Operation Planning for Freight Block Trains Using Released Transport Capacity of Existing Railways

China boasts a vast territory with uneven distribution of resources. Therefore, railway has become the primary way to transport goods and passengers, exerting great impacts on national economy and people’s livelihood. In recent years, the transport demand of both goods and passengers is soaring in the transport corridors between major Chinese cities. However, many trunk railways are almost saturated [1]. The lack of capacity has limited the transport of goods other than those essential to livelihood, such as coal, ore and grain. The railway freight transport is further restricted by the fact that passenger trains have superior track occupancy rights over freight trains. Therefore, the traditional railway transport services (e.g. through trains, transit trains and district trains) are not suitable for transferring goods with high demand of timeliness and high additional value.

The plight of railway freight transport is expected to lighten with the emerging passenger-dedicated lines (PDLs) across China. Some passenger trains have been relocated from existing railways to the PDLs, releasing a great amount of route capacity for freight transport. Statistics show that the operation of four PDLs (Jinan–Qingdao, Beijing–Tianjin, Wuhan–Guangzhou and Shanghai–Ningbo) alone released a route capacity of 230 million ton per year [2]. According to official plans, China will complete a “Four Vertical and Four Horizontal” network of the PDLs, releasing even more route capacity of existing railways. To fully utilize the released capacity, it is necessary to optimize the trainload service for railway freight transport, including but not limited to the departure and terminal stations, the number of cars, and the departure and arrival times.

The optimization of trainload service must consider the current trends in transport demand of China’s railways, and refer to the relevant practices in developed countries. China has now entered a “new normal” of economic development. The once-dominant primary industry is being overtaken by secondary and tertiary industries. Under this new normal, the transport demand of agricultural goods like fertilizer and gain is falling, while that of industrial goods with high added value has shot up. In many developed countries, the latest freight railways have common features like heavy haul, high level of informatization, combined transport and centralized scheduling, creating a mature operation network for freight block trains (FBTs) [3].

To fully utilize the released route capacity, this paper puts forward an FBT operation model based on the linear correlation between the number of trains and the demand increment. The model parameters like the number of trains, operation frequency, maximum load per train were defined and calibrated based on a railway network with multiple routes and nodes [4]. Next, the model was solved with IBM ILOG CPLEX Optimization Studio 12.4, and verified through an example railway network. Finally, the author conducted a sensitivity analysis on the capacity of railway section and the number of trains to future increase the profit of railway transport enterprise.

3.1 Hypotheses

The following hypotheses were put forward before creating the new FBT operation plan:

Hypothesis 1. The carrier mode (i.e. locomotive and car(s)) is not considered in our model.

Hypothesis 2. The impacts of operations on the FBT at way stations (nodes) in the railway network are negligible.

Hypothesis 3. The attributes of the FBT are fixed, namely, number of cars, type of goods, to name but a few.

Hypothesis 4. The railways are all electrified double track railways.

Hypothesis 5. With the increasing operating frequency of the FBTs, the freight demand will have a rapid linear growth.

Hypothesis 6. The FBTs have superior track occupancy rights over ordinary freight trains.

3.2 Symbols

For simplicity, the following symbols were defined as given conditions.

The following symbols are defined. These symbols are regarded as given conditions.

(a) Sets

(1) As shown in Figure 1, the railway network is denoted as G=(N,A), where, N is the set of n∈N way stations (nodes) in the network and A is the set of a∈A railway sections. The railway section refers to the segment of the railway between two adjacent way stations.

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Figure 1. An example of railway network

(2) In the railway network, OD is the set of od∈OD transport routes, where, O is the set of o∈O origins (departure stations) and D is the set of d∈D destinations (terminal stations).

(3) T is the set of t∈T years. Here, T only covers three years, because this paper only focuses on the transport profit in the short term.

(4) K is the set of k∈K types of FBTs. Here, two types of FBTs are discussed, namely, high-speed freight block trains (HFBTs) and normal-speed freight block trains (NFBTs).

(b) Coefficients

(1) $S _ { k } ^ { o d }$ is the income of transporting one unit of goods on route od by a type k FBT, including the freight charge, the surcharge for using electrified railways, and the surcharge for railway construction fund. If the FBT is an HFBT, then $S _ { k } ^ { o d }$ also contains an extra express fee.

(2) $c _ { k } ^ { o d }$ is the operating cost of a type k FBT from the origin o to destination d. This cost consists of departure fee, arrival fee, railway occupancy fee, locomotive traction fee, etc.

(3) α_k is the deduction coefficient of a type k FBT.

(4) $Q_ { t } ^ { o d }$ is the freight demand on route od in year t.

(5) $q_ { k } ^ { o d }$ is the freight demand increment on route od in the next year, for each additional type k FBT.

(6) $Cap_ { t } ^ { a }$ is the capacity of railway section a in year t.

(7) $R_ { k t } ^ { o }$is limit on the number of type k FBTs in origin o in year t.

(8) B_k is the maximum load of a type k FBT.

(c) Decision variables

(1) $\varphi _ { akt } ^ { o d }$ is the relationship between route od and railway section a. If railway section $a$ belongs to route od, $\varphi _ { akt } ^ { o d }$ equals one; otherwise, $\varphi _ { akt } ^ { o d }$ equals zero.

(2) $F _ { k t } ^ { o d }$ is the total load of goods transported by a type k FBT on route od in year t. This decision variable can only take integer values.

