Optimizing service times for a public health emergency using a genetic algorithm: Locating dispensing sites and allocating medical staff

We formulate a p-median facility location model with a queuing approximation to determine the optimal locations of a given number of dispensing sites (Point of Dispensing-PODs) from a predetermined set of possible locations and the optimal allocation of staff to the selected locations. Specific to an anthrax attack, dispensing operations should be completed in 48 hours to cover all exposed and possibly exposed people. A nonlinear integer programming model is developed and it formulates the problem of determining the optimal locations of facilities with appropriate facility deployment strategies, including the amount of servers with different skills to be allocated to each open facility. The objective of the mathematical model is to minimize the average transportation and waiting times of individuals to receive the required service. The mathematical model has waiting time performance measures approximated with a queuing formula and these waiting times at PODs are incorporated into the p-median facility location model. A genetic algorithm is developed to solve this problem. Our computational results show that appropriate locations of these facilities can significantly decrease the average time for individuals to receive services. Consideration of demographics and allocation of the staff decreases waiting times in PODs and increases the throughput of PODs. When the number of PODs to open is high, the right staffing at each facility decreases the average waiting times significantly. The results presented in this paper can help public health decision makers make better planning and resource allocation decisions based on the demographic needs of the affected population.