APPLICATION OF HUFF MODEL IN ANALYSING MARKET COMPETITION – EXAMPLE OF SHOPPING CENTRES IN THE SETTLEMENT OF ZADAR

Predmet istraživanja rada je tržišno natjecanje između trgovačkih centara u naselju Zadru. Osnovu istraživanja čine prostorni podatci prikupljeni različitim metodama i tehnikama, analizirani primjenom alata geografskoinformacijskog sustava (GIS) uz uvažavanje specifičnih tržišnih zakona. Prema kategorizaciji trgovačkih centara, definirano je šire tržišno područje unutar kojeg je analizirano tržišno natjecanje između trgovačkih centara. Izvođenjem demografskog rastera definirana je gustoća potencijalnih kupaca unutar širega tržišnog područja. Analiza natjecanja uključivala je određivanje tržišnih zona trgovačkih centara, pojavu potencijalnoga tržišnog kanibalizma te definiranje dominantnog centra prema varijabli vjerojatnosti odabira. Tržišne zone određene su na temelju atributa vremena vožnje (min). Metodama terenskog istraživanja, izračunom nelinearne udaljenosti te analizom gustoće trgovačkih centara zaključeno je da se između centara javlja tržišni kanibalizam. U svrhu predviđanja tržišne dominacije, primjenom Huffova modela, izračunate su srednje vrijednosti odabira centara unutar zona preklapanja i širega tržišnog područja. Rezultati Huffova modela potvrđuju tržišnu stvarnost, odnosno da veći broj kupaca unutar zona preklapanja i širega tržišnog područja odabire atraktivniji trgovački centar. Preklapanjem demografskog rastera i Huffova modela kvantificirana je razlika u broju ljudi koji posjećuju atraktivniji trgovački centar. Ključne riječi: Huffov model, tržišni kanibalizam, tržišne zone, indeks atraktivnosti

Ključne riječi: Huffov model, tržišni kanibalizam, tržišne zone, indeks atraktivnosti The object of the research is market competition between the shopping centres in the settlement of Zadar.The research is based on the spatial data collected by using various methods and techniques, which were analysed by applying the tools of geographic information system (GIS) with respect to specific laws of market economy.A categorization of shopping centres was made in order to define a broad trade area where the competition between the centres was analysed.A demographic raster was used to define the density of potential consumers within a broad market area.The competition analysis included the determination of the centres' market zones, the occurrence of potential market cannibalism and the definition of the dominant shopping centre according to a variable of choice probability.The market zones were determined based on the attribute of duration of drive (min).On-site research, calculation of non-linear distance and the analysis of shopping centres' density, led to a conclusion that market cannibalism occurs between the centres.For the purpose of predicting market dominance, Huff model was used to calculate average values of preference of centres within the zones of overlapping and the broad trade area.The results of Huff model confirm the market reality that a larger number of consumers within the zones of overlapping and the broad trade area prefer a more attractive shopping centre.The difference in number of people that visit a more attractive shopping centre was quantified by overlapping the demographic raster and the Huff model.
Keywords: Huff model, market cannibalism, market zones, attraction index

