Mathematical Modelling for dynamic Home Health Care routing with Cumulative Objective Function

Abstract

Logistics management in healthcare systems has been a major focus area for operations research in the recent years. In this topic, the optimization of routing problems related to home healthcare has a rising interest due to its specific characteristics. The importance of such problems relies on the impact it has on the patients' well-being. Traditional approaches consider optimization goals related to costs and financial effectiveness. In this paper, we address a specific scenario of the home healthcare problem, for the case where patients request medical services, considering the dynamic nature of new requests which are randomly made by patients. We propose a two-stage solution approach which builds a first solution and adapts the routes as new patients request services. The problem aims to minimize the response time for patients, weighted by a priority criterion assigned according to the medical conditions. Our approach also considers constraints regarding time windows promised to patients, as well as multiple vehicles departing from and arriving to multiple dispatch centers Moreover, we propose a weighted cumulative objective function that sums for every patient the response time weighted by a priority assigned for its services during the request. This customer-oriented objective function seeks to maximize customer satisfaction by reducing the waiting time. Finally, we compare the performance of the model solution using both a commercial solver and a meta heuristic approach achieving a gap of 0.4% for the proposed problem and reducing solve time on average in 81%. Results demonstrate that it is possible to effectively address these problems and maximize customer service.