Social welfare maximization on capacitated networks

Classical location-allocation models consider spatial efficiency or equity as their major objectives, while more recent location-allocation models consider the maximization of social welfare as their primary goal. The purpose of this study are to explore the properties of social welfare functions used in location-allocation modeling, relate those to entropy maximizing models, and use them to determine the optimal location and size of facilities on capacitated networks.

This research introduces a modified version of Wilson's doubly constrained entropy maximizing model, and proves the equivalence between this modified form and other social welfare maximization models; i.e., consumer surplus, users' benefit, and log accessibility. The modified form of entropy maximizing model can also be applied as spatial competition location-allocation model.

The log accessibility maximization model is applied to capacitated networks. The existence and uniqueness of a solution to the log accessibility model on capacitated bipartite and tree networks are proven. A four step solution procedure for the log accessibility maximization model in these cases is then developed. The solution procedure is shown to be both feasible and convenient.

The numerical results for capacitated bipartite and tree-structured networks are discussed. Since many variables are involved in this model—population, facility size, facility location, construction costs, capital budgets, economies of scale, link capacity, transportation cost, flow pattern, and network structure—it is very difficult to obtain generalized results. In the numerical results presented, most variables are hold constant in order to study the effect of congestion on the location-allocation decision process.