Introduction
Over the last several decades there has been a significant development of trade, which is reflected in the increase of the number of the employed, sales area and traffic of goods (Keenan, 2005;Burnett, 2008;Kotler, Armstrong, 2010;Grey, 2014).Trade is much more than just an economic activity and is therefore not an exclusive object of interest of economy (Grimshaw 2000;Baray, Cliquet, 2007;Cannon, 2007;Hungari, 2009).Trade takes place on the market which is defined as an aggregate of all the real and the potential consumers of a product or a service (Kotler, 2002).As a complex phenomenon, it includes an interaction of people and institutions within a limited spatial-temporal frame (Kotler, Armstrong, 2010).Understanding market reality was directed towards researching spatial relations between consumers and shops.
Based on measurable and precise information about structure and features of the market, corresponding marketing decisions are made (GIS for Customer and Market Analytics, 2007).
The development of GIS technology has enabled a more prominent inclusion of geographers into business and trade analysis (Grimshaw, 2000;Keenan, 2005;Pick, 2008).The application of GIS within the retail industry is what is mostly analysed in the available literature (Van Eck, De Jong, 1999;Badea et al., 2008;Mishra, 2009).The analyses of market competition and spatial distribution of shops are the most commonly used analyses within the scientific discipline of geomarketing (Van Eck, De Jong, 1999;Dramowicz, 2005;Suárez-Vega, et al., 2011;Roig-Tierno et al., 2013).Geomarketing can be defined as a scientific discipline whose object of research is the market and its dynamic components, and is based on an integration of informational-communication technologies, marketing strategies and geographic understanding of space (Fig. 1).
Market competition was analysed through the example of shopping centres, since smaller shops tend to rely on the experience of experts when making decisions.On the other hand, in order to reach decisions, shopping centres use multi-criteria analyses (Cheng et al., 2005;Zolfani et al., 2013) that can be modelled only systematically (Sapaj, 2013).
and visualization is a statistical circle. 1 The main objective of the research is to present a modern way to analyse market competition by using GIS.Secondary objectives of the research are the following: 1. To create market zones or areas of influence of centres based on defined variables; 2. To determine whether market cannibalism appears between the centres by using calculation of shopping centres density, field work and the definition of non-linear distance; 3. To generate an index of attractiveness of shopping centres and to use the Huff model to analyse the probability of choosing a centre's within market zones and overlapping zones, and 4. To determine the dominant shopping centre based on the data processed.

Research methodology
The methodology in this scientific paper is based on the application of general scientific research methods and specific GIS methods that include the process of vectorization and interpolation, statistical methods and cartographic visualization.Based on the researched literature, a conceptual model of research was made in the initial phase of the modelling process, followed by a logical and a mathematical phase (Šiljeg, 2013).Logical phase refers to the selection of the most suitable methods with respect to features of input data and defined research objectives.Mathematical phase includes the usage of functions and formulas and, if necessary, a change for the purpose of research (Šiljeg, 2013).In the paper it is reflected in the application of the Huff model, the measurement of shopping centres density and the calculation of the attractiveness index.The research was conducted in four phases.

Collecting data
A contact with managements of the shopping centres "Supernova" and "City Galleria" has been made through an official letter, and they have provided a part of data needed for generating the attractiveness index.The management of "City Galleria" has provided layouts of all the levels of the centre that have been used in the assessment of the undelivered parameters (number and area of the active stores).
For the purposes of deriving the attractiveness index and determining the occurrence of market cannibalism, a field research was made in the period from 10 July to 13 July, 2015.Infrastructural differences among the centres were photographed, as well as the impact of market cannibalism on "City Galleria".Based on the available layouts, field mapping of the centre was executed in order to determine the exact number of active shops, as well as the area of each closed shop.The acquired data was subtracted from the total retail area designated for rent that was provided by the centre's management, which resulted in generating the data about the area of the active shops.
For the purpose of creating a model of market zones based on the variable of drive time, a detailed set of data about road network within Zadar and the broad trade area was downloaded from the Geofabrik website (URL 1).With the help of tools integrated into the software package ArcGis for Desktop, a topological correction of data was pravila kako bi Dijkstra algoritam generirao vjerne modele tržišnih zona.
For the purpose of creating a demographic raster and a model of density of potential buyers, a geodetic survey company Teodolit d.o.o.provided data about urban infrastructure in Zadar County for the year 2015.In order to determine market zones and Huff model, locations of shopping centres were vectorized on the basis of a DOF 2 template (URL 2).

Organizing the database
The acquired data were organized into a single space-oriented database, and were connected to the newly created database within the ArcCatalog through a unique code.Although ArcGIS supports many formats for saving data, file geodatabase format was selected due to its structural and implemental advantages over other formats when it comes to managing data.

