Equilibrium values and dynamics of attractiveness terms in production-constrained spatial-interaction models

A number of mechanisms are explored for modelling equilibrium values of attractiveness terms in production-constrained spatial-interaction models. They include revenue and facility-size balancing, a differential-equation representation of profit maximisation, and mathematical-programming formulations. The different methods turn out to be closely related but offer different and complementary insights. Some dynamic properties of such equilibrium points are explored, including the identification of circumstances which generate discrete changes for smooth changes in parameters. A number of possible algorithms for calculating the points are described.