Part 2. MM4XL Tools > 2. Analytical Tools > Gravitation Analysis > Technicalities
## Business Formulas ### Technicalities The likelihood that a city (or shopping center) will attract shoppers from a hinterland increases with the size of the city (or shopping center) and decreases with distance from the center. Reilly's formula, below, yields the break point between customers who will go to one center and those who will go to the other one, located on an ideal line connecting the two. In the formula, dij is the distance between the two centers, Pi is the size of the peripheral center, and Pj is the size of the central one. Sometimes, however, the definition of population is not a straightforward one, so one can sum several groups together. For instance, if your target is made of drug stores, prescribing doctors, and hospitals sum them together. Each population could be weighted (multiplied) accordingly, for instance, to the square footage, local tax level, or any other variables you may consider relevant. In other cases, the population may be expressed as the size in squared feet of several competing outlets, as we did for our example. Larger places attract more people, so finding more goods and services available at the same location is a strong attraction for customers. This fact can be taken into account, and it may make sense to do so, for supermarkets for instance. But also Hi-Tech stores, casinos, restaurants and bars, discos, cinemas, and more can find this measure useful. The distance may also be adapted. Indeed, one may consider using a functional distance instead of the actual one. Functional distance may be the walking time, driving time or the flying time that it takes customers to reach a given place. *Tip:* For accurate reproductions of any geographic locations we suggest you to visit the URL www.mapquest.com and see if you can find the map of the region(s) you are working with. Finally, some criticisms raised against this technique. William J. Reilly expanded the gravity model and found the law of retail gravitation. The gravity model, or the modified law of gravitation, takes into account the population size of two places and their distance. Since (1) larger places attract people, ideas, and commodities more than smaller places and (2) places closer together have a greater attraction, the gravity model incorporates both these features. Opponents of the gravity model say that the whole rational behind the model has not been confirmed scientifically yet, and it is only based on observation. |