Adaptation of the Model to the Available Data

4.6 Adaptation of the Model to the Available Data

The model and the solution approach we propose are aimed at computing the best paths on the network, once the network topology, its technical characteristics, the demand requirement and the possible profits are known. However, whereas the rail network is currently in use and the related information were collected during the project, there is no current service on the REORIENT Corridor (or, to be more precise, the current service does not reflect the potential of the corridor), thus the demand that one may imagine to attract on the corridor cannot be observed on field, but has to be assessed (e.g. from trade data). In the following we describe which data we use to feed the model, and how we adapt these data.

4.6.1 Network topology and technical characteristics

The data describing the network were mainly collected within the activities performed in Work Package 1 (WP1). In the path design model, we use the network topology, described by a list of line segments, by their endpoints (corresponding to arcs and nodes in graph G , respectively), and by the characteristics of these segments. All the input arcs did not have an orientation, which was set according to a North-South direction, as described in section 4.5.1. To describe segments of the rail network (arcs of the graph) we use the following information:

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• first node i of the arc (original node numerical ID);

• second node j of the arc (original node numerical ID);

• original Arc ID; • average commercial speed on the arc;

• length of the arc, which, together with the average speed, is used to compute the

transit time f (,) ij on the arc;

• maximum axial load c (,) ij of the arc.

The nodes of the rail network may correspond to stations, terminals, shunting yards, junctions, or may simply be the connection of two consecutive line segments. To describe each node we use the following information:

• original Node ID;

• node coordinates; • node geographical name;

• node type: terminal or shunting yard, station, junction, connection of two

consecutive stretches;

• for the nodes that are terminals, processing time P for a wagon and number of available parallel processing lines C : the value of these parameters depends on the scenario that we want to simulate. When all the wagons are delayed by the same amount of time in the terminal, we consider a large number of processing lines in the terminal itself;

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• waiting time for a train stop in a terminal (this stop affects all the wagons that are on the train and are not unloaded in the terminal).

4.6.2 Demand

The assessment of the potential demand has been performed by researchers of the University of Maryland (UMD), starting from ETIS trade data. The demand is transformed, from flow by Tons/year to the number of wagons in the time interval considered, and is categorized according to the 11 ETIS categories:

• Agricultural products and live animals;

• Foodstuffs and animal fodder; • Solid mineral fuels;

• Petroleum products;

• Ores and metal waste; • Metal products;

• Crude and manufactured minerals, building materials; • Fertilizers;

• Chemicals;

• Machinery, transport equipment, manufactured articles and miscellaneous articles; • Crude oil.

For each of these 11 categories, the University of Maryland assessed the demand input for the model, i.e. a matrix specifying the number of wagons to be shipped from each origin to each

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destination in the network. It is worth noting that each demand entry has implicitly a direction, which may be North-South if the origin precedes the destination when moving on the corridor from North to South, and viceversa, thus determining if the wagons are to be considered when designing the paths in one direction or in the opposite one.

For each wagon of the demand matrix, we have to evaluate (1) the “profit” that is earned, according to the model objective function, if the wagon is shipped without delay, (2) the requested transit time for the wagon, which determines the delay when exceeded, and (3) the sensitivity to delayed shipment for the wagon, which determines the reduction of profit.

• Since there is no current service on the network, in our analysis the profit e t of a wagon t represents the priority that we want to give to the shipment of wagon t .

In other words, while all wagons would be shipped having enough train capacity, when the number of trains k is limited we have to choose to which wagons to

give higher priority. We give high priority (i.e. we associate a large “profit”) to wagons containing high value goods, and travelling for long distances. In detail, the “profit” of each wagon t is computed as:

e t = dist o d (, t t ) γ cat t () (36)

where dist o d (, t t ) is the distance, on the shortest path on the rail network, from the origin o t of the wagon and its destination d t , and γ cat t () is the profit earned when one homogeneous wagon of goods of category cat t () is shipped for one unit of distance. The parameter γ cat t () is computed as a function of the monetary value of one homogeneous wagon of goods of category cat t () , see section 4.6.3.

