Urban freight demand estimation: a probability distribution based method

Abstract

The lack of data is one of the most common problems when dealing with the design of solutions that optimize urban freight transport (City Logistics Projects). In fact, to be able to process an effective City Logistics Projects for a certain area of the city, it is necessary to have the data concerning the number of daily deliveries that each commercial activity receives in this area, with detailed information regarding the time of delivery, the type of used vehicle and the amount of delivery. Only in this way is it possible to have a correct and realistic dimensioning of the freight demand. In the reality, it is not always possible to have this data for an adequate period of time. This paper, starting from the existing literature on demand forecasting and from an analysis of real data, provides the proposal of an alternative method of forecasting the demand for goods for a given area in the city when only the typology of commercial activities and a small amount of data are known.

Full text

Urban freight demand estimation: a probability distribution based
method
Alexandra Lagorio 1, Jesus Gonzalez-Feliu 2, Roberto Pinto 3
1,3 Department of Management, Information and Industrial Engineering, University of Bergamo, via G. Marconi,
24044, Dalmine (BG) – Italy
2 Environnement, Ville et Société, Department of Environment and Organization Engineering, Institut Henri,
Fayol, Ecole des Mines de Saint-Etienne, 158 cours Fauriel, 42023 Saint-Etienne Cedex – France
{alexandra.lagorio@unibg.it, jesus.gonzalez-feliu@emse.fr, roberto.pinto@unibg.it}
Abstract. The lack of data is one of the most common problems when dealing with the design of
solutions that optimize urban freight transport (City Logistics Projects). In fact, to be able to process an
effective City Logistics Projects for a certain area of the city, it is necessary to have the data concerning
the number of daily deliveries that each commercial activity receives in this area, with detailed
information regarding the time of delivery, the type of used vehicle and the amount of delivery. Only
in this way is it possible to have a correct and realistic dimensioning of the freight demand. In the
reality, it is not always possible to have this data for an adequate period of time. This paper, starting
from the existing literature on demand forecasting and from an analysis of real data, provides the
proposal of an alternative method of forecasting the demand for goods for a given area in the city when
only the typology of commercial activities and a small amount of data are known.
Keywords: urban freight transport, demand estimation, city logistics; statistic distribution analysis.
1. Introduction
Many factors have contributed transforming urban logistics in recent years: the fragmentation of the
demand for goods, the ever-increasing frequency of deliveries, the continuous spread of the e-commerce
that has transformed every home into a delivery point. All those factors have led to an increase in traffic
congestion and a consequent increase in noise pollution and emissions of air pollutants that have made
urban centers less and less livable cities. In order to cope with these problems, city logistics projects have
been developed and aimed at optimizing urban transport of goods.
However, the implementation of this type of solution requires careful and proper planning that is made
complex by the presence of numerous stakeholders with often conflicting interests and the scarcity, if not
the absence, of the data needed to design the city logistics solution best suited to the context (Lagorio et al.,
2016). In fact, the most widespread city logistics solutions, such as the urban distribution centers, the
loading-unloading areas for the deliveries operations or the delivery of goods by vehicles with low
environmental impact (i.e., cargo-bikes, e-vehicles) require correct information regarding the
infrastructural network, the regulations, the location of the places of delivery (i.e., shops, private houses)
and the demand for goods. While the information about the first elements mentioned is relatively easy to
obtain online (Golini et al., 2018), the estimation of the demand for goods required by an urban center (or
a part of it) is a trivial problem.
In order to estimate the future demand for goods, usually researchers rely on historical series, but in this
case, they are difficult to obtain because, unlike the demand for goods in the industrial sector, we do not
have to deal with one or few suppliers and an exact number of customers. In the case of urban freight
transport, each shop carries out its operations independently from the others, as well as suppliers, each one
keeps track of its operations in a different way and it is therefore also difficult to reconstruct the number of
deliveries spent per store.
