軌道對號列車最佳配位模式之建立 ─以臺鐵北迴線為例

座位分配對鐵道營運與服務相當重要，惟大多數座位分配之研究係以營運收益作為最佳化目標。然而，以政府管理單位性質之臺鐵而言，座位分配之效率性與公平性應較追求營運收益更為重要。基此，本研究旨在構建一個同時追求利用率及公平性最大之臺鐵對號列車座位分配最佳化模式。此外，由於乘客於相鄰列車班次間（例如，半小時或一小時內）之選擇偏好可能差異不大，故本模式除可求解單一列車之座位分配最佳化外（稱為單一列車模式），也可同時求解相鄰班次且具有不同停站型態多班列車之座位最佳化分配（稱為多列車模式）。其中，本研究所定義之利用率，係以延人公里佔延座公里之比例表之；而公平性則以起訖站間之座位分配數量與實際需求數量間差距之平方值表之。單一列車模型僅呈現單一列車的座位分配最佳化，而多列車模式則可考量列車停站型態及旅次需求之不同，而求解特定時段內相鄰列車座位分配的最佳化情形。至於模式求解時，兩目標函數係以簡單加權法合併為單一目標後，利用遺傳演算法加以求解。為驗證本模式之可應用性，本研究以臺鐵北迴鐵路段作為研究對象，並探討利用率與公平性之加權權重值變化下之座位分配求解結果是否合理。研究結果顯示當公平性權重增加時，配位公平性值會隨之提升。此外，即便僅以公平性為單一目標，座位利用率仍可維持在70%左右。而且，多列車模式之求解結果明顯優於單列車模式，其中，尤以公平性指標更為明顯。關鍵字：座位配置、利用率、公平性、遺傳演算法。

關鍵字

座位配置；利用率；公平性；遺傳演算法

並列摘要

Seat allocation is essential for train operation and service. Most of previous studies attempt to optimize seat allocation towards efficiency (maximizing service) or revenues (yield management). However, for the case of Taiwan Railway Administration (TRA), a national administration, it is more important to maximize its service capacity and equity among different service areas. Based on this, this study aims to develop a seat allocation optimization model for reservation-based trains to simultaneously maximize efficiency and equity of a train or neighboring trains subject to train capacity, namely the single train model and the multiple train model. Where, efficiency is defined as a load ratio standing for the total passenger-km divided by total seat-km of a train/trains and equity is the squared difference between allocated seats and real demand among different origin-destination (OD) station pairs. The Single train model considers the optimum of a single train alone; while the Multiple train model simultaneously optimize the seat allocation of neighboring trains within a certain time periods (e.g., one hour) due to different stopping patterns of trains and schedule flexibility of passengers. In order to solve the proposed models, a simple weighted sum of two normalized objective functions is used and solved by genetic algorithms (GAs). To investigate the applicability of the proposed models, a case study on the North-link Line of Taiwan Railway Administration is conducted by varying weights between efficiency and equity. The results show that when the weight of equity increases, the equity value enhances (the deviation of reserved seat from real demand decreases) at the expense of load ratio. However, even only consider the equity objective alone, the load ratio remains above 70%. Additionally, it is also found that the Multiple train model performs better than the Single train model, especially in terms of equity. Keywords: Seat allocation, Efficiency, Equity, Genetic algorithms.