Distance restricted maximal covering model for pharmacy duty scheduling problem

Pharmacies are considered as an integral part of health care systems for supplying medicine to patients. In order to access medicine with ease, pharmacies locations in the context of distance and demand are important for patients. In the case of a few numbers of pharmacies may be on duty at nights or during holidays, pharmacies duty scheduling problem occur and can be associated with location models. In contrast to widely used p-median model which aims to minimize the demand-weighted distance, we maximize the demand covered over the distance between the patients and the pharmacies on duty. Main contribution of the proposed model is the restriction constraint for the distance between pharmacies on duty in order to ensure fairness in an organizational view of point. We propose a distance restricted maximal covering location model (DR-MCLM) in this study. This mathematical model is a mixed integer linear programming model and solved by Lingo optimization software. The distances between the pharmacies and the sites are obtained using Geographic Information Systems (GIS). The model is applied for the case in Adana, one of the biggest cities in Turkey. The results are given on the maps of the city, including the pharmacies on duty and their assignments to sites in each day of the period.