Mathematical Models for On-Line Train Calendars Generation

Linear Programming Model and Online Algorithm for Customer-Centric Train Calendar Generation

“…is section is mainly focused on the third model presented by Amorosi et al [15]. e reason is related to three different considerations: first, the problem is a niche one, so there is very little material about possible solving methods [16]); second, this paper is the only one that considers the Italian railway context, with its particular passenger timetables; third, the third model is the fastest of the three models presented in their paper.…”

“…e reason is related to three different considerations: first, the problem is a niche one, so there is very little material about possible solving methods [16]); second, this paper is the only one that considers the Italian railway context, with its particular passenger timetables; third, the third model is the fastest of the three models presented in their paper. Furthermore, the simulations studied in Amorosi et al [15] are created with the active participation of Trenitalia, so they can be considered as practical cases, in which real-world characteristics have been considered for the 264 instances used in our numerical experiments.…”

“…e idea underlying the method proposed by Amorosi et al [15] consists of several phases. First of all, the method takes as input a periodicity, which is a binary vector that represents the availability of the train in the time-window queried, and associates with each of its entry a progressive index (we will discuss these input data more in detail in section 3).…”

“…In the absence of the original implementation, to build up a comparison as accurate as possible and directly check the strengths and weaknesses of this approach, we have personally developed a mathematical model strongly inspired by the Amorosi et al's [15] model (a detailed description of this model will be given in section 4). is model has three fundamental differences with the work done in Amorosi et al [15]:…”

“…We next introduce a brief overview of the paper structure: Section 2 reviews the most related literature, specifically the third model proposed by Amorosi et al [15], as this is the only available research paper (to the best of our knowledge) that considers the specific train calendar generation problem in the context of the Italian railways; Section 3 describes how the ICT system works and at what point of the process of sharing our algorithm is inserted, and provides the Integer Linear Programming (ILP) model introduced to model the studied problem, which will be compared in Section 4 with the developed online algorithmic method (i.e., the heuristic algorithm) and outlines the proposed method in all its key phases through a high-level flowchart; Section 4 shows numerical simulations performed, arguing some observations about the performance values achieved by the heuristic algorithm and the ILP model and defining strengths and weaknesses of each approach; Section 5 concludes the paper by summarizing the main findings, by suggesting directions to improve the heuristic algorithm, and by summing up other possible applications of the proposed tool.…”