Lecture 20 Huff Model – A probabilistic Analysis of Shopping Center Trade Area20-1 Introduction (Cont.)Slide 320-2 Breaking Point20-2 Breaking Point (Cont.)20-3 Shopping Center Breaking Point20-3 Shopping Center Breaking Point (Cont.)Slide 820-4 Huff Model20-4 Huff Model (Cont.)20-5 An example of Huff Model20-5 An example of Huff Model (Cont.)Slide 1320-6 An example of Huff Model (Cont.)Slide 1519/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC11Lecture 20 Huff Model – A probabilistic Analysis of Shopping Center Trade Area20-1 IntroductionWilliam J. Reilly – Applying the gravity concept to retail trade area analysis:Purpose is to determine the relative retail pulling power of two competing cities on an intervening area.Hypothesis:Two cities attract retail trade from an intermediate city or town in the vicinity of the breaking point approximately in direct proportion to the populations of the two cities and in inverse proportion to the square of the distances from the two cities to the intermediate town.19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC2220-1 Introduction (Cont.)The mathematical expression of Reilly’s hypothesis is as follows:(B).A city town toteintermedia thefrom distance the- ,B. andA city of population the- ,(B).A city by attractedcity teintermedia thefrom trade theof proportion the, Where2bababaabbabaDDPPBBDDPPBB19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC3320-1 Introduction (Cont.)An example of Reilly’s model:A X B20 miles30 milesPop:100000Pop:200000125.120302000000100000022abbabaDDPPBBThe percentage of the population of town x attracted to city A is 53%, to city B is 47%.19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC4420-2 Breaking Point20-2 Breaking PointIn 1947, the Curtis Publishing Company adopted Reilly’s formula to calculate the break point between two cities. Such a boundary line, where Ba=Bb, represents the dominant trading areas for city A and B.B. andA between distance the- B. andA city of population the- ,B. from milesin Bcity andA city between point breaking the Where1abbabbaabbDPPBPPDB19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC5520-2 Breaking Point (Cont.)20-2 Breaking Point (Cont.)An example of this formulation:A B80 milesPop:200000Pop:400000milesPPDBbaabb3.3320000040000001801Break Point from Bis 33.3 miles.19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC6620-3 Shopping Center Breaking Point20-3 Shopping Center Breaking PointThe modified Reilly’s formulation has also been used to estimate trading areas of proposed shopping center within cities.Generally, the square footage of each retail center is substituted for population and travel time between retail centers is substituted for physical distance.See Table-1 for a hypothetical example.19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC7720-3 Shopping Center Breaking Point 20-3 Shopping Center Breaking Point (Cont.)(Cont.)Table 1 – Hypothetical Data Used in Delineating Trading Area of Proposed Shopping CenterShopping Center Sq. Footage of Selling SpaceTravel Time From ABreaking Point From Shopping Center to AA 200000 0 0B 100000 15 6.2C 150000 20 9.3D 50000 10 3.3E 3000000 25 13.819/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC8820-3 Shopping Center Breaking Point 20-3 Shopping Center Breaking Point (Cont.)(Cont.)Limitation of Gravity Model-The calculation of breaking points to delimit a retail trade area conveys an impression that a trading area is a fixed boundary circumscribing the market potential of a retail facility.-Distance exponent is a variable (ranged from 1.5 to over 3 – depending on the trip type as well as other factors.)-Possesses very little theoretical content.19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC9920-4 Huff Model20-4 Huff ModelHow huff improves Reilly’s model:-Will utilize the conceptual properties of the gravity model-Focus on the consumer rather than on the retail firm.Measuring a Shopping Center’s Utility:-The number of items of the kind a consumer desires that are carried by various shopping centers-The travel time that is involved in getting from a consumer’s travel base to alternative shopping centers.19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC101020-4 Huff Model (Cont.)20-4 Huff Model (Cont.)The probability of a consumer at a given point of origin I traveling to given shopping center j can be described: trips.of kinds on various time travelofeffect ereflect th y toempiricall estimated be toiswhich parameter a - jcenter shopping toi base travels'consumer a from gettingin involved time travel the- jcenter shoppingby goods of classparticular a of sale the todevoted space selling of footage square the- jcenter shoppinggiven to travelingiorigin ofpoint given aat consumer a ofy probabilit The )P( Where)(1ijjijnjijjijjijTSCDSDSCP19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC111120-5 An example of Huff Model20-5 An example of Huff ModelFive steps:1. Divide the area into small statistical unit.2. Determine the square footage of retail selling space of all shopping centers included within the area of analysis.3. Compute travel time.4. Calculate the probability of consumers in each unit going to the particular shopping center.5. Map the trading area of the shopping center in question by drawing lines connecting all statistical units having like probabilities.19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC121220-5 An example of Huff Model 20-5 An example of Huff Model (Cont.)(Cont.)6. Calculate the number of households within each of the statistical units. Then multiply each of these figures by their appropriate probability values to determine the expected number of consumers.unit. lstatistica in the consumers ofnumber The - units lstatistica theofeach from consumers ofnumber expected The )E( Wheres)i' all(For .)(1thithijinjijjijjijiCiCCDSTSCE19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC131320-5 An example of Huff Model 20-5 An example of Huff Model (Cont.)(Cont.)7. Determine the annual average per household incomes of each of the statistical