In particular, in order to implement the main city logistics solutions, it is necessary to know the number of
deliveries that each store receives in a week, the number of vehicles from which these deliveries are made,
the type of vehicle used for the delivery, the day of the week and the time of the day in which deliveries
took place. This data should be available for a sufficiently long period of time so that trends, peaks and
seasonality can be observed in the frequency of deliveries.
Nowadays, the following general modeling frameworks are applied to estimate the demand generation
patterns related to urban logistics (Gonzalez-Feliu and Peris-Pla, 2017):

7th International Conference on Information Systems, Logistics and Supply Chain
ILS Conference 2018, July 8-11, Lyon, France
 Deterministic freight trip generation (FTG) or freight generation (FG) models, issued from
establishment-based surveys and mainly related to category classification datasets (Holguin-Veras
et al., 2011). Those models can be based on constant rates calculated for each category (Holguin-
Veras et al., 2012; Gonzalez-Feliu et al., 2014b; Aditjandra et al., 2016) or relate, for each category,
the number of trips (FTG) or the freight quantities (FG) to different variables, like employment
(Holguin-Veras et al., 2013; Gonzalez-Feliu et al., 2014a), area (Jaller et al., 2014; Alho and de
Abreu e Silva, 2014) or income, resulting on constant, linear or non-linear model for each category
(Sanchez-Diaz et al., 2016b). However, models assigning different functional forms to each category
seem to give better results than models with a unique functional form (Sanchez-Diaz et al., 2016a).
 Random-based approaches (Deflorio et al., 2012 ; Faure et al., 2016 ; Lagorio et al., 2016), where,
because of the lack of data, or due to the needs of dynamic information for simulation purposes, the
assignment of a constant rate to each establishment is not pertinent. One possibility, when no other
information is available, is to determine suitable average values (which are in general able to be
estimated, at least roughly) then generate a random value around that average. They assume a
uniform statistical distribution of data, which is not always the case (Gonzalez-Feliu et al., 2014a).
 Probabilistic generation, i.e. random generation not based on a uniform distribution but to other
probability distribution. Although that generation is still not much deployed, we can find two works
deploying it by comparing Normal and Rayleigh distributions (Gonzalez-Feliu et al., 2014a, Lopez
et al., 2016), and the second probability distribution seems to be more pertinent than the first (Lopez
et al., 2016).
However, since more probability distributions can be defined, and analogously to the recent developments
for a deterministic generation (Gonzalez-Feliu et al., 2016, Sanchez-Diaz et al., 2016a), it seems interesting
to explore the quality and relevance of using different probability distributions for a random generation in
FTG.
This paper provides a process that can be followed to estimate the demand for goods in urban areas when
there is no exact data on delivery frequencies. In this paper, the estimation procedure will be illustrated and
the results related to the first phases of the process will be reported as the research is still ongoing.
In the following section, we present the methodology process that leads to the estimation of the demand for
urban goods in the absence of extended datasets on the frequency of goods. Then, first results of the
application of the first phases of the estimation process will be reported. Finally, the limitations, the future
developments of the research and the final considerations with respect to the work carried out so far will be
reported.
2. Methodology
The methodology starting from the data collection and leading to the definition of an urban freight demand
estimation is quite long and it is summarized in Figure 1. The proposed method is a peculiar application in
the urban freight transport field of the general method of generating demand from probability distribution
(Kolassa, 2016; Petrik, Moura and Silva, 2016). In Figure 1 we reported all the steps implemented in this
research to perform the demand estimation using probabilities distributions.
FIGURE 1 Research methodology streamline
(1) Data
collection (2)
Categorization
(3) Preliminary
statistical
analysis
(4)
Identification
of probability
distributions
(5) Test
(6) Application
with Monte
Carlo
simulation
(7) Urban
freight
demand
estimation

7th International Conference on Information Systems, Logistics and Supply Chain
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First of all, some data are necessary to have a starting point for the identification of the probability
distribution of the number of deliveries. In particular, the number of weekly deliveries for each shop in a
defined pilot area is necessary (1).