Analysis and interpretation
A broad trade area was determined by overlapping the layer of statistical circles with the zone of influence defined by a method of linear distance of 9 km, which was set according to the categorization of shopping centres.Following the OSM (OpenStreetMap) categorization, vehicle speed was assigned to each road type.By using the extension Network Analyst, and its tool New Service Area, models of the shopping centres' market zones were made based on defined parameters.
Following the approach of N. T. Donthu and R. T. Rust (1989), E. M. Jansenberger and P. Staufer-Steinnocher, ( 2004) N. Roig-Tierno et al. (2013), a model of density of potential consumers (demographic raster) for both narrow and broad trade area was generated by using a Kernel Density (KDE 3 ) tool.Kernel method is a focal method of neighborhood analysis of continuous data displayed with a raster.The main assumption of this method is that a sample has a specific density in each location within it, regardless of where the phenomenon is located (Pahernik, 2013).Based on the data on the total available area for rent within 2 Digitalni ortofoto 3 Kernel Density Estimation (procjena Kernel gustoće) 2 Digital Ortophoto 3 Kernel Density Estimation za iznajmljivanje unutar trgovačkih centara, izračunata je mjera gustoće za šire i uže tržišno područje, što može upućivati na potencijalnu zasićenost tržišta ponudom trgovačkih centara.
Market Analysis Toolset (URL 3) was used to make Huff models of the store choice probability on the level of features of the urban infrastructure.The analysis was conducted based on the variable of non-linear distance.In the process of generating the model, three deterministic methods of interpolation were compared: inverse distance (IDW), natural neighbour (NN) and triangular irregular network (TIN).The Huff model was upgraded by additional attraction parameters which are listed in the paper, and an attraction index for each centre was derived.By using the tool Intersect, overlapping zones were determined based on the drive time parameter.Through overlapping the Huff model with the models of market zones and overlapping zones an average value of choice for each centre was determined.Finally, the dominant centre was identified and the difference in number of visitors was quantified.

Visualization
Visualization is defined as "the heart of geographic practice" (Craine, Aitken, 2005) and it represents an important step within the process of modelling, because it uses visual shapes in order to give clear explanations of the variability of complex spatial phenomena.For the purpose of interpreting the output results, a set of thematic maps was made.In order to facilitate the determining of spatial variability of the research phenomena among the models, the same scale of colours and the limits of classes were set.
In the shopping centre Supernova the spaces are more compact, bigger, and thus more attractive for famous key tenants (Jakovčić, Rendulić, 2008) or anchorstores that attract larger numbers of consumers.Although City Galleria has had all of its spaces rented before the opening of Supernova, most of the stores in the old part of the mall are today closed.One of the reasons is their design, i.e. size of retail spaces for rent, which are not big enough to attract anchor stores (Fig. 2).
(GLA4 ) the shopping malls Supernova (27,400 sq m) and City Galleria (20,546 sq m) can be classified as communal centre type (Uprava trgovačkog centra Supernova, m2 Center management d.o.o., Uprava Trgovinski centar -Zadar d.o.o.).If classified based on the total area parameter, they would be categorized as regional centres.
Based on the maximum value of distance variable (9 kilometres) that represents the gravitational influence of the community type shopping centre, and through the overlapping of statistical circles, the broad trade area was defined (Fig. 3).A narrow, primary trade area recognized on the level of Zadar settlement consists of 41 statistical circles and 71,471 inhabitants.Broad trade area (primary + secondary) consists of a total of 71 statistical circles and 85,715 inhabitants.

Creating the demographic raster
From the perspective of producers, a market consists of people with clear or hidden wants that manifest through a demand for a specific product (Burnett, 2008).The demand refers to the quantity of products or services that the consumers are willing to buy for a price (Rodrigue et al., 2013).GIS puts the emphasis on the density of consumers, as well as on their purchasing power in relation to the trade area, i.e. gravitational influence of a store (Roig-Tierno et al., 2013).The process of creating a demographic raster was described in the chapter on the research methodology.The final model (Fig. 4) was used in determining the dominant trade centre.

