Periodic location routing problem : an application of mobile health services in rural area

Lack of sufficient healthcare services in rural areas has been a considerable problem throughout the world for a long time. One of the alternative ways to address and solve this problem is providing mobile healthcare services in which the providers are traveling and visiting patients. These services have been obligatory in Turkey since 2010 and there are certain requirements that are enforced by Ministry of Health, such as having multiple routinized visits, having alternative visiting rules and dedicating doctors to specified villages. Based on the characteristics of this problem, it is categorized under Periodic Location Routing Problem (PLRP) literature. The common characteristic of the solution methodologies in the PLRP literature is to predefine a set of alternative schedules and select the best one among those. Unlike the other approaches that have been already studied, the developed integer programming model determines the schedules of the doctors via its constraints, dedicates each doctor to same villages through the planning horizon and satisfies certain visiting rules. The performance of the model is tested by utilizing the data set of Burdur. The proposed model is solved to optimality in reasonable times for the small instances; however, significant optimality gaps remain at the end of predefined time limits of the larger instances. In order to obtain prominent results in shorter durations, a \cluster first, route second" based heuristic algorithm is developed. Based on the computational experiments, it is observed that the solution times are significantly improved and optimal or near-optimal solutions are obtained with the heuristic approach.