Optimal Patient Allocation Considering Traffic Congestion and Hospital Capacities

Abstract

The optimal allocation of patients after a major accident is important because there are constraints such as limited hospital capacity and traffic congestion on the roads connecting the accident location to the hospitals. It is imperative to provide timely treatment to the casualties of such accidents to minimize loss of life. However, most studies that focus on the allocation of patients after accidents do not consider traffic aspects such as congestion on the roads near hospitals or hospital waiting times. This paper proposes a formulation to optimally allocate patients to minimize the sum of the total system travel time and the total waiting and treatment times of patients while considering travel congestion and limited hospital capacities. The developed optimization formulation is nonlinear and therefore a genetic algorithm was developed to solve it. The developed algorithm was tested on a standard transportation network and was found to give close to optimal solutions in a reasonable time. For instance, the proposed genetic algorithm achieved solutions within 4.6% of the optimal value and reduced computation time by an order of magnitude 9 times that of an existing solver when there were 30 hospitals. Sensitivity analysis employing various parameters such as the number of hospitals, hospital capacities, and treatment times, was also performed. The objective function value decreased with the number of hospitals and hospital capacities, but increased with treatment times when the other parameters remained the same. The reasons behind such patterns are discussed.