Flow Map of Products Transported among Warehouses and

Supermarkets

Evgheni Polisciuc, Pedro Cruz, Hugo Amaro, Catarina Mac¸

as and Penousal Machado

CISUC, Department of Informatics Engineering, University of Coimbra, Coimbra, Portugal

Keywords:

Flow Map, Origin-Destination Map, Thematic Map, Flow Visualization, Geovisualization, Big Data.

Abstract:

Representing large amounts of data using ﬂow maps involves dealing with the reduction of visual clutter-

ing. This article presents a method for generating ﬂow maps and visualizing products being transported from

warehouse to supermarkets in a major retail company in Portugal. Our approach uses a swarm-based sys-

tem to reduce visual clutter, bundling edges in an organic fashion and improving clarity. Additionally, the

Dorling cartograms technique is applied to reduce overlapping of graphical elements that render locations

in geographic space. Finally, different design decisions enable a multi-perspective visualization of the same

dataset.

1 INTRODUCTION

Flow maps are a technique used to show the move-

ment of objects from one location to another, such as

people migration, the amount of goods being traded,

amounts of products being transported from ware-

houses to supermarkets, etc. Flow maps say little

or nothing about the pathway, but include the infor-

mation about what is ﬂowing (moving, migrating,

etc.), the direction of ﬂow, and how much is being

transferred. In most cases, the data is represented

using line width, line color and spatial properties.

Flow maps are advantageous in what regards to vi-

sual clarity and ease of visual communication. This

is achieved by merging edges that share similar des-

tinations, or in some cases by tracing them through a

similar path. However, this technique often fails when

applied on large amounts of ﬂow data. The visualiza-

tion might become cluttered, making the map difﬁcult

to read, and difﬁcult to distinguish the grouped indi-

vidual streams.

In this work we describe a method for the genera-

tion of ﬂow maps that is able to depict large amounts

of transitions from one location to another (further

expressed as Origin-Destination or simply OD). This

method uses a customized swarming system to trace

edges in an intuitive and organic fashion, and to re-

duce visual clutter. Our method employs graphic de-

sign decisions to promote clarity of visual commu-

nication in a high density environment. In order to

improve clarity of representation of geographic lo-

cations, a technique, known as Dorling cartograms

(Dorling, 1996), was applied. With this technique,

overlapped points were separated retaining some de-

gree of spatial relationship. Finally, our technique

supports mixed types of points – geo-referenced data

points and those that have no ﬁxed position in space.

This work tackles the issue of depicting large

amounts of products being transported from ware-

houses to hyper and supermarkets of a major retail

company in Portugal. Our dataset has approximately

15 to 90 millions of warehouse-to-supermarket transi-

tions per day over a time span of 6 months. The loca-

tions consist of approximately 60 warehouses, major

part of which are located outside Portugal, 1039 su-

permarkets in Portugal and 230 supermarkets outside

the Portugal, including the geo localization of 680 su-

permarkets.

In the following sections our approach is de-

scribed in more details. Section 3 presents the un-

derlying idea and the method in detail. Section 4 de-

scribes an application of this technique on the given

dataset. Finally, section 5 presents a comparison of

the results obtained by our approach and the existing

one.

2 RELATED WORK

Direct visualization of large amounts of Origin-

Destination transitions can generate high degrees of

visual clutter. In these cases a reduction strategy

Polisciuc, E., Cruz, P., Amaro, H., Maçãs, C. and Machado, P.

Flow Map of Products Transported among Warehouses and Supermarkets.

DOI: 10.5220/0005787301770186

In Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2016) - Volume 2: IVAPP, pages 179-188

ISBN: 978-989-758-175-5

179

Figure 1: Export of French wine by Charles Minard, 1864.

known as edge bundling can be applied. This is

characterized not only by graph simpliﬁcation, but

also by the revelation of the principal streams of

ﬂow. Holten introduced edge bundling for com-

pound graphs (Holten, 2006). His work consisted in

routing edges through a hierarchical layout using B-

Splines. Nowadays, there are several variations of

edge bundling such as force-directed edge bundling

(Holten and van Wijk, 2009), or sophisticated ker-

nel density estimation strategies (Hurter et al., 2012).

