ABSTRACTTrain stopping scheduling has a great influence on both
the user''s travel time loss and the operator''s operating cost
and profit in a high speed rail (HSR) system. This research
develops a fuzzy multiobjective optimal model for train stopping
scheduling which integrates the train stopping schedule and the
operations plan. The objectives of the model are the operator''s
operating costs, the user''s travel time loss, and the operator''s
operating profits. Optimal solutions of the model include the
train stopping schedule, frequency, vehicle fleets, and seats
allocation, which are determined simultaneously according to the
many-to-many demand distribution pattern. The model can be used
to analyze how the optimal train stopping schedule is affected
by the demand distribution pattern.In fuzzy multiobjective
programming, the augmented max-min operator is used to guarantee
a nondominated compromise solution. In order to obtain a
reasonable compromise solution, the positive-ideal solutions are
modified to ensure their non-dominance.The fuzzy multiobjective
optimal model to be solved is a nonlinear integer programming
model. Instead of using links in the train stopping schedule,
the model uses stations representing nodes as variables. As a
result, this nonlinear model can be easily transferred into a
linear integer programming model, as stations can be treated
independently. This optimal approach is usually applicable for
small scale problems. To accommodate a large scale problem, this
research develops heuristic algorithms by using a compensatory
fuzzy sets aggregation operator. The operating cost obtained by
the heuristic algorithms is the same as the optimal solution,
and the difference on the user''s travel time is less than 5%. In
addition, the difference between the lower bounds of operating
costs estimated by the heuristic algorithms and that of the
optimal solution is less than 1.4 %. The lower bounds of
frequency and vehicle fleets obtained by the heuristic
algorithms are closed to the optimal solution. The empirical
study indicates that the heuristic algorithms have practical
advantages over optimal approaches.To analyze how the
uncertainty of the demand volume, fare, and operating unit costs
affects the train stopping schedule and the operations plans, a
possibilistic multiobjective programming model is developed by
integrating the centroid rule for defuzzifying the fuzzy
parameters. The model simplifies existing solution procedure
such as α-cut and possibilistic theory. It can always obtain
the optimal compromised solution among different parameters, and
generate better possibilistic distributions of the objectives
than existing methods.An empirical research is undertaken for
the HSR system in Taiwan. Some conclusions can be summarized as
follows:1. When the number of fixed train stopping schedules
increases from four to seven, the annual operating cost and the
user''s travel time cost decrease from NT$ 6.8 billions to NT$
5.8 billions. The optimal solution with variable train stopping
schedules indicates that the operating cost and the user''s
travel time cost decrease from NT$ 5.8 billions to NT$ 5.6
billions in comparison with the case of seven fixed train
stopping schedules. This suggests that the better the train
stopping schedules matches the demand distribution pattern, the
more the operating cost and the user''s travel time cost can be
reduced.2. The use of the express service and the skip-stop
service in the train stopping schedules can reduce the operating
cost and the user''s travel time cost.3. The fuzzy multiobjective
optimal model can be used to analyze the optimal vehicle
capacity of the HSR system.The results of this research can be
used as the guidelines for optimal train stopping scheduling,
operations planning, and station planning and design. The
optimal train stopping scheduling model developed can serve as a
basis for train scheduling in a HSR system.l time loss and the
operator''s operating cost and profit in a high speed rail (HSR)
system.