Determining market cannibalism
Market cannibalism is a real market threat to all products and shops that are present on a saturated market.There are only a few scientific papers that quantify that threat or examine the measures that help its description (Lomax et al., 1996).A generally accepted definition of market cannibalism does not exist in literature.It is mostly defined as a phenomenon in which a product or a store gains profit that is redirected from the existing product or another store (Lomax et al., 1996).It occurs when a new product or store "eats" the sales volume and the demand of the existing product or store, at the moment when a new store or product penetrates the market of an older product or store (URL 4).
Market cannibalism is often mentioned when trade zones are being determined.When two or more trade zones of certain stores overlap due to their vicinity, that area gains a power of attraction that is equal to their sum.Therefore, potential buyers living in such area are exposed to a bigger commercial offer, which makes the trade area with a rich market offer (Roig-Tierno et al., 2013).A battle for customers, i.e. market competition, between similarly profiled stores occurs in that area (Kelly et al., 1993;Roig-Tierno et al., 2013).
In GIS the measuring of market cannibalism refers to calculation of an area where trade zones of two or more stores overlap (Cisneros, 2015).Strong and lasting market cannibalism can have a negative influence on a product or a store, forcing them to retreat from the market or close down due to a decrease in sales volume and market share.An occurrence of market cannibalism was perceived in the example of shopping centre City Galleria that has begun closing its retail spaces as early as 2010 due to the increased competition (opening of the centre Supernova) (Fig. 5) (Babajko Jamičić, 2010;Burica, 2012).The occurrence called "papered shop windows syndrome" is the most visible in the old part of the centre with smaller shops, while the new part remains active due to open-air market, cinemas, coffee shops and several stores with clothing brands (Babajko Jamičić, 2010;Burica, 2012).
Based on the calculated values, it can be concluded that, in comparison to national average from 2013, the narrow trade area recorded more than double values, while the broad trade area recorded nearly double values, which can indicate a saturation of space with shopping centres' offers.According to this measurement, Zadar does not fall behind the leading cities of Europe.Namely, in 2012 the city of Prague recorded 680 sq m per 1,000 inhabitants, while Zagreb recorded 500 sq m per 1,000 inhabitants, with a growth estimate of 840 sq m per 1,000 inhabitants in the several following years (URL 5).However, the demographic potential, i.e. the density of potential consumers within the broad trade area during summer months is growing due to an increased inflow of tourists, which ultimately reduces the market saturation.
A market does not necessarily need to be saturated if its values of shopping centres density are high, because it depends on the purchasing power of the inhabitants.Given that secondary and tertiary competitive centres (those with an area under 5,000 sq m) are excluded from the analysis, with a relatively low income of population in 2014 (79,843 kn per household) (URL 6), this measurement partially explains the negative trend of closing the retail spaces within the shopping centre City Galleria.It is the high density of retail space that is commonly an indicator of a market conflict and a competition among the centres.Two shopping centres in a city are sufficient, and as the demographic and the purchasing potential Treći parametar odnosi se na udaljenost centara koja je relativno mala (Sl.6.).Iako je prema kategorizaciji trgovačkih centara (Tab.1.) predviđeno da minimalna udaljenost između centara bude 4,5 km ≈ 10-15 min vožnje, ona iznosi tek 3,3 km ≈ 4 min vožnje, što generira velike površine preklapanja tržišnih zona (> 60,55 %) (Tab.2.).
Iz generiranih modela tržišnih zona izvedena je deskriptivna statistika (Tab.2.).Dobivene are insufficient to secure both of them, the stronger centre will always attempt to "suppress" the weaker one off the market.
The third parameter refers to a relatively small distance between the centres (Fig. 6).Although the categorization of shopping centres anticipates that the minimal distance between the centres is 4.5 km ≈ 10-15 minutes of drive, it is merely 3.3 km ≈ 4 minutes of drive, which generates large areas of trade zone overlapping (> 60.55%) (Tab.2).

