THE QUEUING PROBABILISTIC LOCATION SET COVERING PROBLEM AND SOME EXTENSIONS

Abstract

The deterministic location set covering problem seeks the minimum number of servers and their positions such that each point of demand has at least one server initially stationed within a time or distance standard. In an environment in which servers are frequently busy, the problem can be cast as the probabilistic location set covering problem. In the probabilistic formulation, the coverage constraint becomes an availability constraint: a requirement that each point of demand has a server actually available within the time standard, with alpha reliability. The objective of minimizing the required number of servers remains the same. An earlier probabilistic statement of this problem assumed that the server availability constraints. This new generation of probabilistic location model thus corrects the prior assumption of independence of server availability. Formulations are presented and computational experience is offered, together with an extension: the Maximin Availability Sitting Heuristics, MASH.