Then, it is possible to separate the list of shops in different categories basing on the sell product category.
Thus, for each category, we have a list of shops with the average number of weekly deliveries (2). At this
point it is possible to identify some classical statistical parameters (i.e., mean, variance, maximum,
minimum, quartiles) and to perform some preliminary statistical analysis (i.e. correlation tests) in order to
understand if there are some external factors that affect the average number of weekly deliveries such as
the shop surface, the number of employers or the numbers of suppliers (3).
After performing these analyses, it is possible to identify the probability distributions for each freight
category (4). In this paper, the analysis stops at this point but the process is still not concluded. To guarantee
an adequate reliability and replicability of the method it is still necessary to test the goodness of the
distributions, for example, try to define them starting from another pilot area with the same freight
categories (5). If the probability distributions are the same for each freight category, it is possible to estimate
the freight demand for a new pilot area in which the shop categories are known but the average of weekly
deliveries is unknown. The idea is to assign the probability distribution of the freight category to every shop
in the selected area and then perform a Monte Carlo simulation that simulate the number of deliveries for
each shop in the area according to the probability distribution assigned to the shop category (6).
In this way it possible to estimate the urban freight demand of goods of every area of the city in which we
know the category of freight sold by each shop in the area (7).
3. First Results
In this paper, the average number of deliveries per week for every single store was analyzed. Data are issued
form the French Urban Goods Transport Surveys (Ambrosini et al., 2010), already used in Gonzalez-Feliu
et al. (2016) and Sanchez-Diaz et al. (2016a) for deterministic models and in Lopez et al. (2016) for
Rayleigh –based probabilistic ones. In particular, 2,970 single entry constitute the total number of retrieved
data in the collecting period (1996-1999). Three cities were involved in the survey: Marseille, Dijon and
Bordeaux, and data can be used jointly since works using those data show that the freight generator in all
those cities is the single establishment independently of its location (Gonzalez-Feliu et al., 2014b).
Although more recent data has been collected (in Paris in 2012 and in Bordeaux in 2014), the two databases
are not homogeneous (each of them includes 900 to 1100 valid entries, which does not lead to statistically
relevant data for all categories if considered separately) so the joint use of the two surveys is not nowadays
possible (which is instead the case for the data used in this research). Moreover, data of Paris presents some
irregularities and lacks that have not yet been adjusted, and the survey of Bordeaux is not still available
openly. The purpose of this article is to understand if it is possible, for each shops’ category, to obtain a
distribution that can represent the probability of a given number of weekly deliveries, in order to make a
demand prediction.
The first step for doing this is starting from a descriptive statistical analysis.
3.1. Descriptive statistical analysis
The data have a very high variability, with numerous extreme values. Data variability can be seen in Table
1, where for many categories the value of standard deviation is equal or greater than the mean and in
observing the chart for the boxplots (Figure 1).

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TABLE 1 Descriptive statistical analysis for each category of production / commercial activity
FIGURE 2 Boxplot related to the different categories of production / commercial activity
Given these characteristics, we can deduce the presence of large variability within certain categories and
the consequent presence of many extreme values. Before proceeding to each category, outliers have been
eliminated because they could compromise subsequent data analysis.
Outliers have been identified by the formula (Dawson, 2011):
     (1)
Where is the third quartile and is the first quartile. Subsequent data analyses were then carried out on
outbound data.
We can also observe that with such high variability in samples for each category, the mean could not be
used as a valid descriptive parameter of the data. The only categories where the mean can be significant are
in fact Category 14 (Retail Clothing, Shoes, Accessories, Leather Goods), Category 15 (Butchery) and
Category 22 (Bookshop) as it could be seen analysing the boxplots of these three categories.