(3) $P _ { k t } ^ { o d }$ is the number of type k FBTs on route od in year t. This decision variable can only take integer values.

3.3 Mathematical model

Our model aims to maximize the transport profit in the short term. Hence, the objective function can be defined as:

$\max ( S - C )$

$\left\{ \begin{array} { l } { S = \sum _ { o \in O } \sum _ { d \in D } \sum _ { t \in T } \sum _ { k \in K } s _ { k } ^ { o d } f _ { k t } ^ { o d } } \\ { C = \sum _ { o \in O}\sum _ { d \in D } \sum _ { t \in T } \sum _ { k \in K } c _ { k } ^ { o d } P _ { k t } ^ { o d } } \end{array} \right.$    (1)

where, S is the total income; C is the total cost. The difference between S and C is the transport profit of the railway network. Our model is subjected to six constraints: the train flow in each railway section must be smaller than or equal to the capacity of that section; the number of type k FBTs operating in origin o in year t should not surpass the limit; the freight demand on each route in the current year should be increased, only if the number of FBTs on that route is within the limit in the previous year; the total load of goods on each transport route should not exceed the maximum load of all FBTs operating on that route; the total load of goods on each transport route should equal the total freight demand on that route; the decision variables should be satisfy logic restriction. The formulas of the six constraints are presented in turn:

$\sum _ { o \in D } \sum _ { d \in D } \sum _ { k \in K } P _ { k t } ^ { o d } \varphi _ { a k t } ^ { o d } \alpha _ { k } \leq \operatorname { Cap } _ { a } ^ { t } \quad \forall t \in T , a \in A$     (2)

$\sum _ { d \in D } P _ { k t } ^ { o d } \leq \varphi _ { k t } ^ { o } \quad \forall t \in T , k \in K , o \in O$   (3)

$Q _ { t } ^ { o d } = Q _ { 0 } ^ { o d } + \sum _ { t - 1 } \sum _ { k \in K } q _ { k } ^ { o d } P _ { k t } ^ { o d } \quad \forall t \in T , o \in O , d \in D$      (4)

$F _ { k t } ^ { o d } \leq B _ { k } P _ { k t } ^ { o d } \quad \forall t \in T , k \in K , o \in O , d \in D$      (5)

$\sum _ { k \in K } F _ { k t } ^ { o d } = Q _ { t } ^ { o d } \quad \forall t \in T , o \in O , d \in D$        (6)

$P _ { k t } ^ { o d } \in Z ^ { + } F _ { k t } ^ { o d } \in Z ^ { + } \quad \forall t \in T , k \in K , o \in O , d \in D$

$\varphi _ { a k t } ^ { o d } \in ( 0,1 ) \quad \forall t \in T , k \in K , o \in O , d \in D , a \in A$  (7)

Through the above analysis, the design of a practical operation plan was transformed into a capacity constraint problem of a railway network with multiple routes and nodes. The established integer linear programming model can be solved by various mature algorithms or software toolboxes, ranging from the BB algorithm, the cutting-plane algorithm, heuristic algorithms (e.g. genetic algorithm (GA) and simulated annealing (SA) algorithm), MATLAB, LINGO to CPLEX [17]. In this paper, the established model is solved by the professional optimization software: IBM ILOG CPLEX Optimization Studio 12.4.

The most profitable operation plan can be obtained easily based on the known information. However, the transport enterprises may want to further adjust the plan and earn more profit. The only adjustable parameters are the capacity of railway section and the number of trains. The other parameters, such as the transport income, transport cost and maximum load of trains, are fixed values and not likely to change in the short term, if no technical breakthrough is made soon. Hence, the next step is to analyse how the capacity of railway section and the number of trains affect the transport profit.

5.1 Capacity of railway section

The capacity of railway section has a great impact on train operations. A railway section with high capacity allows more trains to operate, thus increasing the transport income. To disclose how this capacity impacts transport profit, the capacity of railway sections in our example were increased in the following manner: each time, the capacity of one railway section was increased by 5, without changing that of any other section. The analysis results are shown in Table 6 below.

Table 6. The transport profits after adjusting the capacity of railway section

As shown in Table 6, the transport profits changed by different degrees through the adjustment, ranging from 0 to RMB 45,843,564 yuan. For example, after the capacity of railway section A→C increased from 8 to 13, the transport profit of the network remained the same as the original value. This means the capacity of railway section A→C already fully satisfy the transport demand in the initial condition, eliminating the need for capacity expansion. Similar results were observed in railway section G→E. By contrast, the capacity growth in the other sections more or less boosted the profit, especially in C→B and E→G. These two sections should be focused in capacity adjustment, for they contribute the most to the network profit. Comparatively, the capacity growth in E→G can bring more profit than that in C→B.

5.2 Number of trains

The transport profit also has something to do with the number of trains operating in each station. In way stations, the limit on FBTs mainly targets the HFBTs. To reveal the effects of the number of trains on transport profit, the number of HFBTs was increased in the following manner: one more HFBT was deployed per day in one of the seven ways stations, without changing the number of HFBTs in any other way station. The analysis results are illustrated in Figure 3 below.

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Figure 3. The level and increment of transport profit after adjusting the number of HFBTs

From Figure 3, it can be seen that the increment of transport profit fell between RMB 132,420 yuan and RMB 31,867,325 yuan. The most marked increment was observed in station E. Thus, the transport enterprise should deploy more HFBTs in this station to maximize the profit.