For a better appraisal of fit, wu have hypothesized that, for a 

 given dealer, the probability of purchase in cell i is not p but is 

 p.' where 



Pi' = Pi^^ ^ ^t^ 



and € is a random error term. The standard deviation, a of c. may be 

 viewed as a type of a coefficient of variation. The value of a has been 

 estimated for each dealer and has a median value of .32. This seems 

 quite good, considering how few factors are included in the model. 



4. An Interactive Computer System 



Conceivably, one could use the model to work out a mathematically 

 optimal pattern of dealers over the city or, more modestly, the optimal 

 location of a new dealer. Such an optimization is probably sterile. 

 A decision on a dealership involves many factors not included in the 

 model: the availability of property, financing, the micro-geography of 

 the location, etc. Perhaps some of these factors can be modeled but 

 as of now they are not. Yet we do not want to wait to take advantage 

 of what we can learn about macro-geography and competitive interaction. 

 What is needed is a convenient way to make the information available 

 to a person working on dealership problems. 



To demonstrate how this can be done, an interactive computer syptem 

 was programmed for the model on the Project MAC time-shared computer 

 at MIT. With the system a user can sit at a remote console of the com- 

 puter, make hypothetical changes in dealerships, and learn immediately 

 the model's prediction of the effects. See Exhibit I for an example 

 of the system in action. Changes that a user can make include adding 

 a dealer, moving a dealer, eliminating a dealer, changing a dealer's 

 a and b parameters, and changing the potential of a cell. 



5. Possible Improvements 



Experimentation with the functional form of the distance relations 

 would be of interest. Similarly, different measures of "distance" might 

 be tried. Travel time has strong intuitive appeal. Much better market 

 segmentation is possible. The natural one would be to break down the 

 cell population by make-model year of car owned. Then make preference 

 could be related to the buying rates of each segment for each make. 

 Another subject for investigation is the effect of clustering of dealers. 

 Perhaps there is a special advantage to being in an "automobile row" 

 because the row itself attracts customers. If so, the model might be 

 modified to account for this. A highly desirable line of research would 

 be to investigate how the a and b parameters are related to various 

 observable characteristics of the dealer. 



Reference 



1. J. W. James, "An Analysis of the Optimum Market Representation 

 Policies Relating to a Large Metropolitan Market," MS Thesis, 

 MIT, 1964. 