For further categories, further investigations are required. If the mean cannot be used as a parameter to
describe the sample of data, we cannot assume that the average number of weekly deliveries is a constant
except for Categories 14, 15 and 22. We must, therefore, make a further assumption. In this case, we can
assume that data of weekly deliveries depends on known internal process features, such as the number of
employees (the only internal process feature available in the dataset used for this research).
To validate this hypothesis, a linear regression of the type was tested on the data:
N. Category Min 1s t Qu Median Mean 3rd Qu M ax sd Outliers
1 AGRICOLTURE 0,0 0,3 1,0 1,9 2,2 11,0 2,6 8,1
2 ARTISANS 0,0 1,0 2,0 3,6 4,0 46,3 6,0 13,0
3 IND CHIMIQUE 0,3 2,0 5,0 17,3 16,7 134,0 29,8 60,9
4 IND BIENS PROD ET INTERM 0,0 1,4 4,0 7,8 8,0 140,7 13,8 27,9
5 IND BIENS CONSOMMATION 0,4 1,0 3,0 7,1 6,0 118,0 13,3 21,0
6 TRANSPORT 0,0 0,3 1,5 4,3 3,8 59,0 10,7 14,1
7 COM GROS PRODUC INTERMED 0,0 2,0 4,0 15,2 10,0 655,0 66,9 34,0
8 COM GROS CONSO NON ALIM 0,0 1,2 3,0 9,0 10,0 212,0 22,0 36,5
9 COM GROS BIENS CONS ALIM 0,1 3,0 7,5 17,6 15,0 224,0 31,5 51,0
10 SUPERMARCHES 1,0 18,8 30,4 65,9 73,3 332,9 80,6 236,5
14 COM D ETAIL HAB,CHAUS,CUIR 0,0 1,0 2,0 2,7 4,0 16,6 2,4 13,0
15 BOUCHERIE 1,0 3,0 5,0 6,6 8,0 36,0 6,1 23,0
16 EPICERIE,ALIM 0,0 2,5 5,0 6,7 8,0 49,0 7,9 24,6
17 BOULANGERIES,PATISSERIES 1,0 2,0 3,9 6,2 8,0 30,1 6,3 26,0
18 CAFES,HOTELS,RESTAURANTS 0,0 1,9 3,0 6,4 7,3 70,0 9,7 23,2
19 PHARMACIES 1,0 21,0 26,0 27,1 34,9 81,0 14,6 76,8
20 QUINCAILLERIES 0,2 1,0 3,0 3,7 5,2 19,5 3,7 17,9
21 COM D' AMEUBLEMENT 0,0 1,0 3,0 0,1 5,7 28,5 6,3 19,8
22 LIBRAIRIE-PAPETERIE 0,5 3,3 7,9 9,6 14,1 26,8 6,8 46,5
23 AUTRE COMM DETAIL 0,0 2,0 4,0 7,1 8,0 72,0 9,4 26,0
24 SERVICES DIVERS 0,0 2,0 3,0 8,9 11,6 74,0 1,4 40,2
25 TERTIAIRE PUR 0,0 0,8 2,0 3,3 3,3 49,2 5,7 10,8
26 TERTIAIRE AUTRE 0,0 0,5 1,0 3,4 2,1 180,2 15,4 7,1
27 BUREAUX NON TERTIAIRE 0,0 0,9 2,0 3,8 4,8 33,0 5,6 16,5
28 ENTREPOTS 1,0 3,3 10,0 52,8 41,5 486,0 107,3 156,2
29 COM NON SEDENTAIRES 0,1 1,0 2,0 3,8 5,0 17,0 4,3 17,0
34 IND LOURDE (CONSTRUCTION) 0,0 1,0 3,1 7,3 8,0 86,0 12,6 29,0

7th International Conference on Information Systems, Logistics and Supply Chain
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    (2)
Where represents the average number of weekly deliveries per activity,  the actual number of employees
working at the same activity, and the parameters relating to the slope and the intercept of the regression
line. The results of the analysis are summarized in Table 2.
