1. EM 4103 Urban Planning II Lecture 9: Overview on Models in Planning and Use in Retail Planning

2. Shopping Models  The analytical models used by planners in assessing existing provision and future needs for retail are known as gravity models.  These models depend largely upon knowledge of the relationship between activity locations and the travel behaviour of the users who undertake such activities.

3. Gravity Models are so called because of an analogy with the ideas of Newton whose Law of Universal Gravitation states that “Two bodies in the universe attract each other in proportion to the product of their masses, and inversely to the square of their distance apart”, as follows: Where F = the force of attraction between the two bodies M 1 and M 2 = the respective masses of the two bodies d = the distance between the two bodies G = the gravitational constant

4. In the analysis of urban systems, the amount of interaction between two areas A and B, is related directly to the size or attraction of the areas and inversely to the distance separating them: Where I AB = the interaction between areas A and B P A and P B = the respective sizes of areas A and B (as measured, e.g in terms of population) d AB = the distance between A and B = an exponent applied to the distance variable K = a constant which is empirically determined

5. Reilly's Law of Retail Gravitation  By this law the market boundary between two retail towns can be identified.  According to this law, shoppers living at any point between two towns A and B will be attracted to the towns in accordance with the relative populations of the two towns, and inversely with the square of the relative distance of that point from the two towns.

6. d AB B P B dB dB A PAPA dAdA Market Boundary A Market Boundary between two Centres

7. Given the choice faced by shoppers living between two cities A and B, the attraction of the shopping centre of City A, with population P A, to individuals living at an intermediate location, distance d A from A, will be Where G A = the force of attraction of A

8. Similarly, the attraction of the shopping centre at City B, with population P B to individuals living at an intermediate location, distance d B from B, will be: Where G B = the force of attraction of B

9. If an individual shops in the City with the strongest overall attraction, the market boundary or breaking point between these two retail centres is the point to which one city exercises the dominating retail influence, and beyond which the other City dominates. This is the equilibrium point where the attraction of A is equal to the attraction of B: G A = G B Substituting into the earlier equation: Shoppers living at this point will be indifferent between the two competing retail centres

10. By cross-multiplying, the market boundary can be identified as follows:

11. B 10 miles A 20 miles Market Boundary Reilly’s law as applied to determine market boundary P A = 100000 P B = 25000

12.  Shoppers will shop only in the town with the stronger overall attraction.  The application of Reilly’s law means discontinuous trade areas.  In practice, however, shoppers are not confronted with the simple bilateral choices that Reilly hypothesised.

13.  A A  B B  E  D D  C Discontinuous Trade Areas for Retail Centres

14. Estimate consumer expenditure available in each residential zone C j Calculate the probability of interaction between residential zones and shopping centres Find the total attraction that shopping centre have on residential zones by summing Calculate attraction measures for each shopping centre Calculate attraction measures for each shopping centre Calculate expenditure flows from residential zones to shopping centres Flow Chart for Typical Shopping Model

15. A Probabilistic Approach to the Gravity Model For a given period, the number of trips (T) made by those living at i to an activity or centre at j will increase with the number of trip makers (P) located at I, and with the number of opportunities (H) available at j to satisfy the demands of these trip makers. The number of trips decreases with the distance (d) or cost of travelling from i to j. K is similar to the gravitational constant, And , , and are the other model parameters, of of which can be empirically determined in the caliberation processes

16. The model may now be re-specified as follows: S = expenditure flow C = the money available for purchases F = total retail space

17. The expenditure available in each zone is the total expenditure available in the subregion: Assuming that  =  = 1,

18. Cross-multiplying: Thus:

19. Existing Shopping Centre A Proposed Shopping Centre C Existing Shopping Centre B Zone 1 Zone 3 Zone 2 Applying the Constrained Gravity Model: The Three Zone Study Area

20. A C B Zone 1 Zone 3 Zone 2 Applying the Constrained Gravity Model: The Three Zone Study Area 2 10 6 5 15 2 10 15 2

21. Estimate consumer expenditure available in each residential zone C j Calculate the probability of interaction between residential zones and shopping centres Find the total attraction that shopping centre have on residential zones by summing Calculate attraction measures for each shopping centre Calculate attraction measures for each shopping centre Calculate expenditure flows from residential zones to shopping centres Flow Chart for Typical Shopping Model

22. Limitations of shopping models  They only describe the spatial interaction of activities within the urban system but do not explain the behavioural reasons for any given pattern of location, and thus cannot be an effective predictive tool.  Secondly, the method necessarily simulates interaction of one activity, which is modelled, while other parts of the urban system are held constant. The technique is thus criticized as being partial in nature.

23.  The approach is criticized as being static and have failed to adequately embrace the dynamic elements of the urban economy.  Gravity models consider activities at an aggregate level e.g. population, expenditure and retail activity, and do not look at the smaller components of these activities.

24. There are also practical and operational limitations as well.  There are problems of defining variables as well as caliberating or measuring them.  In shopping studies, there is the issue of determining levels of consumer expenditure.

25. In general, gravity models can provide broad and useful information for policy makers. However, it is important to note that these techniques are demand-side models and ignore supply-side considerations. They should be supplemented by appraisals of shopping facilities to identify commercial and other factors affecting the supply of shops.

26. A composite General Urban model: The Garin-Lowry Model

27. A General Urban Model: the Garin-Lowry Model  The shopping models described previously are partial models which simulate one part of the urban system.  A general model attempts to describe several parts of the urban system and simulate the allocation and interaction between several land use activities – people, work and homes.

28.  The Garin-Lowry model is one general model that combines a residential location model and a retail location model coupled together through the economic base mechanism  The model operates by deriving dependent population and service employment  It allocates households and retail employment to zones of the study area.

29.  From an estimated level and distribution of basic employment, the model first allocates basic employees to residential zones.  Then the population associated with these basic employees is found.  This population demands services from retail employees, which are allocated in service centres.

30.  In turn, these retail employees are allocated to residential areas and the associated population required to be serviced.  Further increments of population and service employment are derived and allocated, until this process converges, that is, until further increments of population and retail employment are negligible enough to be ignored.

31. A Steel Mill 1000 workers Shops and Schools for 500 workers A Settlement of 1000 Families Addition to the settlement of another 500 families The relationship between service employment and population is an iterative one, and there will be an eventual total balance greater than the first round figures

32. Basic Employment Service Employment Population The model builds on this simple relationship, adding a land use dimension to the essentially economic relationship

33. Level & Location Of Basic Employment (Given) Basic Employees to Residential Zones Dependent Population on Basic Employees Requirement of Service activities (retail Employment) Retail Employees To Service Centres Retail Employees To Residential Zones Dependent Population on Basic employees Requirement of Service activities (Retail Employment) Retail employees To service Centres Allocate Derive Allocate Functional Structure of the Garin-Lowry Model

34. Notts-Derby Study Output from the Model:  Predicted non-basic workers per zone  Predicted population per zone  A complete inter-zonal journey to work matrix  A complete inter-zonal journey to service matrix; this approximates to a ‘journey to shop’ pattern  Internal migration components for population and non-basic jobs

35. Application Overall:  The model can be used at a macro level to test large scale changes or different alternative plans.  It can also be used for testing the impacts of policies such as green belts and new expressways.

36. The Learning Aspects of Models: Lowry in “The Journal of the American Institute of Planners”, May 1965:  The process of model-building is educational.  The participants invariably find their perceptions sharpened, their horizons expanded, their professional skills augmented.

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