Generally, edge bundling consists of drawing similar

edges on the same path, i.e. edges that are related

in geometry and direction are routed along the same

path.

In the geographic context an Origin-Destination

representation, as a rule, refers to the ﬂow visual-

ization (also known as ﬂow maps), which is deeply

rooted in the history of information visualization.

Early examples, such as wine exports from France,

produced by Minard (Tufte, 1983, page: 25), repre-

sent quantity as well as direction of wine exports en-

coded by the thickness of the corresponding edges,

which disjoin from the parent edge (see Figure 1).

The work of Phan et al. (2005) presents an automated

approach to generate ﬂow maps using a hierarchical

clustering algorithm, given a series of nodes and ﬂow

data. Generally, in geographic context, a ﬂow map de-

picts quantities of any type of objects that move from

one location to another – e.g. migrations, transporta-

tion of goods, etc. The advantage of ﬂow maps is that

they reduce visual clutter by merging edges. How-

ever, when representing large amounts of data this

technique presents a series of problems, such as poor

perception regarding the directionality of ﬂow, high

degrees of visual clutter, overlapping of graphical el-

ements that represent locations.

Another important characteristic of this work is

the focus on nature-inspired approaches. The under-

lying idea is based on self-organizing system, and

more precisely on the phenomenon of emergence in

such systems. As the term indicates self-organization

is a process in complex systems, in which the struc-

ture or organization appears without any explicit in-

terference from outside. Self-organizing processes

often result in the occurrence of emergent phenom-

ena. More precisely, when the complex structure or

behavior appear due to the interaction of a collective

of individuals, which were not programmed for that

(Di Marzo Serugendo et al., 2011). In the ﬁeld of data

visualization, there are techniques of graphical repre-

sentation that are based on such systems. For instance

Geoboids (Macgill and Openshaw, 1998) employs a

method to reveal patterns in spatial data through the

use of customized ﬂocking system. In this system,

each, so called geoboid explores geographic space in

accordance with the simple rules of interaction with

other geoboids and the data found nearby. The vi-

sualization, which emerges from this simple process,

shows areas containing interesting information. An-

other series of works by Vande Moere exploit self-

organization and emergence in information visualiza-

tion. He introduces the idea of infoticle, which desig-

nates a particle that responds to data values and static

forces in a particle system (Vande Moere et al., 2004).

The visual output portrays the Internet ﬁle usage of a

medium-sized company over time, conveying the pat-

terns of ﬁle downloads. Another nature-inspired ap-

proach is the information ﬂocking visualization (Mo-

ere, 2004). In this work, Vande Moere uses an artiﬁ-

cial ﬂocking system, originally proposed by Reynolds

(1987), where the forces of attraction and repulsion

are modiﬁed proportionally to the similarity between

the data objects that each boid encodes. The emer-

gent patterns analyzed in a higher-level, where each

composition portrays short-term and long-term data

tendencies in time-varying dataset, conveying mean-

ingful changes over time.

3 FLOW MAP FLOCKING

MODEL

In order to reﬂect the ﬂowing nature of the data we

resort to a ﬂocking system. The underlying model to

construct our ﬂow map shares common characteris-

tics with the work of Polisciuc et al. (2015). The vi-

sualization itself can be seen as a directed graph com-

posed by nodes and edges. The system consists of

artiﬁcial agents (further referred to as boids) each one

tracing an individual Origin-Destination edge. A boid

is characterized by its position in space, direction and

speed. During the simulation each boid leaves per-

IVAPP 2016 - International Conference on Information Visualization Theory and Applications

180

Figure 2: Visual output from the system after 5 full cycles,

image at the bottom. Detail of the computed traces in black,

image at the top. The rectangular and circular nodes repre-

sent origin and destination of the ﬂow, respectively.

sistent traces, further referenced as ghosts, which in-

herit the location at each simulation instance, direc-

tion and the edge being encoded. Since the process

is asynchronous, i.e. each trace is computed sepa-

rately, the boids in the system interact only with the

ghosts instead of other boids. While interacting with

the ghosts, each boid follows simple rules: attract

to friendly ghosts; repel from the unfriendly ones;

and avoid static points, which are the nodes of the

graph. In order to determine the relationship between

the boids and the ghosts we used a pairwise similarity

measures between edges, including geometric proper-

ties and weight of edges. The output of the system is

shown in Figure 2.

