Fairness in ambulance routing for post disaster management

Abstract

Disaster management generally includes the post-disaster stage, which consists of the actions taken in response to the disaster damages. These actions include the employment of emergency plans and assigned resources to (i) rescue affected people immediately, (ii) deliver personnel, medical care and equipment to the disaster area, and (iii) aid to prevent the infrastructural and environmental losses. In the response phase, humanitarian logistics directly influence the efficiency of the relief operation. Ambulances routing problem is defined as employing the optimisation tools to manage the flow of ambulances for finding the best ambulance tours to transport the injured to hospitals. Researchers pointed out the importance of equity and fairness in humanitarian relief services: managing the operations of ambulances in the immediate aftermath of a disaster must be done impartially and efficiently to rescue affected people with different priority in accordance with the restrictions. Our research aim is to find the best ambulance tours to transport the patients during a disaster in relief operations while considering fairness and equity to deliver services to patients in balance. The problem is formulated as a new variant of the team orienteering problem with hierarchical objectives to address also the efficiency issue. Due to the limitation of solving the proposed model using a general-purpose solver, we propose a new hybrid algorithm based on a machine learning and neighbourhood search. Based on a new set of realistic benchmark instances, our quantitative analysis proves that our algorithm is capable to largely reduce the solution running time especially when the complexity of the problem increases. Further, a comparison between the fair solution and the system optimum solution is also provided.

Keywords: Ambulance routing; Fairness; Post disaster management; Team orienteering problem.

Fig. 1

Example: solution of a TOP formulation representing the ambulance tours after a disaster. Each tour starts from the starting dummy node and ends in the ending dummy node, and hospitals are always visited in accordance with the graphic overlay. Numbers on arcs indicate the order in which they are visited in the tour

Fig. 2

Example: how the constraints (9)- (11) work

Fig. 3

Example: fairness solution of a TOP formulation representing the ambulance tours after a disaster. Each tour starts from the starting dummy node and ends in the ending dummy node, and hospitals are always visited in accordance with the graphic overlay. Numbers on arcs indicate the order in which they are visited in the tour

Fig. 4

Comparing the solution provided by the algorithm $\mathcal{A}$ using $z_f$ (circles) and $z_e$ (squares) as objective functions (same color is used for the two solutions of the same instance)