TABLE 2 Linear Regression Analysis
To assess the presence or not of a dependency between the two variables, we were based on several
evaluation tests:
1. Check R2: The more R2 approaches 1, the more effective the model is when interpreting the data.
So, the more the value of R2 is close to 1 the higher is the probability that there is a linear
dependence between the average number of weekly deliveries and the number of employees in the
business (Yang, 2015). In this study, in particular, we consider the existence of a dependence
between the two variables when R^2≥ 0,5 (Gonzalez-Feliu et al., 2014a).
2. F-Test: “the significance test of the regression equation often uses F test by the method of variance
analysis. F-statistics is defined as the average of regression sum of squares to the average of error
sum of squares ratio.” (Yang, 2015). With the given significance level α and the degree of freedom
(m, n-m), we can find Fα. If |F|≥F_α, it indicates that this regression has a significant linear. But
on the contrary, it indicates that this regression does not have a significant linear, namely, all the
independent variables are not responding to dependent variables. The p-values associated to the
F-value should be near zero at 0.0001 (Fite et al., 2002).
3. Pearson coefficient: is another test that can help us to define if there is a dependency between the
two variables. In particular, if the Pearson coefficient is between 0 and 0.3 the dependency is weak,
if the coefficient is between 0,3 and 0,7 the dependency is moderate and if the coefficient is greater
than 0,7 the dependency is strong. So, for this study, we have considerate only strong dependency
and so Pearson coefficients greater than 0,7.
4. Spearman coefficient: Spearman's coefficient indicates instead when there is a nonlinear
relationship between two variables. Even in this case, the more the coefficient approaches 1, higher
is the probability that between the two measured variables there is a nonlinear relationship. We
have considered a possible nonlinear relationship when the spearmen coefficient is greater than
0,7.
Slope Intercept
N. Category a b R^2 F p-value Pearson Spearman
Residuals mean
p-value
Test Shapiro
Polinomial R^2 Anova Test
1 AGRICOLTURE 0,1 1,5 0,1 2,2 0,1 0,27 0,53
5,75E-11 1 0,02
2 ARTISANS 0,8 1,8 0,2 2,0
0,2 0,15 0,26 -9,41E-11 1
3 IND CHIMIQUE 0,1 9,1 0,6 53,9 4.74e-09 0,75 0,55 1,63E-10 1
4 IND BIENS PROD ET INTERM 0,1 0,3 0,5 217,9
2.2e-16 0,70 0,50 5,89E-11 1
5 IND BIENS CONSOMMATION 0,2 4,1 0,5 189,9 2.2e-16 0,72 0,40 -8,54E-11 1
6 TRANSPORT 0,0 3,9 0,0 0,2 0,6481 0,09 0,50 6,10E-10 1
7 COM GROS PRODUC INTERMED 0,6 8,6 0,0 2,6 0,1073 0,12 0,40 6,82E-11 1
8 COM GROS CONSO NON ALIM 0,4 5,2 0,1 6,1 0,01533 0,24 0,42 -2,26E-11 1
9 COM GROS BIENS CONS ALIM 0,3 11,9 0,2 23,0 6,19E-06 0,45 0,35 -1,21E-15 1
10 SUPERMARCHES 0,5 7,9 0,7 126,3
8,76E-12 0,86 0,82 2,20E-15 1 0,74 Linear Regression
14 COM DETAIL HAB,CHAUS,CUIR 0,2 1,9 0,3 34,4 9,95E-17 0,50 0,39 4,85E-16 1
15 BOUCHERIE 0,5 4,9 0,1 8,7 0,1 0,34 0,34 2,16E-16 1
