Abstract
This paper studied the train stop planning problem with variable train length and stop time under stochastic demand (TSPPWVTLSTSD). As we know, stop time and train length were often considered in a fixed manner in train stop planning for high-speed rail (HSR). One obvious disadvantage was that it often resulted in insufficient time for passengers to get on or get off a train. In addition, fixed train length may cause a waste of train capacity. And travel demand was usually assumed to be deterministic, although travel demand usually was stochastic. In this paper, we presented an optimization model that simultaneously optimized the stop-schedule, the stop time schedule and the train length schedule for each train trip under stochastic demand. By formulating deterministic equivalents to the chance constraints, we obtained a deterministic mixed integer model. To solve the problem, a novel column generation-based heuristic solution technique based on Dantzig-Wolfe decomposition principle and column generation procedure was proposed. Some numerical experiments and a case study based on real-world data were used to demonstrate that the proposed solution method can yield a service plan within a reasonable time compared with ILOG Cplex. Besides, the variable train length and stop time model needed fewer carriages and also gave rise to less total time loss compared with the fixed scenario.
Highlights
Constructing a reasonable service plan is of vital importance both to high-speed rail operators and passengers
The Dantzig–Wolfe decomposition technique and column generation procedure were mainly used to generate the set of possible combinations of stop-schedules, train length schedules and stop time schedules for train trips
Defines the set of possible combinations of stop-schedules, train length schedules and stop time schedules for train trips on route r based on constraints (20)-(33), where proj(xr,yr,wr )X r represents the projection of X r in space xr, yr, wr
Summary
Constructing a reasonable service plan is of vital importance both to high-speed rail operators and passengers. Wang et al [17] studied LPP using a two-layer nonlinear optimization model, in which transit routes, the stop-schedule of each individual train trip, and passenger assignments were determined. Based on classified stations and categorized passenger flows, Zhang et al [27] proposed an integrated optimization method for a high-speed rail stop-schedule plan, which contained an integer programming model. Furini et al [60] proposed a column generation–based formulation for the twodimensional two-staged guillotine cutting stock problem with multiple stock size, in which the slave problem was a mixedinteger linear model They developed a column generation heuristic algorithm to solve the problem. Constraints (14)–(18) give restrictions on decision variables: xgrp ∈ {0, 1} ∀r ∈ R, g ∈ r , p ∈ Sr (14)
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