Defining the trade zones overlapping
Trade areas are defined as places where retail generates its sale during a period of time (Myles, 2004).D. Huff (1964) describes them through a statistically expanded concept, as geographically defined regions that contain potential consumers whose probability of buying a product, visiting a store or using a service of a company is above 0 % (Baray, Cliquet, 2007).The process of creating trade zones has been described in the methodology.It is necessary to understand the drawbacks of the created models.Namely, they include bigger areas due to an assumption that a vehicle moves with the highest allowed speed, without peak traffic load (waiting at traffic lights, traffic jams, etc.).Therefore, the models are the most suitable for representing the situation in winter months, when traffic is lighter (Fig. 7).
Descriptive statistics are derived from the generated trade zone models (Tab.2).The acquired

Creating the Huff model
The Huff model represents a market penetration approach that takes the competition into consideration, and assumes the existence of spatial variations in the shares of households that visit a store.Within it, the trade area is conceptualized as a probability surface, which represents the likelihood of customer "patronage".The creation of probability surface is based on a spatialinteractive model that includes the following variables: distance of consumer and attractiveness of a shopping centre (Dramowicz, 2005).It is based on the assumption that a probability of visiting and shopping in a centre is in function of the centre's location distance, its attractiveness, and the distance and the attractiveness of its atraktivnošću te udaljenošću i atraktivnošću njegovih konkurenata (Huff, McCallum, 2008.).Osnovna pretpostavka je da će osoba suočena s nizom alternativa odabrati onu koja je izravno proporcionalna percipiranoj korisnosti te alternative.Izbor ponašanja te osobe je vjerojatan (Huff, McCallum, 2008.).Vjerojatnost da će potrošač koji se nalazi na lokaciji i odabrati trgovinu j može se procijeniti Huffovom formulom (Myles, 2004.;Huff, McCallum, 2008.):Ponderi povezani s varijablama rijetko se procjenjuju statistički, a često se dodjeljuju proizvoljno (Huff, McCallum, 2008.)ili na temelju Reillyeva gravitacijskog zakona maloprodaje (Yrigoyen, Otero, 1998.).Spomenuti zakon temelji se na Newtonovu općem zakonu gravitacije, a tvrdi da je privlačna moć trgovine izravno proporcionalna njezinoj atraktivnosti, a obrnuto proporcionalna udaljenosti od koje se nalazi kupac.Kao tipičnu vrijednost pondera za parametar atraktivnosti uzima se vrijednost 1, dok se za parametar udaljenosti uzima vrijednost 2 (Yrigoyen, Otero, 1998.;Dramowicz, 2005.).Parametar (b) u Huffovoj formuli odnosi se na koeficijent raspada povećanjem udaljenosti (distance-decay effect) koji određuje snagu inverznog odnosa između vjerojatnosti da će kupac odabrati trgovinu i udaljenosti ili vremena vožnje koju kupac mora svladati do te trgovine.Veći koeficijent znači da je kupac spreman manje putovati da bi posjetio trgovinu.Prema ESRI-u, vrijednost zadanog parametra udaljenosti iznosi 1,5 s naglaskom da najčešće korištene vrijednosti competitors (Huff, McCallum, 2008).The initial assumption is that a person confronted with a series of alternatives would choose the one which is directly proportional to its perceived usefulness.That person's choice of behaviour is probable (Huff, McCallum, 2008).The probability that a consumer located on a location i would choose a store j can be estimated by using the Huff formula (Myles, 2004;Huff, McCallum, 2008): where: P(C ij ) = probability that an individual (i) would pick an alternative (store) (j) S j = index or attribute of attractiveness (j) T ij = distance or drive time between a consumer (i) and a store (j) a = weighting factor that refers to attractiveness, and is estimated empirically b = weighting factor that refers to distance, and is estimated empirically N = total number of stores including store j Weighting factors related to variables are rarely estimated statistically, but are commonly assigned arbitrarily (Huff, McCallum, 2008) or based on the Reilly's law of retail gravitation (Yrigoyen, Otero, 1998).This law is based on the Newton's law of universal gravitation, and states that the power of attraction of a retail store is directly proportional to its attractiveness, and inversely proportional to the distance of a customer.The value 1 is used as a typical value of weighting factor for the attractiveness parameter, while the value 2 is used as a distance parameter (Yrigoyen, Otero, 1998;Dramowicz, 2005).The parameter (b) in the Huff formula refers to a coefficient of decay with distance (the distance-decay effect) that determines the strength of an inverse relation between the probability that a consumer would choose a retail store and a distance or a drive time that a consumer must overcome to reach it.A higher coefficient would mean that a customer is willing to travel less in order to visit a retail store.According to ESRI, the value of the set distance parameter is 1.5, since the mostly used values vary between 1 and 3.The highest values are set for variraju između 1 i 3. Najveće vrijednosti postavljaju se za manje nespecijalizirane trgovine, jer kupci nisu voljni svladati veliku udaljenost za namirnice svakodnevne namjene.Najmanji koeficijenti dodjeljuju se trgovinama koje imaju rijetku i specifičnu robu za koju su kupci spremni svladati veće udaljenosti (tehnika, markirana roba).Trgovački centri sadrže velik raspon različitih tipova trgovina, od onih svakodnevne namjene do specifične i rijetke robe, ali uglavnom prevladavaju trgovine odjeće i obuće, koja se ne kupuje na dnevnoj bazi zbog čega je vrijednost parametra postavljena prema ESRI-evoj zadanoj vrijednosti.

