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Article Request Page
GIS Application to Define Biomass Collection Points as Sources for =
Linear=20
Programming of Delivery Networks
B. Velazquez-Marti, E. Annevelink =
Published in Transactions of =
the ASABE=20
Vol. 52(4): 1069-1078 ( Copyright 2009 American Society of =
Agricultural=20
and Biological Engineers ).
Submitted for review in October 2008 as manuscript number PM 7677; =
approved=20
for publication by the Power & Machinery Division of ASABE in June =
2009.=20
The authors are Borja Vel=EF=BF=BDzquez-Mart=EF=BF=BD, =
Researcher and Docent,=20
Department of Mechanization and Agrarian Technology, Polytechnic =
University of=20
Valencia, Valencia, Spain, and Bert Annevelink, Senior =
Scientist,=20
Department of Biobased Products, Agrotechnology and Food Science =
Group,=20
Wageningen University and Research Centre, Wageningen, The =
Netherlands.=20
Corresponding author: Borja Vel=EF=BF=BDzquez-Mart=EF=BF=BD, =
Department of=20
Mechanization and Agrarian Technology, Polytechnic University of =
Valencia,=20
Camino de Vera s/n, 46022 Valencia, Spain; phone: +34-963877290; fax:=20
+34-963877299; e-mail: borvemar@dmta.upv.es.
Abstract. Much bio-energy can be obtained from wood =
pruning=20
operations in forests and fruit orchards. Several spatial studies have =
been=20
carried out for biomass surveys, and many linear programming models =
have been=20
developed to model the logistics of bio-energy chains. These models =
can assist=20
in determining the best alternatives for bio-energy chains. Most of =
these=20
models use network structures built up from nodes with one or more =
depots,=20
with arcs connecting the depots. Each depot is a source of a certain =
biomass=20
type. Nodes can also be biomass storage points or production =
facilities (e.g.,=20
power plants) where biomass is used. The arcs in the networks =
represent=20
transport between depots. In order to combine GIS spatial studies with =
linear=20
programming models, it is necessary to build a network from a digital =
map of=20
biomass production centers, such as orchards. Biomass collection =
points should=20
therefore be defined as sources in the delivery network model. In this =
work, a=20
mathematical calculation method is developed to select the actual =
biomass=20
collection points on a map. The database for this model is composed of =
area=20
surveys of forest and agricultural biomass storage points given in GIS =
maps=20
(shape files). The limits of the area studied and different types of =
biomass=20
are defined and located in different layers of the GIS maps. These=20
energy-biomass production maps are overlaid with a 1 km =EF=BF=BD 1 km =
grid of the=20
area studied. The result is a grid in which the different types of =
total=20
available biomass in each quadrant are known. Harvesting and =
collection costs=20
are also defined. The connections between all n =EF=BF=BD m quadrants =
of the area=20
studied are defined by the available road network. Every quadrant is=20
associated with a point on the road network. The selection criteria =
for=20
sources of biomass (sub-areas) are the following: firstly, a minimum=20
production of available biomass type is required; and secondly, =
harvesting and=20
collection costs should be minimal. The algorithm provides the =
location of=20
points where biomass from the associated area can be concentrated. =
These=20
biomass collection points are then taken as source nodes in the =
network during=20
the implementation of the logistics models. In the next step, the =
network is=20
analyzed by linear programming techniques to supply the optimal =
position of=20
energy plants or factories, given the available biomass sources. =
Keywords. Bioenergy, Biomass supply, Borvemar model, =
Logistics.
Modeling the logistics of bio-energy chains helps to determine the =
best=20
alternatives for bio-energy systems. By means of purpose-built =
computer=20
models, either one specific objective can be optimized by linear =
programming=20
or several heterogeneous objectives can be combined by applying goal=20
programming: maximize profits, minimize costs, minimize greenhouse gas =
emissions, maximize energy returns, minimize energy use, and maximize =
energy=20
profit (Berruto and Busato, 2008). The Wageningen University and =
Research=20
Centre developed the Bioloco (biomass logistics computer optimization) =
model=20
(Annevelink and de Mol, 2007; Diekema, et al., 2005), an optimization =
model=20
that uses integer linear programming. The input is a network structure =
in=20
which all relevant parameters are included (fig. 1). These parameters =
are cost=20
data (e.g., transport costs per kilometer, pre-treatment costs, and =
energy=20
conversion costs) along with capacity constraints or parameters such =
as=20
storage losses or seasonal variations in supply or demand. A file with =
all the=20
input data needed for optimization is generated from a special =
database.=20
Bioloco is therefore a system for analyzing biomass network models. =
The=20
network model is built up from nodes with one or more depots, with =
arcs=20
connecting the depots. Each depot is a source of a certain biomass =
type, or a=20
storage point for a certain type or production facility (e.g., a power =
plant)=20
where biomass is used. Arcs represent transport between depots, =
combined with=20
pre-treatment for loading and/or unloading, taking into account =
seasonal=20
fluctuations in supply and demand, moisture losses due to drying, and =
dry=20
matter losses due to biological processes (heating). The flows in the =
network=20
are regulated by the biomass required by the production facilities and =
the=20
supply capacity from the sources of biomass.
