Some deterministic and stochastic nonlinear optimization modelling for the spatial allocation of multicategorical resources: with an application to real health data

Abstract

This paper is a sequel to two previous articles, which presented deterministic mathematical modelling for the prediction of single-category patient/client/customer “flows” as an aggregate within a large geographical domain and formulations of several deterministic nonlinear optimization models based on objectives of equity, efficiency, and accessibility for single-categorical resources. This paper presents some formulations of both deterministic and stochastic nonlinear optimization models for planning the spatial distribution of public service facilities and their utilization as a function of multicategorical resource types and the consumer's zone of residenceover a large geographical domain. The stochastic model is useful for large-scale systems planning when parameter values are subject to change over the planning horizon rather than being held fixed, as in the deterministic model. The mathematical solution to the deterministic model, its parameter estimation by log-linear regression, and some preliminary results for a Massachusetts hospital data base are presented.