16 EPICERIE,ALIM 0,3 5,8 0,1 5,0 0,0 0,23 0,17 -1,63E-16 1
17 BOULANGERIES,PATISSERIES 0,1 5,9 0,0 0,7 0,4 0,08 0,01 2,72E-16 1
18 CAFES,HOTELS,RESTAURANTS 0,6 2,5 0,5 164,8 2.2e-16 0,73 0,46 3,63E-16 1
19 PHARMACIES 1,2 19,8 0,1 9,6 0,0 0,38 0,21 1,06E-15 1
20 QUINCAILLERIES 0,7 2,2 0,1 4,3 0,0 0,31 0,10 6,32E-17 1
21 COM D' AMEUBLEMENT 0,1 3,5 0,4 25,2 9,44E-03 0,61 0,54 8,60E-18 1 0,02
22 LIBRAIRIE-PAPETERIE -0,1 10,1 0,0 2,2 0,1 -0,16 -0,11 1,44E-16 1
23 AUTRE COMM DETAIL 0,1 6,3 0,1 13,9 0,0 0,22 0,41 -3,99E-16 1
24 SERVICES DIVERS 0,4 6,9 0,0 5,2 0,0 0,22 0,42 1,68E-16 1
25 TERTIAIRE PUR 0,0 3,1 0,0 4,1 0,0 0,13 0,45 -4,46E-17 1
26 TERTIAIRE AUTRE 0,0 3,3 0,0 0,0 0,9 0,01 0,49 -6,92E-17 1
27 BUREAUX NON TERTIAIRE 0,0 3,1 0,3 27,7
1,58E-03 0,54 0,58 1,36E-16 1 0,02
28 ENTREPOTS 1,0 35,1 0,1 3,3 0,1 0,23 0,38 -1,12E-15 1
29 COM NON SEDENTAIRES 0,3 3,3 0,0 0,2 0,7 0,09 -0,08 - 2,60E-16 1
34 IND LOURDE (CONSTRUCTION) 0,2 3,3 0,3 40,8
5,44E-06 0,54 0,44 -6,36E-16 1

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5. Test of normality of the residuals: to evaluate the correctness of a regression model, one of the
most common tests is to verify the normality of residual errors. In this study, the normality of
residual errors was verified with the Shapiro-Wilk test.
The categories for which there is a relationship between the average number of weekly deliveries and the
number of employees are: Category 3 (Chemical industry), 4 (Manufacturing industry manufacturing B2B),
5 (manufacturing industry of B2C goods), 18 (HoReCa, Hotel, Restaurants, Café sector). Category 10
(supermarket) is the only one that has presented both a high coefficient of Pearson and Spearman. In this
case, a nonlinear (quadratic) regression test was also performed. The results of the two regressions were
then compared with the ANOVA test, which showed that linear regression is the one that best describes the
relationship between the average number of weekly deliveries and the number of employees for
supermarkets. We have also tested polynomial regression for categories 1 (Agriculture), 21 (Street traders)
and 27 (Non-tertiary office), but the linked R2 value is far minor than 0,5, so we assumed that there are no
polynomial dependencies between the two variables for these three categories.
At this point, we can say that for distributions that are not well represented by a constant, or by a regression
(linear or not), a different estimation method is needed.
3.2. The probability distribution for freight trip generation
For each category, we have identified a probability distribution that was able to approximate the distribution
of the data for the deliveries, so that we can not only consider values with a greater frequency but also those
variables values of the demand that seems to characterize the number of average deliveries per week in
urban centers. To do this, the EasyFit software was used, which is a support device for distributing fittings
from input data (in our case the average number of weekly deliveries per single point of sale per category).
