An integer programming model for the deployment of mobile health clinics

Facility location and resource allocation play an essential role in the operational management of mobile health clinics (MHCs) as optimization of both can help medical service providers improve their service coverage under limited resources. In this paper, we consider the issue of maximizing the coverage of immunization services provided by MHCs in vulnerable communities such as school zones and census tracts. Since demand in communities overlaps with neighboring communities, this leads to the so-called mobile facility location with overlapped demand (MFL-OD). To capture the overlapped demand in different communities, we introduce a novel integer programming model with linear and bilinear constraints (BLCIP) and show that the BLCIP model is NP-hard. A polynomial-time approximation algorithm is proposed for the BLCIP, and the approximation ratio of the obtained solution is estimated. We implement the proposed model and approximation algorithm for a case study in the Houston Independent School District and its associated communities. Preliminary experiments demonstrate the efficacy of the proposed model and the efficiency of the proposed approximation method.