maximum Transfer Accessibility with Heterogeneous Walking Time

“…As an extension of Kang et al [4], Kang et al [7] proposed a mixed integer linear programming (MILP) model, which was solved by CPLEX upon applying a two-phase decomposition method. Yang et al [8] further constructed a last train timetabling model considering the uncertainty of transfer demand based on the mean-variance theory. Yin et al [22] formulated a bilevel programming model to decide the departure times and the dwell times of last trains, in which the upper level is to maximize the social service efficiency including social welfare (the sum of successful transfer passengers) and subsidy, and the lower level is to minimize the revenue loss for the operating companies, i.e., the difference between the operation cost and subsidy.…”

Integrated Optimization on Train Control and Timetable to Minimize Net Energy Consumption of Metro Lines

“…Additionally, the solution space is quite large in this integrated optimization problem, and the variables are continuous. Therefore, it is necessary to enhance the local search ability of genetic simulated annealing (GSA) algorithm, and neighborhood search strategy (or local search) is used which has been proved to be an effective search technique and is widely implemented in railway operation and management [45][46][47][48]. The procedure of NS-GSA is shown in Figure 8.…”

A Passenger-Oriented Optimization Model for Implementing Energy-Saving Strategies in Railway Contexts

“…This work, instead, is focused on strategies involving the design of suitable speed profiles and the optimization of operational parameters within the timetable by taking into account effects on user perspectives. Indeed, recently, numerous studies have been developed for analyzing user behaviors and related quality perceptions (see, for instance, [23][24][25][26][27][28][29][30][31][32][33][34][35]) in the case of transportation systems, including rail and metro systems.…”

“…where v max ot and v max rt are the maximum travel speeds reached by a rail convoy in the Time Optimal scenario (i.e., the maximum performance scenario) associated, respectively, with the outward trip (ot) and the return trip (rt); v min ot and v min rt are non-null conventional minimum speeds for which the rail service make sense (for instance, the pedestrian speed equal to 4 km/h) associated, respectively, with the outward trip (ot) and the return trip (rt). Hence, according to Equation (33), speed limits are defined in non-empty compact (i.e., closed and limited) sets by satisfying the non-emptiness and compactness conditions. Moreover, functions TRT ESS ot (•) and TRT ESS rt (•) are expressed as compound functions of continuous functions and, therefore, are continuous.…”