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A1.7 Application to residential location models It will al ready be clear from the discussion in Section 5.1

that the structure of the basic residential location model is essentially the same as that of the shopping model. Both are singly constrained spatial interaction models, the shopping model being usually considered as production constrained, the residential location model as attraction constrained. It is therefore a straightforward matter to apply all the results of the previous subsections, which have been presented for the shopping model, to the residential location model. This is left as an exercise to be taken up as required - and is in part carried out in the next subsection on the Lowry model in relation to its residential location component. A1.8 Mathematical programming versions of the Lowry model

The essence of the original Lowry model, and many others of the same type, was outlined in Section 5.2.4. There are a great many ways in which the Lowry model can be represented as a single mathematical programming model - pioneered by Coelho and Williams (1977). These are discussed in some detail in the paper by Macgill and Wilson (1979). Here, we shall simply look at the basic principles for constructing such models and choose one aggregate example as an illustration, and then develop a suitable disaggregated version for Chapter 6, in the section on central place theory below.