Indeks atraktivnosti centara
Trgovački centar posjeduje mnogo atributa koji ga čine atraktivnim potrošačima.U literaturi se najčešće koristi samo veličina, odnosno ukupna površina prodajnog prostora kao mjera koja less specialized stores, because consumers are not willing to overcome great distances to buy common merchandise and groceries.The lowest coefficients are assigned to stores that offer rare and specific merchandise that can motivate consumers to overcome greater distances (technical merchandise, famous brands, etc.).Shopping centres contain a big range of various types of retail stores, from those of convenient purpose to those with specific and less common merchandise, but shoe and clothing stores are in the majority since their merchandise is not purchased daily -that is why the value of the parameter is set according to ESRI's default value.
The index of attractiveness of the shopping centres was calculated based on the approach of E. Dramowicz (2005) and C. Schürmann (1999).Following the methodology of C. Schürmann (1999) the weight coefficient 1.2 was added to the parameter of the area of active retail space.He takes into consideration the fact that there is no linear relation between the retail space area and the customer's perception of usefulness.After that, following the approach of E. Dramowicz (2005), a total z value of attraction parameters was calculated for both centres.According to the formula below, the index of attractiveness was calculated for both shopping centres: where:  In order to create the Huff model of probability of a shopping centre selection as a place of purchase, the tool Market Analyst Toolset was downloaded from ESRI's pages (URL 3).Using the downloaded tool, Huff's models of probability of a shopping centre selection were derived for the broad trade area based on the centres' vectorized location, transportation network of the broad trade area and the location of features (Fig. 8 and Fig. 9).Slika 8. Vjerojatnost odabira centra Supernove kao mjesta kupnje Figure 8 The probability of Supernova shopping center selection as a place of purchase Analizom Huffova modela, odnosno srednjih vrijednosti odabira centra unutar širega tržišnog područja te zona preklapanja, prepoznat je dominantan trgovački centar.Prema srednjim vrijednostima odabira trgovine, uočljive su dvije pojave.Prva je dominacija trgovačkog centra Supernova koji unutar svih definiranih zona ostvaruje veće srednje vrijednosti odabira trgovine.Te vrijednosti rastu s povećanjem tržišne zone, odnosno atributa vremena vožnje (min) na temelju kojeg je zona generirana.To je posljedica specifičnog položaja Supernove (rubni dio grada) te njezina jačega gravitacijskog utjecaja na okolna manja naselja.Dominantnost se očituje u tome da u tržišnim zonama centra City Gallerie (CG) veću vjerojatnost odabira ima centar Supernova (S) (Tab.4.).
Srednja vrijednost odabira nije najbolji pokazatelj dominacije trgovačkog centra zato što su različiti tipovi stambenih objekata (zgrade, obiteljske kuće) prikazani na isti način (točkasti podatak) te svaki ima jednu vrijednost postotka vjerojatnosti odabira iako u njima živi različit broj stanovnika.Kako bi se preciznije utvrdio dominantan trgovački centar, potrebno je spojiti Using the Huff model analysis, i.e. average values of a shopping centre choice within the broad trade area and the overlapping zones, the dominant shopping centre was identified.With respect to mean values of shopping centre choice, two occurrences can be seen.The first one is the dominance of the shopping centre Supernova that shows higher mean values of shopping centre choice within all defined zones.These values grow with the enlargement of the trade zone, i.e. of the attribute of drive time (min) based on which the zone was generated.It is a result of the specific position of Supernova (periphery of the city) and its stronger gravitational influence on the surrounding smaller settlements.The dominance is reflected in the fact that even in the City Galleria (CG) centre's trade zones, Supernova (S) has a higher probability of being chosen (Tab.4).
However, mean choice value is not the best possible indicator of shopping centre dominance because various types of residence buildings (apartment buildings, family homes) are represented in the same way (point data) and each of them has a single value of probability percentage even though they are occupied by a different number Slika 9. Vjerojatnost odabira centra City Gallerie kao mjesta kupovine Figure 9 The probability of City Galleria shopping center selection as a place of purchase podatke demografskog rastera i Huffova modela čime će se utvrditi broj stanovnika unutar širega tržišnog područja s vjerojatnošću odabira većom od 50 % za svaki trgovački centar.Na temelju toga podatka preciznije će se odrediti tržišna dominacija određenog centra.
According to the derived data, shopping centre Supernova has 34,743 inhabitants more, with a choice probability higher than 50 % in comparison to the City Galleria centre (Tab.5).This confirms the dominance of the Supernova centre and reflects the actual market situation observed through the field research.
When the Huff model is interpreted, it is necessary to know the limits of its application.Namely, the derived attractiveness index of a centre is never completely accurate since it is not possible to quantify all of the social and subjective factors (pleasant environment, perception of place, ambience, need for socializing, and perception of marketing dominance) that occur in the mind of a potential consumer as factors of a shopping mall's attractiveness.Furthermore, spatial mobility and behaviour of consumers do not always follow the market rules that are based on gravitation laws.
U ovome radu dokazana je primjenjivost Huffova modela u analizi tržišnog natjecanja.Primjenom alata integriranih unutar GIS-a generirane su tržišne zone za oba trgovačka centra prema varijabli vremena vožnje.Na temelju izvedenih zona definirane su zone preklapanja u kojima se odvija borba za pokroviteljstvo kupca.Zaključeno je da se između trgovačkih centara u naselju Zadru javlja tržišni kanibalizam.S obzirom na stvarnu tržišnu situaciju, odnosno na zatvaranje velikog broja prodavaonica u centru City Galleria, za očekivati je bilo da će srednja vrijednost vjerojatnosti odabira centra Supernova results in identifying the preferences of large stores in an urbanized environment, this research actually proves its applicability.Namely, in the mentioned authors' research the same distance parameter (1) was set for all types of shopping malls (hypermarket, supermarket, retail store and shopping centre), even though they contain different varieties of trade products in the context of their purpose, and are not comparable as such.The unique parameter of distance can be set only in case of analyzing market competition for the same type of shopping centres or the same type of product.Furthermore, the only parameter of attractiveness used in the preference model, i.e. shopping mall choice probability, is the area of retail space, which could finally have led to more difficult interpretation of the output results.