In this section we describe our ﬂocking system;

our similarity metrics; implementation and optimiza-

tion considerations; and the graphical variables used

in this ﬂow map.

3.1 Model

As previously mentioned, our model consists of a set

of boids characterized by location in space, direc-

tion, speed and the ﬁeld of vision. The boids move

in space reacting to the presence and characteristics

of other neighboring boids. A pairwise interaction

between boids and ghosts determines their behavior.

If the agents encode similar edges, they are consid-

ered friendly. If the agents encode dissimilar edges,

they are considered unfriendly. Otherwise, they ig-

nore each other. The degree of similarity, which is

described in the following sub section, affects the

force of attraction or repulsion between agents and

ghosts. Therefore, friendly agents advance together as

a group and unfriendly agents repel from each other

avoiding collisions.

Each trace is computed individually, starting at the

origin node and ﬁnishing at the destination node. The

computation of each trace only starts when the previ-

ous one has ﬁnished, and so forth for all the traces.

In each iteration the boid’s paths are updated accord-

ing to the current state of the system. More precisely,

during the execution cycle each boid interacts with

the ghosts left by other boids and never with their

own ghosts. The process repeats until the visual result

is acceptable and the user decides to stop it. During

the computation of each trace the acceleration vector

and the speed of the boid B with position ~p

is deter-

mined by the characteristics of each ghost G within

the ﬁeld of vision V F

. The acceleration vector is

computed as following: i) compute a vector relative

to the ghosts; ii) compute a vector relative to the static

points; iii) compute a normalized vector pointing to-

wards the destination (see section 3.3 for implemen-

tation details). Having all the three vectors computed,

they are weighted, and then added to the acceleration

vector; the acceleration is added to the speed vector;

and the speed is limited to the predeﬁned maximum

and is added to the current location. The maximum

deﬁned speed reﬂects on the visual output resulting in

high and low curvature of edges for speed limited to

1 and 5 (in relative spatial units), respectively.

3.2 Edge Similarity

Edge similarity (further referred to as similarity score

or simply score) is calculated on the input graph tak-

ing into account geometric properties of edges. The

output from pairwise calculation is then stored in nxn

matrix, where n is the number of edges. The score

consists of the following three components:

Angle. The boids implement different behaviors

and the angle between

OD vectors dictates whether

Flow Map of Products Transported among Warehouses and Supermarkets

181

boids are friendly or not. The angle α ∈ [0, π] that

the two vectors make is linearly mapped to the range

[−1,1]. The sign translates directly into the direction

of the force during the interaction between boids.

Distance. Determining the minimum Euclidean

distance between two line segments is a typical prob-

lem in areas dealing with geometric data. We used an

algorithm proposed by Lumelsky (1985), which takes

as input the coordinates of the end points of the two

segments and outputs the distance. This algorithm is

efﬁcient, since the distance is not computed until the

endpoints do not satisfy certain condition. This is,

the endpoints are not the closest points and the seg-

ments do not intersect. In order to translate the dis-

tance to the range [0, 1] the following function was

used: k/(d + k), where d is the distance and k is a

constant, in our case empirically deﬁned as 10.

Length difference. The similarity between edges is

proportional to the absolute difference between their

lengths. In other words, the edges that have equal

lengths are considered similar and vice versa. In the

end, the values are normalized in order to equalize

scaling. Formally, let l and p be the lengths of the

pairs of edges, we calculate 1 − (|l − p|/max(l, p)).

In order to calculate the ﬁnal score as a mea-

sure of similarity, we apply the following function:

(distanceScore + lengthScore) × angleScore. As can

be seen, the angle score is prioritized, again because

of the behavior. In other words, if two edges are paral-

lel and pointing towards the same direction, the length

and the distance scores come into calculation. In this

case, if the lengths are similar and the distance be-

tween segments is small the boids that encode these

edges have high attraction forces and route the traces

through similar paths.

