### Literature Review  
In this section, some studies related to the study are surveyed. The following three related problems are discussed in this section: the problem of adding additional trains, line planning problems (LPs), and train timetable problems (TTPs). A practical problem solved in our work is that of adding additional trains. Meanwhile, we aim to design the operation zone, the number of trains, and timetable etc. Two related classic problems, i.e., LPP and TTP, are discussed in this section. The problem of adding trains is an emerging problem that some researchers have begun to address. Researchers [2; 3; 4] studied the problem of adding additional trains. [PERSON] and [PERSON] [2] considered the problem of adding additional trains as a job shop problem and presented a constructive algorithm and simulated annealing approach to solve the model. [PERSON] and [PERSON] [3] studied the problem of inserting additional freight trains into the timetables of existing passenger trains. [PERSON] et al. [4] focused on the problem of adding passenger trains on a high-speed railway corridor, wherein the timetables of existing trains can be modified. Although researchers focused on the problem of adding additional trains, there are still several issues that have not been considered in the literature. First, the number of additional trains was not considered. In most cases of adding trains, more additional trains are better, but researchers have not determined the ideal number of additional trains to save on operating costs and meet passenger demand. Second, the timetables of additional trains, operational zone, stop plan, etc. have not been considered in the literature. Third, passenger demands were ignored in the models of the above studies. The purpose of adding additional trains is to meet passenger or freight demand, so passenger demand is a very important element of the problem of adding additional trains. [PERSON] et al. [5] presented a bi-objective integer programming model to solve the problem of adding additional trains in a high-speed railway corridor in peak periods. The number of trains, stop plans, train types, and timetables for additional trains were designated in the model, in which passenger demand was also considered. However, several problems have not been considered in the above studies. OD passenger demands have not been considered. Although passenger demand was discussed by [PERSON] et al. [5], the number of passengers who get on and off was not tackled. Obviously, OD passenger demand is more accurate than a macroscopic view. The other issue is that the operational zone was not considered. These gaps are addressed herein. The problem of adding trains falls into the scope of railway operations. One related problem is the LPP. LPP involves designing a line system such that travel demand is satisfied and certain objectives are met [6]. Most researchers studied LPP, determining the operational zone and number of trains for each zone without consideration of a timetable [7; 8; 9; 10; 11; 12]. Researchers studying TTP focus on the timetables of trains. TTP is very popular in the area of railway operations, and numerous researchers have given it attention [13; 14; 15; 16; 17; 18; 19]. Recently, passenger demand has become an important factor considered by researchers on TTP [20; 21; 22; 23; 24]. Some researchers on LPP paid attention to passenger demand [25; 26; 27; 28]. Specifically, [PERSON] and [PERSON] [25] introduced a passenger flow assignment product to determine the stop plan under a given operational zone and the frequency for each. A similar passenger flow assignment method is introduced by [PERSON] et al. [27] and [PERSON] et al. [28]. The passenger flow assignment method is referred to in this paper to cope with passenger distribution when adding additional trains. Whether LLP or TTP, most researchers have considered either the operational zone and the number of trains or the timetable.