###### Abstract  
The intercity railway is subject to variation and fluctuation in demand both in time and space over a day to a large extent. In that case, more advanced line planning techniques are practically needed to match the non-equilibrium passenger demand. We propose an integer linear programming model for adapting to the fluctuating demand and improving rail line profit, in which the multi-period planning approach and flexible train composition mode are taken into consideration. In particular, we also consider the limitations of the carriage and the dynamic transfer of resources during a finite period to ensure the better implementation of the line planning and subsequent operation plans. Our purpose is to improve on previous line planning models by integrating the multi-period strategic-level line planning decision with resource constraints. Since the problem is computationally intractable for realistic size instances, an improved round heuristic algorithm that is based on linear relaxation is proposed and we compare the round heuristic performance with the commercial solver Gurobi on artificial instances. The numerical experiments that are based on an intercity railway in China certify the effectiveness and applicability of the proposed model and algorithm. We evaluate the impact of different optimization parameters and reserved carriages and the computation results show that in comparison to the fixed composition mode, the proposed approach can improve the utilization efficiency of carriage resources and increase the line profit by 1.9% under the same carriage resource conditions. line planning; flexible compositions; fluctuating demand; multi-period; carriage resources transfer; intercity railway +
Footnote †: journal: Applied  
rate of rolling stocks, and then further save operation costs [1; 2; 3; 4], which is conducive to the sustainable development of the transportation industry [5]. This paper proposes an integer linear programming model for adapting to the fluctuating demand considering carriage resources transfer under flexible compositions. We are motivated by the study of [PERSON] [6] and [PERSON]. [7]. The line planning problem with fluctuating demand was treated by [PERSON] [6] and he presented a multi-period line planning mathematical model framework. There are three important features that are considered in that model: first, the variation and fluctuation of demand in both time and space are considered; second, a dynamic transfer of resources from one line to another throughout the planning horizon is considered; third, the available capacities are given by the line decisions, which generalizes the way of introducing the capacity through the number of carriages. While this model implicitly assumes that all trains stop at all stations and the passenger demand in both directions of the intercity line is symmetrical. [PERSON] proposed an optimization model of the train plan on the intercity railway that was oriented for elastic demand to maximize train operation benefits. Their models optimize the train stop schemes and departure times. However, only the line planning in one direction is generated and the transfer of resources between periods is not considered. In this paper, we concentrate our efforts on solving the line planning problem with asymmetrical fluctuating demand, multi-type stop-patterns, and limited carriage resources for a given intercity line. The main scientific contributions of this paper are as follows:  
1. We consider a multi-period planning problem incorporating line frequency, capacity, stop-pattern, and the transfer of resources. 2. Given the asymmetric fluctuating demand, the upstream and downstream line planning are generated simultaneously. 3. Resource transfer between different periods and different directions is considered to ensure the availability and allocation of operational resources throughout the periods. 4. Under the limited resources, the behavior that passengers may choose an alternative mode or continue to wait is considered. 5.