attraction model P. Fadda, G. Fancello Dipartimento Ingegneria Territorio sez. Trasporti, · 2014. 5. 13. · P. Fadda, G. Fancello Dipartimento Ingegneria Territorio sez. Trasporti,

A methodology and a proposal for retail trip

attraction model

P. Fadda, G. Fancello

Dipartimento Ingegneria Territorio sez. Trasporti,

CRIMM Centra Ricerche Modelli di Mobilita,

Universita degli Studi di Cagliari,

piazza d'Armi, 16-09123 Cagliari, Italy

AbstractOne of the emerging issues in town planning is that of the effects of thelocalisation of business and services activities on mobility. In Italy in particularthe transformation of sectors such as the food distribution chain and the lack ofcare in planning the localisation of new activities are causing uncontrolledchanges with devastating effects on the urban system.The authors propose a trip generation model for corner shops and supermarket:the model is disaggeratate for frequency of trip and calibrated for Italian reality,where consumers' behaviours are quite different compared to Englishexperiences.

1 Introduction

One of the emerging issues in town planning is that of the effects of thelocalisation of business and service activities on mobility. In Italy inparticular the transformation of sectors such as the food distribution chainand the lack of care in planning the localisation of new activities accordingto efficiency criteria related to the problems of induced traffic, are causinguncontrolled changes with devastating effects on the urban system.This can be explained by the fact that mobility induced by retail attractorsis 17% of the total urban mobility, which is a significant share of non-systematic trips. Moreover, the shift towards large distribution and harddiscount has affected the habits of the users and consequently theirdisposition to trips, which have taken on different connotations withrespect to the past. Moreover there is a tendency to place retail activities

Transactions on the Built Environment vol 33, © 1998 WIT Press, www.witpress.com, ISSN 1743-3509

170 Urban Transport and the Environment for the 21st Century

away from urban centres, in more peripheral areas, in the interest of largeretail poles that create imbalances in the mobility system.In some countries single attractor mobility models have been set upaccording to their characteristics, but when applied to different realities,the models did not provide significative results because of the differentbehavioural characteristics of the users(e.g. Bromley^, Cairns'*).Therefore the present research is not only aimed at defining the coefficientsof the algorithms, but at redefining their structures completely, startingfrom the very determination of the significative variables describing thebehaviour of the users (e.g. Barnard̂ ).The research undertaken at the Cagliari University CRIMM is focused onsmall and medium-sized retail attractors, since greater differences in tripbehaviour than with the large hypermarkets have been observed in Italy ascompared to other countries. It has in fact been observed that, as regardsthe larger attractors, models set up for other countries can also be usedwith discretion in Italy. To this purpose a programme to define the TIA(Traffic Impact Analysis) of hypermarkets is being set up.This work presents the final results in the model definition phase, whichwere partly announced at the IVth S.I.D.T. Scientific Seminar in 1995.These results complete the phase relating to the optimisation representation

models of mobility attracted by small and medium-sized businessgenerators. The algorithms provide a very good representation level. Newstudies are at present under way at the same retail attractors, in order toanalyse change in user behaviour, thus the validity of the model itself, inan urban sector recently undergoing structural changes due to theintroduction of a hypermarket in its distribution network (e.g. Fadda ***).

2 MethodologyThe method provides for an extended investigation of the users at thevarious attractors, as a result of the observed differences between Italy andother countries (UK, USA and France) in user trip behaviour, functionalorganisation of the retail sector, and type of transportation supplied, withparticular reference to public transport (e.g. Recker®).Data relating to trip behaviour, trip attitudes, user perception of thetransportation supply system, preferences, choice alternatives, etc., havebeen collected. Seven shops in the Cagliari area, representing 1000 users,have been analysed. Some of the shops were in an area where a largehypermarket was planned to open at the time.The data were processed with the multiple correspondence and clustertechniques. As already shown in previous papers, the subdivision of usersinto clusters with respect to frequency of use of the shops proved to be the


Urban Transport and the Environment for the 21st Century 171

better technique in simulating the different trip choices of the users.Furthermore, in order to check the weight variation of the variables onvarying the analysed reality, an analogous investigation was carried out on12 shops in three different areas in England, to a total of 800 interviews;this was justified by the fact that trip behaviour is very different in the twocountries. In the analytic phases of the phenomenon, a significativepartition of the studied population was possible defined, and for eachcluster it was possible to define the representative variables of choice ofmobility. Subsequently, from the contingency table and by calculating the

value of the % , we checked variable independence and possiblecorrelations in the description of the phenomenon. For each cluster, a setmade up of 4 or 5 variables was determined, and the model was calibratedon the variables. Consistently with choices made in similar cases, thestructure of model was oriented towards deterministic functions(Koppelman®).