3.3 Implementation and Optimization

This sub-section describes each step of the compu-

tation of the acceleration vector of a boid in detail

provided in pseudo-code. First, a vector for a boid

B relative to the ghosts is computed as following:

Integer c = 0

for each G in VF:

Float s = similarity value for G

if s >= 0:

Vector bg = vector from B towards G

end if

if s < 0:

Vector bg = perpendicular to direction of B

// left or right perpendicular depends

// on the position of G in relation of B

end if

normalize bg

multiply bg by s

add bg to v

c = c + |s|

end for each

divide v by c

return v

Second, a vector for a boid B relative to the static

points is computed as following:

Integer c = 0

for each static point SP:

Float dd = radius of SP

Float d = distance from B to SP

if d < dd:

Vector spb = vector from SP to B

normalize spb

multiply by (dd - d)

add spb to v

c = c + 1

end if

end for each

divide v by c

return v

Finally, when the boid approximates its destina-

tion, all the forces, except the destination force, are

ignored and the speed is limited to 1. This restriction

ensures that each boid reaches its destination.

In order to reduce the computation cost we ap-

plied a hierarchical structure of spatial data – more

precisely – a quadtree. This type of structures is based

on the principle of recursive decomposition and smart

subdivision of spatial data (Samet, 1984). This hierar-

chical representation is useful because it focus on in-

teresting subsets of data, and is efﬁcient in execution

times and performance of getting and setting opera-

tions. We used the quadtree to store and access ghosts

of boids.

In our implementation, the get operation is

straight-forward. At execution time, we access ghosts

that are inside the region that is deﬁned from the ﬁeld

of vision of the boid being computed. Then we only

iterate over the elements that are within this ﬁeld. The

set operation is conditional and is performed as fol-

lowing: ﬁrst, check if in a certain range there are no

existing ghosts; if this condition is true, then update

their positions and the direction vectors; otherwise,

add a newly created ghost to the quadtree.

Finally, each ghost is updated taking into account

the data value they encode. The idea is the following:

the ghosts that encode large values have greater im-

pact over the ones that encode smaller values. There-

fore, making the traces that have less impact fol-

low the ones that have bigger impact. The following

IVAPP 2016 - International Conference on Information Visualization Theory and Applications

182

pseudo-code exempliﬁes the function that updates the

existing ghosts:

Float dv = normalized data value of G0

for each G in VF of G0:

// update position

Vector gg0 = vector from G to G0

normalize gg0

divide gg0 by count G in VF of G0

multiply gg0 by dv

add gg0 to position of G

// update direction vector

Vector v = direction vector of G0

multiply v by dv

add direction vector of G to v

normalize v

set v to direction vector of G

end for each

4 APPLICATION

In this section we describe a visualization application

of our method for the ﬂow map. We apply this tech-

nique to visualize the ﬂow of products among ware-

houses and supermarkets. In other words, the visual-

ization depicts movements of stocks of products in-

side a major retail company in Portugal.

4.1 Data Description

Our dataset consists of approximately 15 to 90

millions of warehouse-to-supermarket transitions of

product per day over a time span of 6 months. Each

transition has the following attributes: product id,

quantity of products in transit (further referenced as

stock in transit or SIT), quantity of products deliv-

ered (further referenced as stock on hand or SOH),

warehouse id, supermarket id, and the date of transi-

tion. The locations consist of approximately 60 ware-

houses, some of which are located outside the Por-

tugal, 1039 supermarkets in Portugal and 230 super-

markets outside the Portugal, including the geo local-

ization of 680 supermarkets (see also (Polisciuc et al.,

2015; Mac¸

as et al., 2015a,b)).

In order to get a graph representation of the data

we proceeded to the calculation phase. First, the

data were aggregated by days. Each day sums-up

SIT quantities by aggregating pairs of warehouse-

supermarket locations, which constitute the edges and

the nodes of the graph. Finally, the total of SOH quan-

tities per supermarket is calculated. Therefore, we get

a weighted directed graph whose edges are directed

from warehouse to supermarket nodes and weighted

by SIT quantities. The nodes that represent supermar-

kets have assigned SOH quantity, while the nodes that

represent warehouse have none.

