THE QUEUING PROBABILISTIC LOCATION SET COVERING PROBLEM AND SOME EXTENSIONS

The deterministic location set covering problem seeks the minimum numb er of servers and their positions such that each point of demand has a t least one server initially stationed within a time or distance stand ard. In an environment in which servers are frequently busy, the probl em can be cast as the probabilistic location set covering problem. In the probabilistic formulation, the coverage constraint becomes an avai lability constraint: a requirement that each point of demand has a ser ver actually available within the time standard, with alpha reliabilit y. The objective of minimizing the required number of servers remains the same. An earlier probabilistic statement of this problem assumed t hat the server availability constraints. This new generation of probab ilistic location model thus corrects the prior assumption of independe nce of server availability. Formulations are presented and computation al experience is offered, together with an extension: the Maximin Avai lability Sitting Heuristics, MASH.