3 Analysis and results

The results of this paragraph refer only to daily, more-than-once-weeklyand non-habitual frequency users. As already observed, the weeklyfrequency user category gave good results in the previous study (Faddâ ).The parameters were the same as in the previous tests: R and R thatmeasure the distance between simulated and found data, "t statistics^ andprob(t) that assess the degree of significativity of each coefficient in themodel, "F Fisher statistics" and prob(F), that locate a possible casualdistribution of data and finally "Durbin-Watson test" that detectsautocorrelation phenomena.

The algorithm used with the daily frequency user category is different instructure from the one used in the earlier study. Rather than a linear typeof function, we used a relation of the multivariate type in this case, withthe variables exponentially related to the coefficients and the single termslinked to each other in a multiplicative relation.The following are the main schemes adopted and the results obtained:

scheme n°l) y = (xrA)*(x2̂ B)*(x3X:)*(x4''D)*(x̂ E)*F y = no. of daily frequency clientsscheme n°2) y = (x, "A)*(x2/\B)*(x3X:)*(x4''D)*(xrE) x^ = net av. shop area (in sq m)scheme n°3) y = (x,̂ A)*(x2̂ B)*F x = no. fam. (th.) in the neighbor.scheme n°4) y= (xrA)*(x̂ B)*(X3̂ C)*F x^ = shop quality coefficientscheme n°5) y = (x, ̂A)*(x2̂ B)*(x̂ D)*F x^ = product quality coefficientscheme n°6) y = (x,/Vl)*(x2̂ B)*(x3̂ C)*(x̂ D)* F x - no. of parking sites in a 150 mscheme n°7) y= (xrA)*(x2̂ B)*(x3/"C)*(x̂ E)*Fscheme n°8) y= (xrA)*(x2/"B)*(x̂ D)*(x̂ E)*Fscheme n°9) y= (



1t

Probm2

tProbm

3t

Probm4

tProbm

5t

Probm6

tProbm

7t

Probm8

tProbm

9t

Probm

A0.20

-1 48-2280 100491.320.241.222.170.09-042-1.140320.100 160.880841.970.14-028

-0.80-0.010.99

R048

083.3880030.331.030.340.291.120320894.710.010.531 940.140421.55022085

3672600.08

r-1.16

1.861660.19

-2.36-2.15009

-1.24-1.310.28-2.37•2.330 10

0.060.010.99

n1.09

3.77383003

1.793.400.021.041.470.230300940412.03

1.045070.01

F-0.15

-1.17-2.600.08

-

-

-

2.180.670.55

-0.21

-045-0010.99

F1.72

6350.470.660860.410700.490650.54

2.230550610.17

R* R\^ TVW F PrnhfF)0.89 0.63 232 341 024

095 089 131 1611 0.022

040 017 2.99 1.72 0.27

078 061 2.85 478 0.08

088 080 1.92 10.49 002

089 073 2.20 594 008

083 062 250 3.88 0.14

088 073 1.20 579 009

045 -026 2.44 063 0.67

The results obtained with the function scheme are more significativethan in the previous study. This shows that a multivariate logarithmguarantees a higher simulation potential; a "hybrid" scheme betweenthe linear and the multivariate type could also be used in scheme 9), butthe results obtained showed its total inefficiency;from the analysis of the data, the four above mentioned variablesproved the most significative in describing the model; the results showthat each of these variables "explains" a part of the simulatedphenomenon. As, a matter of fact the algorithm schemes with thehighest R and R values are those that include all the variables in theagedata analysis. Moreover the individual variables change theirsignificativity on changing the scheme, as can be seen from a reading ofthe "t statistics" and prob(t) values. This shows that in fact all variableshave a high simulation potential. The only schemes where it was not



possible to calculate these values because the function convergence was

not obtained, were 1) and 8);# "Fisher F statistics" and prob(F) values show that for schemes 2 and 5

function convergence is not due to a casual arrangement of the analysedterms, but to a real interpolation of the obtained function;

* Since in the 9 schemes Durbin-Watson test values are clearly higherthan unity, there are no autocorrelation phenomena.

