Maximal Benefit Location Problem for A Congested System

Some servers are to be located at nodes of a network. Demand for services of these servers is located at each node and a subset of the nodes is to be chosen to locate one server in each. Each customer selects a server with a probability dependent on distance and a certain amount of benefit is achieved after giving service to the customer. Customers may waive receiving service with a known probability. The objective is to maximize the total benefit. In this paper, the problem is formulated, three solution algorithms are developed and applied to some numerical examples to analyze the results.