Conclusion
All models, including the market ones, represent a simplified image of reality and have their advantages and limits.Spatial phenomena are too complex for the derived models to reflect the actual reality completely.Quality of a model is a result of accuracy and precision of the collected data and of the usage of specific methods, techniques and procedures in modelling.This paper proves the applicability of the Huff model in the analysis of market competition.By using the tools integrated within GIS, trade zones for both shopping malls were generated according to the drive time variable.Based on the derived zones, the overlapping zones in which the competition for consumer patronage occurs were defined.It was concluded that market cannibalism occurs between the shopping centres in the settlement of Zadar.Given the actual market situation of a large number of stores in the City Galleria centre being closed, it was to be expected that the mean value Tablica 5. Broj stanovnika s vjerojatnošću odabira (> 50%) za oba centra unutar širega tržišnog područja unutar zona preklapanja i tržišnih zona biti veća od vjerojatnosti odabira centra City Galleria, što je rezultatima istraživanja i potvrđeno.U svim tržišnim zonama i područjima preklapanja centar Supernova bilježi veću srednju vrijednost vjerojatnosti odabira u odnosu na konkurentski centar.Nadalje, ako se promatra broj kupaca unutar širega tržišnog područja koje ima vjerojatnost odabira veću od 50 %, atraktivniji centar bilježi 34 743 potencijalnih kupca više.

