旅客量指派均衡下之列車整合座位配置模式

An Integrated Seat Allocation Model for Scheduled Trains under Passenger Assignment Equilibrium

本研究考慮多列列車座位配置及各時段旅運需求選擇均衡行為，建立一雙層列車間最適座位配置模式。上層模式求解各列車最佳座位配置以最大化整體客座利用率及最小化旅客總旅行成本；下層模式則利用使用者均衡進行旅客量指派。其中，乘客旅行成本包含貨幣成本、旅行時間、行程延滯及訂票困難度。由於雙層數學模式求解相當困難，故本文利用遺傳演算法求解上層模式，並以染色體代表各列車各起迄座位配置方案，同時以Frank-Wolfe 演算法求解下層乘客列車指派均衡問題。最後，以臺鐵實際訂票資料進行實例應用探討。結果顯示模式能有效分配各列車各起迄對最適之座位配置數，同時透過使用者均衡分析也發現在尖峰時段，旅客能選到成本最低列車的比例遠低於離峰時段。

This study aims to propose a bi-level seat allocation model among neighboring trains by accommodating the train choice behaviors of travelers, where the upper level is to maximize overall railway seat utilization ratio and total passenger travel cost and the lower level is an user equilibrium model in which passengers with various departure times tend to choose their best train with the minimal generalized travel cost, including out-of-pocket cost, in-train travel time, schedule delay, and difficulty in seat booking subject to the available seats allocated by the upper level. Due to the complexity of bi-level models, this study employs genetic algorithms (GAs) to solve the upper level problem where a chromosome represents a feasible seat allocation plan of all trains in consideration. The goodness fit of the chromosome is the objective value of the upper level which is determined by passenger assignment of the lower level solved by Frank-Wolfe algorithm. To investigate the applicability of the proposed model, a field case of Taiwan Railway Administration is then conducted. The results show the proposed model can successfully determine the best of seat allocation of all trains in consideration. It is also found that the proportion of passengers in choosing their lowest travel cost train during rush hours is much lower than that of off-peak passengers.