The dial-a-ride problem in the case of a patient transportation system in Brazil

Abstract

Despite its importance, the role played by logistics is often overlooked in health care. Patients often need to be transported to medical facilities and treatment units. In Brazil, the transportation department of municipal health care systems need to provide transport to patients from small municipalities to public hospitals located in large cities, as some medical services are only provided in these hospitals. The problem of transporting patients can be modelled as a Dial-a-Ride Problem (DARP). The DARP is a variant of the Vehicle Routing Problem (VRP) where a transportation request includes both a pick-up and drop-off locations and not only time window constraints but also other users' constraints are considered. The general goal of DARP is to calculate a route plan to meet a set of transportation requests by using a given fleet of vehicles at minimum cost. In this paper, we aim at solving the DARP arising in the daily operation of the transportation sector of the municipal health care system in Ouro Preto, Brazil. Every day, the transportation department transfers patients from their pick-up location, which is either the patient's home or a collective point, to public hospitals located in the capital Belo Horizonte. Whether a patient is collected from their home or a public location (collective point) depends on the patient's condition. Patient transportation requests also differ regards to patient's vehicle requirement. That is, a transportation request can include either a single patient or a patient and a companion person and based on the patient's need (e.g. in a wheelchair) a specific v ehicle m ight n eed t o b e allocated to the patient. To provide the transportation service, the sector leases a fleet o f h eterogeneous v e hicles. The vehicles have different (leasing) costs and load capacities. The main difference between the problem faced by the Ouro Preto's health care system and DARPs from the literature is that the proposed problem must have no transportation request rejected. That is, all patients must be served. To solve this problem, we introduce a variable neighbourhood search (VNS)-based metaheuristic. The VNS method counts with a greedy method to find a n i n itial s o lution a n d a r a ndomised v a riable neighbourhood descent (RVND) method as the local search procedure. Solutions are evaluated using a cost function which includes routing cost and penalty cost for violating time window constraints. The VNS shaking procedure includes six inter-route operators, whereas the RVND method includes three. We calibrate the parameters of the VNS, namely neighbourhood combination, penalty for time window constraint violation, and stopping criteria, using a well-known calibration tool, the iRace package. We validate the performance of the proposed VNS on benchmark instances from Parragh (2011). We also create different test problems based on data provided by the public health care system and test the proposed approach on them. The computational experiments on Parragh (2011)'s instances show that our VNS is able to find o ptimal s olutions i n s hort c omputational times. When VNS was not able to find the optimal solution, the gap was less than 2.95%. The results on the designed test problems indicate that by using the proposed approach, the transportation sector can lease fewer vehicles than it has been currently renting to attend daily patient transportation requests. We can conclude that the VNS metaheuristic is an efficient t ool f or t he m unicipal h ealth c are t ransportation s ector t o i mprove routing and vehicle costs.