4.2 Flow of Products Visualization

This visualization depicts amounts of products that

have been transported and the amounts of products

that have been delivered during one day. It is impor-

tant to describe the process to get a readable layout

of mixed graph. There are two challenges to visu-

alize this particular graph: not all the locations have

a geographical positions; but, the ones that do have,

can overlap. The ﬁrst issue was solved by ﬁxing the

nodes that have a geographical location, and by using

force-directed graph layout algorithm (Fruchterman

and Reingold, 1991) to compute the location of other

ones. This algorithm is efﬁcient in what concerns

about the graph topology, since it considers clusters

of nodes and not individual nodes. The second issue

was solved by applying Dorling cartogram technique

over the precomputed layout. The beauty of this al-

gorithm is that it preserves original relative position-

ing of geo-referenced elements. This enables the map

of Portugal to be recognizable, making the locations

distinguishable and increasing visual clarity (see Fig-

ure 3).

In the visualization each trace represents the quan-

tity of products in transit from warehouse to super-

market. These quantities are encoded by two means –

color and line thickness. The two graphical elements

are complimentary and make use of different map-

pings. The color uses a linear mapping. The values

are mapped to a pale yellow-purple-dark blue gradi-

ent, being pale yellow and dark blue for lowest and

highest values, respectively. The thickness variable,

on the other hand, uses an exponential scale, empha-

sizing high values. Finally, we use an arrow, which is

rendered at the end of a trace and scaled proportion-

ally to the thickness of the line, in order to represent

the direction of the ﬂow (see Figure 3). The orienta-

tion of the arrow is determined in three steps. First,

the length l and the with w of the arrow is computed.

The w and l are equal to the 2x and 3x thickness, re-

spectively. Second, the last vertex v of a trace that is

located at the minimum distance from location of the

node c plus its radius and the l is determined. Third,

the arrow orientation is deﬁned by the vector pointing

from v to c.

In order to represent different types of nodes we

use different graphical elements – squares and cir-

cles to represent warehouses and supermarkets, re-

spectively. The nodes are colored according to coun-

try they represent. Since our data contains a high

number of countries, the color could become ineffec-

Flow Map of Products Transported among Warehouses and Supermarkets

183

Figure 3: For the sake of simplicity this image shows only transitions from one warehouse. The whole graph can be seen in

the Figure 7.

tive. In this case, we calculate the total number of

locations, aggregating by country, sort the countries

in descendant order, and consider only the ﬁrst two

countries, which are Portugal and Spain, and treat the

others as an unique instance. The colors used was

green, red and blue for Portugal, Spain and others,

IVAPP 2016 - International Conference on Information Visualization Theory and Applications

184

Figure 4: A visualization of edge overlapping. The number

of overlapped edges is represented with the color from pale

green to intensive red. This image shows only the transi-

tions from a selected warehouse.

respectively. Finally, the nodes that have geographic

reference were rendered with the graphical shape of

an X in the center of the node (see Figure 3).

Due to the high degree of traces overlapping, it

is hard to identify main streams. For that reason, we

proceed with a color-temperature visualization of the

ﬂow map. Using the same graph we apply different

graphical elements. In this visualization the traces are

colored according to the total number of overlapping

elements. More precisely, we compute the number of

overlapped segments that build-up the traces located

within a deﬁned range. Then at the render instance

this value is mapped to a color scale from intensive

red to a pale green, where red and green mean high

and low degrees of overlaps. This representation is

useful to get another perspective of such complex vi-

sualization (see Figure 4).

5 RESULTS

The visualizations shown in this section depicts our

data. All the visualizations that we generated use the

technique described in section 4, except in the line

thickness. To facilitate the comparison in this small

scale we reduced visual complexity: lines with con-

stant thickness; no arrows at the end of the traces;

nodes colored in white.

The very ﬁrst comparison reveals the efﬁciency of

visual clutter reduction. As can be observed, the force

directed edge bundling (FDEB) method (see Figure 5,

image in the middle) generates less visual clutter in

comparison with our approach. When using swarms,

main streams of ﬂow are visually distinct from each

other leaving enough space for the ones with less im-

pact. In addition our approach considers edge weight,

therefore, resulting in meaningful representation of

data being visualized (see Figure 5).