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• The requested transit time D t for a wagon is set equal to the transit time on the fastest path (i.e. the shortest path with respect to transit times) connecting the

origin and destination nodes of the wagon. With this set-up, we force trains to travel on the fastest available routes, when possible. When a decision among different routes has to be taken, the model will select the one determining the minimum loss of profit for the wagons on the considered train, by taking into account the profit and the sensitivity to delayed shipment of the wagons.

• For each wagon, the number of pieces and the parameters µ and η of the

corresponding piecewise linear function determine the penalty that the wagon incurs when shipped in a time exceeding the time needed to move on the fastest path from its origin to its destination, without intermediate stops. For each category of goods we use a different function; all functions are composed by two pieces, the first one, with lower gradient, representing the penalty for a short delay, and the second one, with larger gradient, representing the penalty for a larger delay, the base set up of these parameters is described in section 4.6.3.

4.6.3 Base case settings

Some parameters described in the previous sections cannot be obtained “on field”, and their setting depends on the particular scenario that is considered. In this section we report the basic setting of these parameters, whose values may be modified when more sophisticated scenarios have to be represented.

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Demand parameters

The parameter γ cat t () is the profit earned when one homogeneous wagon t of goods of category cat t () is shipped for one unit of distance. It is a function of the average monetary

value of one homogeneous wagon of goods of category cat t () .

Category

NTS/R γ

Agricultural products 0 3.713 and live animals

Foodstuffs and animal fodder 1 3.858 Solid mineral fuels

2 3.662 Petroleum products

3 3.394 Ores and metal waste

4 3.435 Metal products

5 3.848 Crude and manufactured minerals,

6 3.952 building materials

Fertilizers 7 3.469 Chemicals

8 5.000 Machinery, transport equipment,

9 5.025 manufactured articles and miscellaneous

Crude oil 10 3.618

Table 4-1. γ values for each NTS/R good category

The average weight of the goods filling a wagon of each category is obtained by the ETIS base 1 ; while the average value of one weight unit of goods of each category is obtained from

1 D5 Annex report WP 3: ETIS- Database methodology development and database user manual– Freight

transport demand V2.0. ETIS documentation available online at: http://www.etis-eu.org/

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TRANSTOOLS 2 ; with this information we can compute the average value of one wagon filled with goods of a given category. However, the value distribution is too wide, while we

only want to set a priority list among different categories, instead of associating the value of one wagon with the profit the model obtains when the wagon is shipped. Thus, we set γ cat t ()

as the natural logarithm of the average monetary value (in Euro) of a wagon t filled of goods of category cat t () . The numerical values are reported, for each category, in Table 4-1.

NTS/R categories

Table 4-2. Parameters for the computation of the functions describing the sensitivity to delay of different goods categories.

Figure 4-7. Cost delay function, goods with high sensitivity to transit time.

2 TRANSTOOLS Deliverable 2: WP 2. Available online: http://www.inro.tno.nl/transtools/Deliverables.htm

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Figure 4-8. Cost delay function, goods with low sensitivity to transit time.

The function we use to penalize the delayed shipment has two linear components, described by parameters µη 1 , 1 for the first component and µ η for the second component. 2 , 2

In the basic setting, we distinguish two type of goods, those whose shipment is significantly affected by time, and those whose shipment is not significantly affected by time. The numerical values are reported in Table 4-2, and the corresponding functions are plotted in Figures 4-7 and 4-8. It may be noted that, for the first group, whose cost delay function is plotted in Figure 4-7, the profit obtained by shipping a wagon is reduced to 0 when the delay

equals the requested transit time D ; while for goods of the second group, whose cost delay function is plotted in Figure 4-8, this happens when the delay doubles the requested transit time D .

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