In order to combine GIS area studies with linear programming models =
such as=20
Bioloco, it is necessary to build a network from a map using a model =
such as=20
the Borvemar model, which was developed in the research described in =
this=20
article to achieve the combination of GIS maps with network models. =
The=20
objective of the Borvemar model is to find possible locations where =
biomass=20
can be collected. The selected biomass collection points can then be=20
considered as biomass sources in the Bioloco network model.
=20
Figure 1. Example of a network model in Bioloco.
The Borvemar Model
Network models of linear programming can only handle a limited =
number of=20
source locations during the optimization procedure (Buckmaster and =
Milton,=20
2005; Sokhansanj et al., 2006; Busato and Berrito, 2008); otherwise, =
the=20
problem would become too large to solve. Therefore, the high number of =
detailed areas within a GIS map has to be combined into larger =
sub-areas, each=20
of which contains several quadrants of the GIS map. The objective of =
the=20
Borvemar model is to combine quadrants of the GIS map in order to =
locate=20
biomass source points (sub-areas) for implementation of Bioloco or =
similar=20
models within the network model. The database for the Borvemar model =
is=20
composed of spatial surveys of forest and agricultural biomass given =
in GIS=20
maps (shape files). These maps give information on the species and =
plants per=20
hectare of food biomass that also supply streams of residual biomass =
and=20
thereby provide energy biomass production maps. Previously, several =
studies=20
have been conducted to quantify the potentially available biomass from =
different agricultural or forest systems. Coefficients of production =
of=20
residual biomass from pruning and renewal of fruit trees and straw =
from cereal=20
harvests are calculated according to species, variety, and cultivation =
system=20
used. The limits of the studied area should be defined in advance, =
e.g., a=20
country (such as The Netherlands or Spain), a province, or a region. =
Other=20
cartographic data (shape files) necessary to implement the model are: =
a=20
transportation net, orography, hydrology, urban areas, and =
administrative=20
limits.
Bioloco defines the different types of biomass .=20
The energy-biomass production maps are overlaid with a 1 km =EF=BF=BD =
1 km grid in the=20
studied area (fig. 2). The quadrants are given names ;=20
and=20
form an n =EF=BF=BD m matrix. The result is a grid in =
which the total=20
available biomass in every quadrant is known ( m ij ). =
The=20
ratios of every type of biomass in every quadrant are also known. =
Every a=20
ij has an associated vector of ratios ,=20
such that .=20
The parameter r ija is the ratio of biomass type a =
inside quadrant a ij ; the parameter r ijb =
is=20
the ratio of biomass type b inside quadrant a ij =
, etc.=20
In addition, a harvesting or collecting cost vector is=20
defined. The parameter H a is the cost of harvesting =
type a=20
biomass; the parameter H b is the cost of harvesting =
type=20
b biomass, etc. The product is=20
the harvesting cost for all biomass in quadrant a ij =
.=20
=20
Figure 2. Grids with quantified biomass in Hoya de Bu=EF=BF=BDol =
county (Valencia,=20
Spain) (IEE, 2006).
Grids should be connected by the transportation network. The =
connections=20
among all n =EF=BF=BD m quadrants in the area studied =
are defined by the=20
road network. Every quadrant is associated with one point of the road =
network.=20
This connection is carried out by means of the Network Analyst tool in =
the=20
software ArcGIS. A distance parameter D ( a ij , =
a=20
nm ) can be defined as the distance between quadrant a =
ij=20
and a nm by the road that connects them. All =
distances D=20
( a ij , a nm ) define a matrix n =
=EF=BF=BD=20
n .
Another simplified method of connecting grids is to calculate the =
Euclidean=20
distance between every quadrant center, and multiply this value by a =
parameter=20
called CR ("curvature of the road"), which can vary between 1.1 =
and 1.8=20
(IEE, 2006).
