Measuring and evaluating the Home Health Care Scheduling Problem with Simultaneous Pick-up and Delivery with Time Window using a Tabu Search metaheuristic solution

Abstract

The Home Health Care Scheduling Problem (HCSP) with Simultaneous Pick-up and Delivery and Time Window (HCSPSPDTW) consists of finding the optimal crew composition and the best routes to follow in order to satisfy some logistics actions such as the delivery of medical services from the hospital to patients, and the pickup of unused drugs and biological samples from patients to the hospital in a transportation network. The HCSPSPDTW is a bi-objective problem where the traveled time and distance should be minimized. In this paper, we present a hierarchical approach for solving the HCSPSPDTW: the inner optimization problem solved by the k-means++ clustering algorithm, asks for finding the closest visits in terms of distance to avoid long travels. The outer problem is a Vehicle Routing Problem (VRP) modeled by a mixed-integer mathematical model and solved using Tabu Search (TS) metaheuristic. In order to evaluate the performance of the proposed algorithm, this study used some modified test problems from Solomon’s benchmark. The obtained results show that the proposed approach was able to generate better solutions than similar algorithms while using less computation time. For instance, the proposed approach outperforms other algorithms by generating less routing cost for 83.93% instances, less used vehicles for 98.73% instances, and by spending less computational time for 98.7% instances. The proposed HCSPSPDTW solving approach is the solver module of a decision support system that will help Home Health Care companies to make appropriate decisions on scheduling their daily plans which will lead to can lead to a significant reduction of transportation costs and improvement of staff satisfaction.