From a comparison of the results, it can be seen that the the observed datais best interpolated with the model relating to scheme 2), for whichexcellent results have been found on all the statistically significant

parameters. The obtained function is:

that gives the following expression when transformed into logarithmics:log(y)= [-1.47*log (x,)] + [0.83Mog(x2)j + [1.86*log(x,)] + [3.77*log(x,)] + |-1.17*!og(xs)]

where the log value of the number of attracted users appears in the firstmember. It is interesting to note that in the international literature thelogarithmic form is the most commonly used for mobility simulationmodels attracted by commercial type generators.In agreement with what has previously been pointed out, too in this casethe coefficient of the "net available shop area (in sq m)" is of a negativesign. In fact, this category refers to the daily type of users, who prevalentlyvisit small shops (corner shops, small supermarkets). Moreover, thenegative sign referring to the variable "no. of parking sites in a 150 mradius" is justified in the same way, since the users are prevalently

pedestrians.To check the representation power of the chosen function, seven shopshave been chosen from the sample, and their observed daily mobility valuewas compared with the value calculated by the model. The obtained resultsare summed up in the tab. 1 (page 9).It can be seen that on the whole the model performs very well, with anexpected error of about 12%. It can be stated therefore that for thecategory under study, this model is to be considered final.

As regards the more-than-once a week user category, even in this case amultivariate type of function was used instead of a linear type of function

that has not given good results previously.The main adopted schemes and the results obtained are reported below:

scheme n°l) y = (x,̂ A)*(X2̂ B)*(x3X:)*(X4̂ D)*(x5̂ E)*F y = no. of more- week freq.clientsscheme n°2) y = (x̂ A)*(x2̂ B)*(x3̂ )*(X4̂ D)*(X5̂ E) x^ - net av. shop area (in sq m)scheme n°3) y = (x,"A)*(X2̂ B)*F x^ - no. fam. (th.) in the neighbor.



scheme n°4) y= (x,*A)*(x2*B)scheme n°5) y= (x̂ A)*(x2̂ B)*(x3X:)scheme n°6) y= (x,"A)*(x2"B)*(X3*C)*(X4"D)scheme n°7) y = (xî )*(x2*B)̂ X3̂ )*(x4*D)*scheme n°8) y= (x̂ A)*(X2"B)+(x3̂ )*(x4'"D)*scheme n°9) y= (x̂ A)+(x2̂

x^ = no. of analog.shops in a 500 mx^ = shop quality coefficientx = product quality coefficient

1

2

3

4

5

6

7

8

9

tProbm

tProbm

tProbm

tProbm

tProbm

tProbm

tProbm

tProbm

tProbm

A-4.46

-19.1-20.80.001.001.190.280.682.360.051.001.190281.821.080.34-19.5-18.70.000.380.580.620.38

R556

23.421.90000.200.580580.0170.070.940.330.610.560.250.460.6724.018.80.000.270.60.61-0.01

r-15.5

-88.9-22.00.00

-

-

-1.54-0.520.62-2.20-0.550.61-91.2-18.60.00-0.18-0.060.961.01

r>11.1

46.421.30.00

-

-

-2.46-1.090.3347.518.70.00-1.88-0.390.73-1762

F F R* R\w HAV F9.01 0.001 0.88 0.57 2.65 2.91

32.6 - 0.99 0.99 2.00 1311.822.40.00

0.039 0.54 035 2.88 2.930.160.88

0.49 0.40 268 5.80

0..54 035 2.88 2.93

0.71 0.49 2.45 3.26

33.4 0.99 0.99 099 2.49 1047.319.3 1.000.00 0.421.43 -46.8 0.75 0.13 2.59 1.210.56 -0.830.63 0.49-165 -62.5 0.57 -0.49 3.04 0.54

Prnh(F)0.275

0.00003

0.143

0.052

0.143

0.14

0.0009

0.51

0.75

even in this case the multivariate type of structure clearly gives themost true-to-life results. In the case of schemes 1) and 9) the "statisticst" and prob(t) values do not appear since function convergence was notreached;significativity of all variables obtained by data analysis is confirmed bythe excellent results obtained for schemes where the variables arealways present and consequently by the poor results obtained by theschemes where the number of variables is less than four;schemes 2) and 7) are where excellent results were obtained, withpractically similar values: all statistical parameters used in the search



for the best algorithm have clearly confirmed the goodness of the twochosen models; for both the hypotheses of casual data arrangementsand auto-correlation phenomena can be ruled out;