(1)=20
While all the quadrants are possible biomass producers, only a =
limited=20
number can be the location of a production facility (e.g., a power =
plant) for=20
the transformation of biomass. Because urban areas, lakes, rivers, =
slope=20
areas, roads, electric lines, airports, and other locations cannot be=20
considered, the quadrants corresponding to these areas are deleted. =
The main problem when combining the GIS map with the optimization =
model is=20
to concentrate the biomass from an area in a few collection points, =
which will=20
then be analyzed by the linear programming model. Every collection =
point is=20
associated with a sub-area { A 1 , A 2 =
,=20
..., A n } that contains one or more quadrants a =
ij=20
, where the biomass is collected and transported to the point. The =
criteria for the selection of biomass sources (sub-areas) are the =
following:=20
To select the different sub-areas { A 1 , A =
2=20
, ..., A n } within the n =EF=BF=BD m =
matrix, it is=20
necessary to follow n iterations. The steps within an iteration =
are=20
described next, and an example is given below.
Iteration 1
Step 1. Every quadrant a ij is checked to find =
those=20
that have a quantity of a specific type of available biomass greater =
than Q=20
t located inside a radius R (e.g., R =3D 60 =
km).
D ( a ij , a nm ) < R =
=20
tonnes of biomass (selected types)
where m ( a ij , a nm ) is the =
biomass=20
of the selected type to be transported from every quadrant a =
nm=20
to a ij , such that D ( a ij , =
a=20
nm ) < R .
Step 2. The quadrants that satisfy the previous conditions =
are=20
selected.
Step 3. For every quadrant a ij selected, the =
cost of=20
harvesting and collecting all available biomass from all other a =
nm=20
to a ij is calculated such that D ( a =
ij=20
, a nm ) < R . The cost is obtained by =
equation 2:=20
=20
(2)
where CF i are the fixed transportation costs =
measured in=20
Euros per cycle of transportation (=EF=BF=BD/travel), which includes =
the operator's=20
costs during loading time (3 to 4 h); CV are the variable=20
transportation costs (=EF=BF=BD/km) and include fuel consumption and =
operator's costs;=20
and CT is transport capacity (e.g., 5 t/travel).
Step 4. All the selected quadrants a ij =
are=20
ordered according to their costs. Quadrant a ij with the =
lowest=20
costs is selected. Thus, the first sub-area, A1, is formed with all =
a=20
nm , such that D ( a ij , a =
nm )=20
< R and C ij is minimum.
Iteration 2
Step 1. All remaining quadrants a ij are =
checked again=20
to find those that have a quantity of available biomass greater than =
Q=20
t within a radius R , such that .=20
Step 2. The quadrants that satisfy the previous conditions =
are=20
selected.
Step 3. For every a ij selected, which has an=20
associated sub-area, the cost of harvesting and collecting all =
available=20
biomass from a nm to a ij is calculated, =
such that=20
D ( a ij , a nm ) < R . =
The cost=20
is obtained by equation 2.
Step 4. All the quadrants a ij are ordered =
according=20
to their costs. The quadrant a ij with the lowest costs =
is=20
selected. Thus, the second sub-area, A2, is formed with all a =
nm=20
, such that D ( a ij , a nm ) =
< R=20
and C ij is minimum.
Iteration n
Step 1. Every quadrant a ij is checked to find =
those=20
that have available biomass greater than Q , within a radius =
R ,=20
such that .=20
Steps 2 through 4 are then repeated.
Example Calculations
Figure 3 illustrates a hypothetical grid (10 =EF=BF=BD 10) of an =
area where the=20
available biomass of a certain type b in every quadrant is =
known. Every=20
quadrant represents an area of 1 km =EF=BF=BD 1 km. The number inside =
every quadrant=20
represents the number of tonnes of biomass that can be collected from =
it. To=20
select sub-areas, a minimum productivity of 50 t/year of biomass type =
b=20
is defined, which should be available to provide feasible =
collecting=20
operations. The maximum collection distance is fixed at 2 km ( R =
=3D 2=20
km). According to iteration 1 of the Borvemar model, every quadrant =
a=20
ij is checked to find those that have more than 50 tonnes =
of=20
biomass type b available within a radius of less than 2 km. =
Distances=20
are normally defined by a matrix generated from the road =
transportation=20
network, but in this example we have used Euclidean distances. For =
every=20
quadrant, the area to check is defined by figure 4.
=20
Figure 3. Available type b biomass in each 1 km =EF=BF=BD 1 =
km quadrant of a=20
studied area in tonnes.
=20
Figure 4. Area closer than 2 km to a ij .
Table 1 shows tonnes of available biomass for every possible =
sub-area of 2=20
km radius. The logistical costs considered were the following:=20
-
Harvesting-collection costs, H =3D 2 =EF=BF=BD/t.
-
Fixed transport costs, CF =3D 0.5 =EF=BF=BD/cycle of =
transportation.
-
Variable transport costs, CV =3D 1.5 =EF=BF=BD/km.
