ROUTING URBAN TRANSPORT NETWORK WITH WEIGHING ARCS FUZZY NUMBERS AND APPLICATION IN EMERGENCY MEDICAL AID

The paper examines the problem of traffic assignment at certain routes in the urban transportation network based on the first principle of Wardrop – (UE – users equilibrium), and the second – (SE – system equilibrium) the average time for the system is minimal. The network is represented as a directed graph with Fuzzy arcs’ weights and travel times as a function of traffic flows. The algorithm of route selection is based on the incremental approach to release part of the flow for certain destination along the shortest route determined with considering the presented Fuzzy weights. The modified Dijkstra's algorithm is used according to which the arcs’ weights are represented as Fuzzy numbers. The paper focuses on the routing of an emergency care ambulance depending on the coverage of the outpatient emergency care centre on the area of the received call and taking it back into the headquarters after the patient has been driven to the closest hospital. The coverage of the regions in the city of Sofia has been defined in advance by applying the wellknown mathematical model of selecting the centres location through implementing the task of coverage (set covering problem), a task of mixed integer and linear programming. The target function and constraints and binary variables are defined in the Solver Add-in.