Zahvale
Zahvaljujemo upravama trgovačkih centara Supernova i City Galleria na ustupljenim podatcima te dostavljenoj dokumentaciji što je omogućilo izvođenje analize tržišnog natjecanja.Zahvaljujemo neovisnim recenzentima koji su svojim komentarima značajno unaprijedili kvalitetu ovoga rada. of choice probability for the centre Supernova within the overlapping zones and the market zones would be higher than the choice probability of the City Galleria centre, which was confirmed by results of the research.In all the market zones and overlapping areas the centre Supernova records a higher mean value of choice probability in comparison to its competitor.Furthermore, if a number of consumers within the broad trade area that has a choice probability higher than 50%, the more attractive centre is estimated to have 34,743 potential consumers more.
In order to improve its current market situation, the centre City Galleria is advised to begin a process of enlarging its small retail spaces for lease, which would open a possibility for attracting more anchor stores that attract higher numbers of consumers.
Figure 2 Closed shops in the old part of the City Galleria, July 2015.Source: field research

Tablica 2 .
Udio preklopljenih tržišnih zona trgovačkih centara Table 2 Proportion of overlapping trade areas of shopping centersNaziv centra Name of the mallPreklopljena površina tržišnih zona (%)The overlapped area of trade areas (%) Tržišne zone Supernove i City Gallerie Figure7Trade areas of Supernova and City Galleria gdje je: P(C ij ) = vjerojatnost da će pojedinac (i) odabrati alternativu (trgovinu) (j) S j = indeks ili atribut atraktivnosti (j) T ij = udaljenost ili vrijeme vožnje između kupca (i) i trgovine (j) a = ponder koji se odnosi na atraktivnost, a procjenjuje se empirijski b = ponder koji se odnosi na udaljenost, a procjenjuje se empirijski N = ukupan broj trgovina uključujući trgovinu j sum of values that indicate the attractiveness of a centre on location j GLA j = total gross leasable area (GLA) of the centre j N at = number of active stores in the centre j P at = area of active retail space with a weight coefficient (α) of the centre j N p = number of parking spaces in the centre jThe derived value indicates the sum of attractive features of a centre.If the z value of the centre Supernova is set as the attractive index 1, putting it into a relation with the z value of the centre City Galleria results in its index: z vrijednost atraktivnosti centra Supernove I cg = z vrijednost atraktivnosti centra City Gallerie 1 = indeks atraktivnosti Supernove x = indeks atraktivnosti centra City Gallerie U svrhu kreiranja Huffova modela vjerojatnosti odabira trgovačkog centra, s internetskih stranica ERSI-a preuzet je alat Market Analyst Toolset (URL 3).Primjenom preuzetog alata, na temelju vektoriziranih lokacija trgovačkih centara, prometne mreže širega tržišnog područja te lokacija geoobjekata, izvedeni su Huffovi modeli vjerojatnosti odabira trgovine za šire tržišno područje (Sl.8. i Sl. 9.).where: I s = z value of attractiveness of the centre Supernova I cg = z value of attractiveness of the centre City Galleria 1= index of attractiveness of the centre Supernova x = index of attractiveness of the centre City Gallerie Tablica 1. Kategorizacija trgovačkih centara prema parametru GLA Table1Categorization of shopping centers according to the GLA parameter Mautner, 1996, 1996.Source: Mautner, 1996

Table 4
Mean selection value of shopping center within trade areas and overlapping zones

Table 5
Population with the selection probability (> 50%) for both shopping malls within a wider market area