-
Transport capacity, CT =3D 5 t/cycle of transportation. =
The cost to transport a tonne of biomass to every sub-area center =
can be=20
seen in table 2.
Table 1. Amount of biomass that is available within 2 km radius of =
every=20
a ij in tonnes.=20
35.62 |
52.53 |
58.43 |
50.92 |
61.38 |
41.96 |
46.19 |
44.25 |
41.43 |
37.86 |
45.80 |
68.01 |
69.79 |
76.28 |
68.40 |
59.26 |
45.73 |
59.17 |
53.33 |
46.40 |
46.10 |
59.30 |
72.55 |
63.33 |
61.44 |
62.56 |
52.98 |
39.29 |
55.34 |
53.70 |
32.17 |
46.14 |
55.64 |
49.23 |
45.44 |
52.37 |
47.25 |
39.88 |
48.64 |
51.21 |
25.81 |
34.31 |
36.04 |
49.59 |
50.17 |
47.69 |
53.80 |
61.98 |
50.42 |
41.56 |
25.59 |
39.41 |
36.40 |
37.21 |
64.41 |
72.29 |
71.70 |
56.58 |
54.94 |
43.70 |
25.17 |
42.55 |
50.68 |
56.12 |
64.62 |
86.71 |
76.21 |
69.91 |
55.80 |
44.48 |
32.80 |
41.11 |
52.73 |
67.67 |
75.91 |
69.81 |
72.88 |
66.75 |
56.59 |
39.97 |
32.49 |
44.35 |
54.53 |
54.18 |
59.18 |
65.94 |
57.58 |
47.56 |
38.69 |
39.13 |
20.33 |
36.56 |
41.91 |
43.25 |
43.79 |
33.69 |
32.92 |
30.48 |
32.04 |
25.26 |
Table 2. Collecting cost per ton of biomass in every possible =
sub-area.=20
2.434 |
2.489 |
2.511 |
2.505 |
2.544 |
2.426 |
2.492 |
2.525 |
2.441 |
2.448 |
2.458 |
2.466 |
2.460 |
2.492 |
2.487 |
2.470 |
2.480 |
2.569 |
2.479 |
2.438 |
2.537 |
2.484 |
2.510 |
2.476 |
2.479 |
2.549 |
2.570 |
2.503 |
2.500 |
2.488 |
2.528 |
2.508 |
2.553 |
2.538 |
2.494 |
2.546 |
2.561 |
2.521 |
2.491 |
2.484 |
2.505 |
2.452 |
2.493 |
2.593 |
2.552 |
2.475 |
2.509 |
2.583 |
2.528 |
2.443 |
2.542 |
2.541 |
2.512 |
2.518 |
2.556 |
2.507 |
2.475 |
2.482 |
2.527 |
2.492 |
2.485 |
2.530 |
2.546 |
2.526 |
2.487 |
2.495 |
2.455 |
2.505 |
2.537 |
2.536 |
2.503 |
2.448 |
2.496 |
2.524 |
2.504 |
2.468 |
2.500 |
2.532 |
2.526 |
2.502 |
2.504 |
2.493 |
2.512 |
2.477 |
2.486 |
2.544 |
2.555 |
2.496 |
2.386 |
2.454 |
2.428 |
2.506 |
2.513 |
2.481 |
2.484 |
2.500 |
2.577 |
2.546 |
2.478 |
2.450 |
The sub-area with a quantity of available biomass higher than 50 =
t/year=20
with the lowest cost is defined by quadrant a 77 , =
which is=20
shown in figure 5. The quantity of available biomass of type b =
in=20
sub-area A1 is 76.21 t/year, and the collecting costs are 2.455 =
=EF=BF=BD/t. In order=20
to carry out iteration 2, the quadrants of sub-area A1 are deleted =
from the=20
grid in figure 3, which leads to figure 6.
=20
Figure 5. Sub-area A1 from iteration 1.
=20
Figure 6. Available biomass in each 1 km =EF=BF=BD 1 km quadrant =
for iteration 2.=20
In table 3, the number of tonnes of available biomass for every =
possible=20
sub-area in iteration 2 are recalculated. The cost to transport a =
tonne of=20
biomass to every sub-area center in iteration 2 can be seen in table =
4. The=20
sub-area with a quantity of available biomass higher than 50 t/year =
with the=20
lowest cost is defined by quadrant a 23 , which is =
shown in=20
figure 7. Following iterations 1, 2, 3, and 4 defined by the Borvemar =
model,=20
four sub-areas (collection points A1, A2, A3, and A4) are created =
(fig. 7). In=20
order to carry out iteration 5, sub-areas A1, A2, A3, and A4 are =
deleted from=20
the grid in figure 8.
