Urban transportation systems are subject to a high level of variation and fluctuation in demand over the day. When this variation and fluctuation are observed in both time and space, it is crucial to develop line plans that are responsive to demand. A multi-period line planning approach that considers a changing demand during the planning horizon is proposed. If such systems are also subject to limitations of resources, a dynamic transfer of resources from one line to another throughout the planning horizon should also be considered. A mathematical modelling framework is developed to solve the line planning problem with a cost-oriented approach considering transfer of resources during a finite length planning horizon of multiple periods. We use real-life public transportation network data for our computational results. We analyze whether or not multi-period solutions outperform single period solutions in terms of feasibility and relevant costs. The importance of demand variation on multi-period solutions is investigated. We evaluate the impact of resource transfer constraints on the effectiveness of solutions. We also study the effect of period lengths along with the problem parameters that are significant for and sensitive to the optimality of solutions.

城市交通系统在一天中会出现高度变化和需求波动的情况。当在时间和空间上都观察到这种变化和波动时，制定响应需求的线路计划至关重要。提出了一种多周期生产线计划方法，该方法考虑了计划范围内需求的变化。如果这样的系统也受到资源的限制，则还应考虑在整个计划范围内将资源从一条线动态转移到另一条线。开发了数学建模框架以考虑到在多个期间的有限长度计划期间进行资源转移的以成本为导向的方法来解决线路计划问题。我们使用现实生活中的公共交通网络数据作为计算结果。我们从可行性和相关成本方面分析多期解决方案是否优于单期解决方案。研究了需求变化对多周期解决方案的重要性。我们评估资源转移约束对解决方案有效性的影响。我们还研究了周期长度的影响，以及对解决方案的优化非常重要且敏感的问题参数。