In our approach each boid attempts to avoid the

boids with opposite directions, as such the traces are

never routed through the same trail. This enables sep-

aration of streams that encode opposite directions. In

contrast, this is not the case when using the FDEB.

This type of algorithms does not take into account the

directionality of streams, which is an emergent char-

acteristic of the swarm-based approach. Finally, since

the boids in the system attempt to avoid static points,

the nodes are clearly visible and do not visually inter-

fere with the lines (see Figure 5, image on the left).

As previously mentioned, our method is sensible

to the parameters of maximum speed and the ﬁeld of

vision of boids. The bigger the ﬁeld of vision the less

bundled the edges. Also, main streams tend to ag-

gregate more edges comparing to the lower values.

Maximum speed, on the other hand, translate into the

“waviness” of traces. Using bigger values boids tends

to draw traces in a more organic manner. However,

there is a loss in detail of trace and overall visual-

ization. Figure 6 (image in the middle) displays the

visual output using maximum speed 5 and radius of

vision ﬁeld equal to 50 degrees.

Finally, our approach gives diverse perspectives

over the same dataset. Depending on the sorting or-

der the visualization can emphasize streams that rep-

resent low or high values (see Figure 6, image on the

left). Additionally, our approach enables a visualiza-

tion of the density of streams by applying an appro-

priate color scheme described in section 4.

Flow Map of Products Transported among Warehouses and Supermarkets

185

Figure 5: Comparison between the techniques straight lines (left), FDEB generated using 5 cycles, 50 iterations and stiffness

10 (image in the middle), our approach using SIT quantities in calculations (right).

Figure 6: Flow map generated by our method without considering SIT quantities (left), parameters of maximum speed set to

5 and vision ﬁeld set to 50 degrees (image in the middle), inverse sorting order (right).

6 CONCLUSIONS

As previously mentioned, applying the ﬂow map on a

large amount of data is challenging, since it involves

dealing with high degrees of visual clutter. In this ar-

ticle we presented a method for generating ﬂow maps

that overcomes the cluttering issue in visualization.

Our approach relies on a nature-inspired algorithm

resulting in emergent visual patterns. Ultimately, re-

sulting in edge bundling to reduce visual clutter and

to promote visual clarity in the representation. In ad-

dition, we explored different graphical languages ap-

plied on the generated graph to give diverse perspec-

tives over the same dataset.

IVAPP 2016 - International Conference on Information Visualization Theory and Applications

186

Our method consists of a set of boids that trace a

path to represent each edge in the graph. Each sin-

gle boid follows simple rules through the interaction

with the neighboring trails. The similarity between

the edges, which belongs to the range [-2, 2], deter-

mines whether boids are friendly or not. This makes

the boids to attract or repel from each other. Further-

more, in cases when the similarity is zero, the boids

ignore each other. In addition, the boids that represent

more products have higher impact on other members

of the system. Finally, every boid attempts to avoid

static points, which are the nodes of the graph.

We described two types of graphical representa-

tion. We presented the main visualization, which

depicts transitions of products from warehouses to

supermarkets. The total amounts of products being

transported are represented with color and line thick-

ness. The directionality of movement is indicated by

an arrow at the end of each trace. The nodes use color

to show different countries, while the shape of each

node indicate either its is a warehouse or a supermar-

ket. Finally, the ﬁxed nodes are marked with an “X”

in the center of the node. Additionally, the sorting or-

der of the edges reﬂects the emphasis on low or high

values. Then, we presented a graphical approach to

distinguish main streams of ﬂow. This is achieved by

coloring the edges by their degree of overlapping. In

this case, the red and green colors represent high and

low number of overlapped traces, giving a visual rep-

resentation of the complexity of the graph.

ACKNOWLEDGEMENTS

This project is partially funded by SONAE: Sonae Viz

– Big Data Visualization for retail, and by Fundac¸

para a Ci

encia e Tecnologia (FCT), Portugal, under

the grant SFRH/BD/109745/2015.

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Flow Map of Products Transported among Warehouses and Supermarkets

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Figure 7: Final render of whole graph with the focus on the continental part of Portugal.

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