Table 3. Biomass that is available inside of 2 km radius around =
every a=20
ij in iteration 2.=20
35.62 |
52.53 |
58.43 |
50.92 |
61.38 |
41.96 |
46.19 |
44.25 |
41.43 |
37.86 |
45.80 |
68.01 |
69.79 |
76.28 |
68.40 |
59.26 |
45.73 |
59.17 |
53.33 |
46.40 |
46.10 |
59.30 |
72.55 |
63.33 |
61.44 |
62.56 |
49.80 |
39.29 |
55.34 |
53.70 |
32.17 |
46.14 |
55.64 |
49.23 |
45.44 |
46.27 |
34.73 |
29.94 |
48.64 |
51.21 |
25.81 |
34.31 |
36.04 |
49.59 |
36.92 |
23.87 |
21.87 |
35.25 |
37.06 |
41.56 |
25.59 |
39.41 |
36.40 |
27.14 |
36.62 |
17.00 |
15.47 |
13.26 |
27.97 |
33.53 |
25.17 |
42.55 |
43.53 |
40.59 |
28.61 |
25.43 |
0.00 |
15.85 |
27.92 |
33.60 |
32.80 |
41.11 |
52.73 |
52.68 |
44.08 |
23.76 |
20.10 |
21.51 |
36.73 |
36.04 |
32.49 |
44.35 |
54.53 |
54.18 |
43.13 |
40.21 |
29.97 |
30.06 |
33.70 |
39.13 |
20.33 |
36.56 |
41.91 |
43.25 |
43.79 |
24.79 |
23.39 |
28.91 |
32.04 |
25.26 |
Table 4. Collecting cost in every possible sub-area for iteration =
2.=20
2.434 |
2.489 |
2.511 |
2.505 |
2.544 |
2.426 |
2.492 |
2.525 |
2.441 |
2.448 |
2.458 |
2.466 |
2.460 |
2.492 |
2.487 |
2.470 |
2.480 |
2.569 |
2.479 |
2.438 |
2.537 |
2.484 |
2.510 |
2.476 |
2.479 |
2.549 |
2.562 |
2.503 |
2.500 |
2.488 |
2.528 |
2.508 |
2.553 |
2.538 |
2.494 |
2.536 |
2.538 |
2.477 |
2.491 |
2.484 |
2.505 |
2.452 |
2.493 |
2.593 |
2.511 |
2.385 |
2.513 |
2.619 |
2.493 |
2.443 |
2.542 |
2.541 |
2.512 |
2.490 |
2.563 |
2.471 |
2.611 |
2.642 |
2.510 |
2.444 |
2.485 |
2.530 |
2.521 |
2.513 |
2.514 |
2.631 |
-- |
2.675 |
2.567 |
2.514 |
2.503 |
2.448 |
2.496 |
2.494 |
2.492 |
2.543 |
2.631 |
2.513 |
2.494 |
2.495 |
2.504 |
2.493 |
2.512 |
2.477 |
2.434 |
2.541 |
2.569 |
2.435 |
2.342 |
2.454 |
2.428 |
2.506 |
2.513 |
2.481 |
2.484 |
2.435 |
2.541 |
2.543 |
2.478 |
2.450 |
=20
Figure 7. Sub-areas A1, A2, A3 and A4 from iterations 1 through 4 =
of the=20
Borvemar model.
=20
Figure 8. Available biomass in each 1 km =EF=BF=BD 1 km quadrant =
for iteration 5.=20
In table 5, the number of tonnes of available biomass for every =
possible=20
sub-area in iteration 5 is shown. Table 5 shows that no sub-area has a =
quantity of available biomass higher than 50 t/year. Therefore, within =
the=20
constraints specified, only four collecting sub-areas are selected, =
and their=20
centers are used as a source node by the Bioloco model to optimize =
logistical=20
operations. Each sub-area has the following values:=20
-
Sub-area A1 has 76.21 t/year of available biomass with collecting =
costs=20
2.455 =EF=BF=BD/t.
-
Sub-area A2 has 69.79 t/year of available biomass with collecting =
costs=20
2.460 =EF=BF=BD/t.
-
Sub-area A3 has 54.18 t/year of available biomass with collecting =
costs=20
2.477 =EF=BF=BD/t.
-
Sub-area A4 has 53.33 t/year of available biomass with collecting =
costs=20
2.479 =EF=BF=BD/t.
The total amount of biomass selected according to the restrictions=20
specified by the Borvemar algorithm is 253.51 t/year, and the average =
costs=20
are 2.466 =EF=BF=BD/t.