• in both scheme 2) and scheme 7) the coefficient of the variable "netavailable shopping area (in sq m)" is negative since, also because of thesimilarity of the representative variables used, the behaviour of themore-than-once weekly users is very similar to that of the daily users;

• from "t statistics" and prob(t) values, the high significativity of all thevariables in the description of the phenomena emerges; it is to bepointed out that in scheme 7) the values relating to the constant revealthat it is substantially useless, thus making the two models equal.

Therefore the chosen algorithm is no.2: the determined function is:

y - [x.*(-!9.1)]*[X2*(23.4)]*[x j*(-88.9)J* 1x̂ (46.4)]*[xs*(32.6)]Transformed into logarithmics:

logCv)= [-19.1 *Iog (x,)] + [23.4*log(x2)] + |-88.9*log(xj)l + [46.4*log(x+E y - no. of occasional frequency clientsscheme n°2) y= (A*Xi)+(B*X2)+(C*X3)+(D*x-4) x = aver, distance shops and nearest parkingscheme n°3) y = (x,̂ A)*(X2̂ B)*(x3̂ C)*(X4̂ D)*E x = no. of parking sites in a 150 m radiusscheme n°4) y = (x,*A)*(X2"B)*(X3"C)*(X4"D) x^ - no. of opening hours other than 9.00-13.00

and 17.00-20.00scheme n°5) y = (X|*A)*(X2*B)*(X4*D)*E x = aver. dist. from the district, road networkscheme n°6) y= (x,*A)*(X2*B)*(x3*C)*Escheme n°7) y = (x,"A)*(x2̂ B)*(X3/\C)*(X4̂ D)+Escheme n°8) y= (xi*A)*(x2*B)+Escheme n°9) y= (



1

2

3

4

5

6

7

8

9

tProbm

tProbm

tProbm

tProbm

tProbm

tProbm

lProbm

tProbm

tProbm

A0.190.440.690.561.300.260.201.070.360.351.800.140.251.570.19-0.16-1.340.250.421.550.22-3.29-0.550.600.24

B0.340.670550.801.650 170.591.720.181.3015.570.000662.130.090.180.800.461.2513.30.001.841.640.160.66

C-6.28-0.3507518.041.730 15-0.11-0.550.62-0.04-0.210.84

-0.41-1.290.26-0.14-0.620.58

2.71

D-0.19-1.440.24-0.16-1.050.35-0.29-2.020.13-0.51-3.910.01432-2.520.06

-

-0.58-3.030.05

-

-9.80

E R* R\gg DAY F119 0.46 -0.25 1.29 0.641.550.21

0.02 -0.69 2.21 0.04

157 0.80 0.54 1.64 3100.720.52

0.68 0.45 163 2.93

11. 1 0.78 0.62 1.82 4.920.850.44947 0.50 0.13 2.27 1.361.070.3436.01 0.87 0.70 221 5072.060.1366.95 0.56 039 110 3.273.410.0154.7 0.32 -0.59 2.47 0.35

Probm0.669

0.987

0.189

0.163

0.079

0.374

0.106

0.123

0.832

It can be seen immediately that the values of the associated statisticalparameters in all the schemes are on average lower that those found forall the proposed models. It is also seen that it is more difficult to modela category of users with a behaviour that is not easily classified, acategory moved by a casuality that is characterised by many uncertainvariables that are not easily determined. Repetitiveness of action (inthis case the trip) characterising non-habituality as such, the kind ofrepetitiveness, that is, that would allow a better representation, is infact missing in the type of behaviour associated with the users.Moreover, owing to the peculiarity of the trip itself, the variables thatcome into play are clearly more numerous than those referring toanother type of trip. For this reason the obtained results can beconsidered good, in spite of a lower performance than with previousmodels;in this case also the validity of the linear function, the function that isthat has given good results also for the weekly frequency category of



users, has been tested. However, we have preferred to use a

multivariate function, that should be analogous to the previous two

cases;• the schemes where the results have been more satisfactory are no. 3 and

no. 7, that is those that contain all the variables shown in the analysisof the previous data;

• from the "t statistics" and prob(t) values it emerges that the mostsignificative variable is the "no. of parking sites in a 150 m radius";this is due to the fact that the non-habitual users are mainly passingusers, that prevalently use private cars, and therefore the presence of aparking site in the neighbourhood becomes a key element in choosingthe shop.

