Kalabalık p-ortanca problemi için dış yaklaşım algoritması

In this thesis, we study a generalization of the p-median problem, which is awell-known facility location problem. Given a set of clients, a set of potential facilities,and a positive integer p, the p-median problem is concerned with choosingp facilities and assigning each client to an open facility in such a way that the sumof the travel times between each client and the facility that serves that client isas small as possible. The classical p-median problem takes into account only thetravel times between clients and facilities. However, in many applications, thedisutility of a client is also closely related to the waiting time at a facility, whichis typically an increasing function of the demand allocated to that facility. In anattempt to address this issue, for a given potential facility, we dene the disutilityof a client as a function of the travel time and the total demand served by thatfacility. The latter part reects the level of unwillingness of a client to be servedby a facility as a function of the level of utilization of that facility. By modelingthis relation using an increasing convex function, we develop convex mixed integernonlinear programming models. By exploiting the fact that nonlinearity onlyappears in the objective function, we propose dierent variants of the well-knownouter approximation algorithm. Our extensive computational results reveal thatour algorithms are competitive in comparison with the o-the-shelf solvers.