Table 5. Biomass available inside 2 km radius of every a =
ij=20
in iteration 5.=20
11.21 |
9.46 |
13.95 |
11.70 |
37.66 |
29.51 |
29.85 |
14.10 |
6.89 |
0.00 |
13.52 |
11.82 |
0.00 |
25.30 |
36.10 |
42.65 |
28.53 |
22.64 |
0.00 |
6.77 |
16.85 |
13.23 |
17.47 |
17.95 |
36.04 |
45.19 |
37.00 |
10.10 |
14.52 |
16.71 |
16.04 |
21.46 |
26.27 |
25.56 |
34.93 |
46.27 |
23.88 |
17.94 |
25.98 |
28.03 |
25.81 |
24.08 |
28.39 |
38.94 |
36.92 |
23.87 |
21.87 |
27.87 |
29.97 |
30.94 |
25.59 |
39.41 |
24.94 |
19.82 |
25.06 |
17.00 |
15.47 |
13.26 |
25.29 |
33.53 |
25.17 |
31.74 |
27.43 |
12.52 |
8.55 |
11.98 |
0.00 |
15.85 |
27.92 |
33.60 |
25.16 |
27.52 |
16.91 |
12.75 |
3.31 |
4.99 |
9.83 |
21.51 |
36.73 |
36.04 |
29.97 |
24.23 |
20.26 |
0.00 |
4.99 |
13.70 |
23.73 |
28.17 |
33.70 |
39.13 |
14.42 |
23.15 |
9.68 |
10.16 |
6.38 |
6.43 |
15.05 |
28.91 |
32.04 |
25.26 |
Extensions to the Method
The main disadvantage of the Borvemar model is that a large number =
of=20
quadrants could be excluded, which would subsequently not be available =
for=20
selection by the biomass collection algorithm. In the example, the =
available=20
biomass of 52% of the quadrants is not mobilized. To overcome this =
problem,=20
several options are available:
Option 1: Repeat the calculation process several times with=20
different values for the minimum amount of biomass and maximum =
collecting=20
distance (for example Q b =3D 40 t/year and R =3D =
3 km).=20
Results of the calculations with these parameters are shown in figure =
9a. It=20
can be noted that the percentage of quadrants with non-mobilized =
biomass has=20
significantly decreased to 7%. It is therefore possible to modify the=20
algorithm so as to find a procedure that selects the optimum value for =
Q=20
and R to maximize the number of quadrants mobilized. =
However, this=20
aspect has yet to be developed.
Option 2: After the last iteration with a certain value for =
Q=20
and R , it is possible to perform further calculations for =
the=20
quadrants that are not allocated a lower value for the minimum amount =
of=20
biomass and the new maximum collecting distance. In this case, some =
smaller=20
sub-areas appear together with the large sub-areas selected, filling =
in the=20
gaps that were left by the first calculation process. For example, =
after the=20
first calculation process, sub-areas with Q b =3D 20 =
t/year and=20
R =3D 1 km were checked. The results (extra sub-areas A5 to A8) =
are shown=20
in figure 9b.
Option 3: An extension buffer with a selected thickness can =
be=20
applied to add more quadrants around the sub-areas already selected. =
The=20
quadrants that can be added to the sub-areas are allocated according =
to the=20
lowest transportation cost related to the respective concentration =
points=20
(figs. 9c and 9d).
=20
Figure 9. (a) Sub-areas obtained when Q =3D 40 t/year and =
R =3D 3=20
km; (b) sub-areas obtained after first calculation with Q =3D =
40 t/year=20
and R =3D 2 km, and sub-areas obtained in the second =
calculation with=20
Q =3D 20 t/year and R =3D 1 km; (c) buffer of 1 km =
applied to the=20
sub-areas A1, A2, A3 and A4 obtained with Q =3D 50 t/year and =
R =3D=20
2 km; and (d) buffer of 2 km applied to sub-areas A1, A2, A3, and A4 =
with Q=20
=3D 50 t/year and R =3D 2 km.
The calculation model has been validated with practical cases. The =
Borvemar=20
model was applied to the digital map obtained for the quantification =
of=20
biomass in the county of La Hoya de Bu=EF=BF=BDol, Valencia, Spain =
(fig. 2). For this=20
county, the total amount of biomass (21,830 t/year) was calculated and =
distributed as: 84% wood residues from fruit-bearing trees, 5% forest=20
residues, 10% residues from olive trees, and 1% gardening residues. =
The communications network was analyzed using ArcGIS. The =
geodatabase was=20
created by means of the ArcCatalog module, where the feature datasets =
are=20
loaded from shape files. The datasets were classified in several =
feature=20
classes (points, quadrants, and routes). The shape files of routes =
should have=20
all relevant parameters: type of road (freeway, secondary road, etc.), =
flow=20
velocity, one-way vs. two-way, and length.