TABLE 3 Distributions fitting results
Again, we can observe that there are some categories for which we get "abnormal" parameters, as in the
case of categories 4 (Manufacturing industry manufacturing B2B), 5 (manufacturing industry of B2C
N. Category Distribution Parameters
1 Agricolture Weibull α= 0,79918 β=1,3039
2 ARTISANS Gamma α= 1,1847 β=2,2554
3 IND CHIMIQUE Lognormal
σ= 1,3941 μ=1,5996
4 IND BIENS PROD ET INTERM Burr k= 4,979 α= 1,0766 β=19,712
5 IND BIENS CONSOMMATION Burr k= 2,7957 α= 1,2399 β=7,4653
6 TRANSPORT Gamma α= 0,79848 β=3,1054
7 COM GROS PRODUC INTERMED Gamma α= 0,95355 β=6,082
8 COM GROS CONSO NON ALIM Lognormal
σ= 1,2977 μ=1,1959
9 COM GROS BIENS CONS ALIM Weibull α= 0,94319 β=9,7551
10 SUPERMARCHES Exponential
λ=0,02175
14 COM DETAIL HAB,CHAUS,CUIR Gamma α= 1,6536 β=1,5489
15 BOUCHERIE Lognormal
σ= 0,73738 μ=1,516
16 EPICERIE,ALIM Gamma α= 1,8445 β=2,8525
17 BOULANGERIES,PATISSERIES Burr k= 0,56442 α= 2,6012 β=2,5434
18 CAFES,HOTELS,RESTAURANTS Lognormal
σ= 0,96563 μ=1,0974
19 PHARMACIES Normal
σ= 12,821 μ=26,133
20 QUINCAILLERIES Weibull α= 1,2501 β=3,4116
21 COM D' AMEUBLEMENT Burr k= 2,0009 α= 1,3589 β=5,0667
22 LIBRAIRIE-PAPETERIE Weibull α= 1,2112 β=10,334
23 AUTRE COMM DETAIL Lognormal
σ= 1,0449 μ=1,2913
24 SERVICES DIVERS Lognormal
σ= 1,3302 μ=1,3189
25 TERTIAIRE PUR Weibull α= 0,91997 β=2,1655
26 TERTIAIRE AUTRE Weibull α= 1,009 β=1,5379
27 BUREAUX NON TERTIAIRE Weibull α= 0,72468 β=2,6404
28 ENTREPOTS Lognormal
σ= 1,4097 μ=2,0695
29 COM NON SEDENTAIRES Lognormal
σ= 1,2284 μ=0,6825
34 IND LOURDE (CONSTRUCTION) Lognormal
σ= 1,1576 μ=1,0569

7th International Conference on Information Systems, Logistics and Supply Chain
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goods), 7 (Wholesale trade for B2B), 9 (Wholesale trade food consumer goods) and 22 (Bookshops). These
abnormal values, which are also shown in Table 1, are related to the main statistical values Descriptive for
each category, are due to the fact that these categories are very heterogeneous. For examples in the category
9 fresh, frozen and cans foods are included. We know that each of these typologies of food required different
typologies of transportations and storage. So, for these categories is better to find another way for
estimation, such as a generation of a random distribution between the values of the first and third quartiles.
4. Conclusion
This paper proposes a first approach to select the probability distribution related to FTG rates in urban
logistics, mainly focusing on retailing and service activities. The paper proposed a methodology to test and
compare different probability distribution and select the most relevant one for each retailer/service category,
on the basis of statistical indicators. The methodology is applied to a dataset extracted from a detailed
establishment survey in France, from where the statistical distribution characteristics of each category can
be studied. Results show that the normal approximation is not the most suitable form most categories,
although lognormal distributions is mainly suitable. Each category results on a different probability
distribution and the parameters to characterize them are defined. When small data quantities are available
(and, as shown in Gonzalez-Feliu et al., 2016, in some cases we can have categories with small samples
which do not justify the Normal approximation), the proposed works allows to feed simulation-based
approaches (mainly Monte-Carlo based) which can be a valid alternative to deterministic generation.
Moreover, for other uses (mainly dynamic works); those models give a more realistic view of data variation
and dynamics. However, those results are preliminary and need to be completed, mainly with a pertinent
simulation to assess them then they need to be related to transport flow construction and scenario
construction.
5. References
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7th International Conference on Information Systems, Logistics and Supply Chain
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