Our model of ambulances allocation is a dynamic coverage one that aims to minimize the total lateness during emergency intervention. The objective function (1) expresses the total lateness of emergency interventions. ݇ represents the intervention, ܭ is the set of demands received from several sectors that are districts of the city. ݐis the date of demand arrival and ݀ is the end of intervention ݇ (the patient arrival to hospital by ambulance). The total lateness (fitness) is calculated using a discrete event simulation model during a horizon ܶ and repeated for a number of iterations.
The model regroups two emergency management levels. The first one is tactical. It consists to ensure the best distribution of ambulances in hospitals and fire stations as potential waiting sites. The second level is operational; it concerns the ambulance deployment and redeployment once an emergency call is received. Emergency demands are addressed from intervention sectors according to Poisson distribution. ߣPoisson parameter represents the duration between two emergency calls (Fig. 2). So, more two calls are close; this parameter tends to zero. Thus, Poisson distribution seems suitable to estimate demands received from intervention sectors during two periods; day and night. Once a call ݇ comes at instant ݐ, we deploy an ambulance from a waiting site ݅ to an intervention sector ݆. The ambulance reaches the sector ݆ at the instant ݎݐ++ௗೕ.ݎ is the lateness related to the lack of vehicles. ݀ is the distance between the site ݅ and the sector ݆. ܸ represents the ambulance speed. So the number of ambulances in this waiting site ݅will be decremented. When the patient arrives in the hospital ’݅ at instant ݀ݎ=ݐ++ௗೕ+ௗᇲೕ, the ambulance becomes available. ݀(ݐ−) is then the lateness of the emergency intervention ݇ minimized in function (1). The follow simulation scenario is deployment of the available vehicle. If the next intervention demand is not met due to the lack of ambulances in the waiting sites, we will affect the ambulance parked in the hospital directly to this new intervention demand. Otherwise, the ambulance is redeployed to the nearest waiting site ݅and the number of vehicles in this site will be incremented.
This section contains the methods used for the resolution: a heuristic method and an ACO hybridized by a GLS ‘guided local search’. The local search serves to find an improved fitness around the current solution. Furthermore, the GLS has to guide the movement of the local search. We consider firstly that demands are expressed from an intervention sector. Then, the duration between two emergency calls is distributed according to the Poisson law of a periodicity equals to two (day and night). Our model deploys the nearest available ambulance in order to minimize the total lateness of the emergency intervention. Once located in hospital after a patient transportation, the available ambulance will be redeployed to another emergency intervention which it has not yet received a response, or will be allocated to a waiting site. Code Shoppy