Secondly, the network calculation was carried out by means of =
ArcMap=20
software, in which the feature dataset was opened and analyzed by =
means the=20
Network Analyst module . The ArcMap tool used for the analysis =
is New=20
Closest Facility, which calculates the route length from one point to =
all=20
possible incident points. Several analysis settings are required to be =
specified, such as impedance (length) and research tolerance (1000 m), =
which=20
is the distance to connect the quadrant with the route.
When the quadrants are connected to the communications network, the =
Borvemar algorithm is implemented. A minimum productivity of 1000 =
t/year of=20
wood biomass was required for each sub-area, which is considered =
available to=20
provide feasible collecting operations. The maximum collection =
distance is=20
fixed at 4 km ( R =3D 4 km). The results of the calculation are =
shown in=20
figure 10. Twelve sub-areas were obtained (table 6). The amount of =
biomass to=20
be mobilized is 13,818.87 t/year, or 63.28% of the total. The average =
cost is=20
16.53 =EF=BF=BD/t.
Table 6. Sub-areas associated with collection points as determined =
by the=20
Borvemar model.=20
Sub-area |
Available Biomass
(t/year) |
Collecting Costs
(=EF=BF=BD/t) |
A1 |
1201.21 |
15.75 |
A2 |
1269.39 |
15.86 |
A3 |
1004.18 |
15.94 |
A4 |
1302.13 |
16.12 |
A5 |
1026.21 |
16.45 |
A6 |
1030.39 |
16.67 |
A7 |
1103.18 |
16.75 |
A8 |
1103.33 |
16.82 |
A9 |
1136.21 |
16.92 |
A10 |
1109.19 |
16.95 |
A11 |
1230.12 |
17.03 |
A12 |
1303.33 |
17.21 |
=20
Figure 10. Sub-areas associated with collection points as =
determined by the=20
Borvemar model for Hoya de Bu=EF=BF=BDol county (Valencia, Spain) when =
Q =3D 1000=20
t/year and R =3D 4 km.
Other parameters were tested such as:=20
-
A minimum productivity of 700 t/year of wood biomass and maximum=20
collection distance of 3 km ( R =3D 3 km). These values =
produce 17=20
sub-areas with an amount of biomass to be mobilized of 14,876 t/year =
(68% of=20
the total) but with a cost of 17.38 =EF=BF=BD/t. This is higher than =
the previous=20
calculation (16.53 =EF=BF=BD/t).
-
A minimum productivity of 1000 t/year of wood biomass and maximum =
collection distance of 5 km ( R =3D 5 km). These values =
produce 11=20
sub-areas with an amount of biomass to be mobilized less than first=20
calculation, 12,876 t/year, but with a cost of 15.98 =EF=BF=BD/t. =
This is lower than=20
previous calculations (16.53 =EF=BF=BD/t).
After the first calculation (fig. 10), further iterations were =
included to=20
fill the gaps that were left by the first calculation process. A =
minimum=20
productivity of 700 t/year of wood biomass and maximum collection =
distance at=20
3 km ( R =3D 3 km) was tested. Only one smaller sub-area =
appears together=20
with the large sub-areas previously selected (fig. 11). The new amount =
of=20
biomass to mobilize was 14,810.87 t/year, or 67.80% of the total. The =
average=20
cost was 16.63 =EF=BF=BD/t.
=20
Figure 11. Sub-areas obtained after first calculation with Q =
=3D 1000=20
t/year and R =3D 4 km and sub-areas obtained in the second =
calculation=20
with Q =3D 700 t/year and R =3D 3 km for Hoya de =
Bu=EF=BF=BDol county=20
(Valencia, Spain).
In addition, a buffer of 2 km was used after the first calculation =
(fig.=20
10) to obtain figure 12. The new sub-areas increased the amount of =
biomass to=20
mobilize (17,393 t/year), but the collecting costs were affected =
(table 7). It=20
can be observed that the cost per tonne of biomass increased in some=20
sub-areas, but it decreased in other sub-areas. Therefore, it cannot =
be=20
predicted if the buffer approach would increase or decrease the cost. =
This=20
variation of the cost depends on specific characteristics of the area. =
In the=20
tested area (La Hoya de Bu=EF=BF=BDol county), applying the buffer =
over the sub-areas=20
of figure 10 produced a new average cost 15.81 =EF=BF=BD/t.