From a comparison of the most significant data it can be seen that schemeno. 7) is the one that presents the best results; the determined function isthe following:

y = [X,̂ (0.42)]*[X2̂ (1.25)]*[X3̂ (-0.14)]*(X4̂ (-0.58)]-H(36.01)Since this function contains a sum operator, it cannot be transformed intoa linear function by going through a log function.In the table below there are the results of performance level of algorithms:

Shopn.lShop n.2Shop n.3Shop n.4Shop n.5Shop n.6Shop n. 7Average

DAILY USERS

foundvalue11910439269797065

model.value

13210530268655664

Sensitivity90%99%74%99%82%78%97%88%

MORE-THAN-ONCE AWEEK USER

foundvalue1092510859307

model.value1092510859207

sensitivity

100%100%100%100%66%100%100%95%

NON HABITUAL USER

foundvalue14074169771472868

model.value

14177169551423644

Sensitivity

99%96%100%71%96%77%64%86%

tab. 1: Comparison between found value and model result

In spite of the difficulties in codifying the behaviour of non-habitual usersthrough a model, the average sensitivity value (86%) is very good. It isimportant, however, to point out that, the results obtained for the daily andmore-than-once a week frequency users are either equal or vary within avery restricted interval. In this case, however, since the model's sensitivityfluctuates between a minimum of 64% and a maximum of 100%,prediction is more uncertain. It is important to point out, however, that



taking into account the complexity of the phenomenon represented and ofthe known difficulty in schematising the behaviour of non-habitual users,the results obtained during calibration are good enough to consider thismodel final for this category.

4 ConclusionThe study has reached the objective of defining the representativealgorithms capable of reliably simulating for each category of user themobility attracted by small and medium-sized shops. In some cases (more-than-once a week frequency users) the results have been very good, withnegligible error percentages, while in others (non-habitual users) theresearch has been harder and gave less significative results, but still it hasbeen reliable in prediction of the mobility. In the present phase, theobjective is to incease the data bank in order to extend the reference basefor the calibration of function coefficients on a greater number ofgenerators in different parts of the country. This extension is intendedmainly for comparison with the regional data relating to Sardinia, the onlyreality so far taken up as a reference in defining the model.

5 ReferencesBarnard, P. O., Modelling shopping destination choice: a theoretical andempirical investigation, Australian Road Research Board, SR 36, Victoria, 1987.Bromley R., Thomas C., Retail change: contemporary issues, UCL Press,London, 1993.Cairns, S., Travel for food shopping: the Fourth Solution, Traffic Engineeringand Control, 36 (7) pp.411-418, 1995Fadda P., Fancello G., Choice factor analysis in food shopping travel behaviour,Proc. 2nd Urban Transport & the Environment - eds. J.M. Baldasano, L.J.Sucharov, Comput. Mechanics Publ., Southampton &Boston, pp.481-492, 1996.Fadda P, Fancello G (1995) 'La mobilita attratta da generatori di tipocommerciale: la defmizione di una metodologia per il caso italiano 'Proc. ofSeminario S.I.D.T., Franco Angeli, Milano pp.45-64, 1997Fadda P, Fancello G (1995) 'Disaggregation level and variables choice in retailtrips: comparison between Italy and England, behaviour' Proc. 1st UrbanTransport & the Environment - eds. L.J. Sucharov, Comput. Mechanics Publ.,Southampton &Boston, pp.375-384, 1995Koppelman, F S (1980) 'Consumer Analysis of travel choice Behavior' Journalof Advanced Transportation, 10 (4), 133-161Recker W, Kostyniuk L, (1978) 'Factors influencing destination choice for theurban grocery shopping trip', Transportation, 1 (3), 19-33


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attraction model P. Fadda, G. Fancello Dipartimento Ingegneria Territorio sez. Trasporti, · 2014. 5. 13. · P. Fadda, G. Fancello Dipartimento Ingegneria Territorio sez. Trasporti,