Using a genetic algorithm to solve a non-linear location allocation problem for specialised children's ambulances in England and Wales

Since 1997, special paediatric intensive care retrieval teams (PICRTs) based in 11 locations across England and Wales have been used to transport sick children from district general hospitals (DGHs)to one of 24 paediatric intensive care units (PICUs). The national quality standard says that a PICRT should arrive at a patient’s bedside within 3 hours from accepting the referral. In this paper we develop a location allocation optimisation framework to help inform decisions on the optimal number of locations for each PICRT, where those locations should be, which local hospital each location serves and how many teams should station each location. Our framework allows for stochastic journey times, differential weights for each journey leg and incorporates queuing theory by considering the time spent waiting for a PICRT to become available (if all teams are away fromthe base when a referral comes in). A two-stage genetic algorithm is used to solve the resultingnonlinear optimisation problem and the optimal locations of PICRT stations and the allocation ofDGHs are obtained based on available data. An additional problem with this optimisation is how to distribute a given number of teams, with which we applied a greedy algorithm. We examine the average waiting time and the average time to bedside under different number of operational PICRT stations, different number of teams per station and different levels of demand. We show that consolidating the teams into fewer stations for higher availability leads to better performance and only with a level of guaranteed availability will the geographic advantage of more stations further improve performance.