Table 7. New sub-areas associated with collection points as =
determined by=20
the Borvemar model when Q =3D 1000 t/year and R =3D 4 km =
after a=20
buffer of 2 km.=20
Sub-area |
Available Biomass
(t/year) |
Collecting Costs
(=EF=BF=BD/t) |
A1 |
3701.24 |
16.45 |
A2 |
3219.33 |
15.23 |
A3 |
3104.18 |
16.14 |
A4 |
3602.13 |
15.12 |
A5 |
3526.41 |
14.95 |
A6 |
3030.39 |
15.57 |
A7 |
3103.18 |
17.25 |
A8 |
3303.87 |
15.45 |
A9 |
2936.21 |
15.98 |
A10 |
3709.13 |
14.98 |
A11 |
2630.14 |
16.75 |
A12 |
3303.43 |
15.71 |
=20
Figure 12. New sub-areas associated to collection points as =
determined by=20
the Borvemar model for Hoya de Bu=EF=BF=BDol county (Valencia, Spain) =
when Q =3D=20
1000 t/year and R =3D 4 km after a buffer of 2 km.
Summary and Discussion
To be able to combine GIS spatial studies with linear programming =
models,=20
it is necessary to build a network from a digital map. In this work, a =
mathematical calculation method, the Borvemar model, has been =
described to=20
select the actual points on the map at which biomass can be collected =
and=20
which can subsequently be considered as biomass sources in a network =
model.=20
The algorithm provides the location of points where the biomass of =
the=20
associated area can be concentrated with a minimum amount of available =
biomass=20
and limited area. These points, which represent sources of biomass, =
should be=20
connected with the other points where it is possible to locate =
consumption=20
facilities (power plants). Using these concepts, a network structure =
was=20
built. The optimization of the selection of the source points to =
supply the=20
power plants was solved by linear programming in the structured =
network from a=20
digital map.
The algorithm described herein was applied to a rural region of the =
Comunidad Valenciana (Spain), La Hoya de Bu=EF=BF=BDol. This county =
has an area of=20
816.18 km 2 , and the amount of available biomass is 20,388 =
t/year.=20
Three criteria were tested for choosing the collecting sub-areas:=20
-
A required productivity of 1000 t/year of wood biomass and a =
maximum=20
collection distance of 4 km ( R =3D 4 km). These values =
produced 12=20
sub-areas with an amount of biomass to be mobilized of 13,818.87 =
t/year, or=20
63.28% of the total. The average cost was 16.53 =EF=BF=BD/t.
-
A minimum productivity of 700 t/year of wood biomass and a =
maximum=20
collection distance of 3 km ( R =3D 3 km). These values =
produced 17=20
sub-areas with an amount of biomass to be mobilized of 14,876 t/year =
(68% of=20
the total) but with a cost of 17.38 =EF=BF=BD/t.
-
A minimum productivity of 1000 t/year of wood biomass and a =
maximum=20
collection distance at 5 km ( R =3D 5 km). These values =
produced 11=20
sub-areas with an amount of biomass to be mobilized less than that =
of the=20
first calculation, 12,876 t/year, but with a cost of 15.98 =
=EF=BF=BD/t.
Two extensions were also tested:=20
-
Further iterations were included to fill the gaps that were left =
by the=20
first calculation process. New sub-areas were evaluated with a =
minimum=20
productivity required of 700 t/year wood biomass and a maximum =
collection=20
distance of 3 km ( R =3D 3 km). Only one smaller sub-area =
appeared=20
together with the large sub-areas selected. New amounts of biomass =
to=20
mobilize were 14,810.87 t/year, or 67.80% of the total. The average =
cost was=20
16.63 =EF=BF=BD/t.
-
Over the results obtained with a required productivity of 1000 =
t/year of=20
wood biomass and a maximum collection distance of 4 km ( R =
=3D 4 km), a=20
buffer of 2 km was applied, increasing the sizes of the 12 sub-areas =
initially obtained. The cost per tonne of biomass increased in some=20
sub-areas but decreased in other sub-areas. Therefore, it could not =
be=20
predicted if the buffer increased or decreased the cost per tonne. =
This=20
variation of the cost depends on specific characteristic of the =
area. In the=20
tested area (La Hoya de Bu=EF=BF=BDol county), the buffer over the =
sub-areas of=20
figure 10 produced a new average cost 15.81 =EF=BF=BD/t. =
Acknowledgements
We would like to thank the R&D&I Linguistic Assistance =
Office,=20
Universidad Polit=EF=BF=BDcnica de Valencia (Spain), for granting =
financial support=20
for the linguistic revision of this article.
REFERENCES
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and R. M.=20
de Mol. 2007. Biomass logistics. In Proc. 15th European Biomass =
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Berruto, R., and =
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Buckmaster, D. =
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Copyright =C2=A9 2008 American Society of Agricultural =
and Biological=20
Engineers. All rights reserved.
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