Facility Location with Client Latencies: Linear-Programming based Techniques for Minimum-Latency Problems

We introduce a problem that is a common generalization of the uncapacitated facility location (UFL) and minimum latency (ML) problems, where facilities not only need to be opened to serve clients, but also be sequentially activated before they can provide service. This abstracts a setting where inventory demanded by customers needs to be stocked or replenished at facilities from a depot or warehouse. Formally, we are given a set F of n facilities with facility-opening costs {fi}, a set D of m clients, and connection costs {cij} specifying the cost of assigning a client j to a facility i, a root node r denoting the depot, and a time metric d on F {r}. Our goal is to open a subset F of facilities, find a path P starting at r and spanning F to activate the open facilities, and connecting each client j to a facility (j) F, so as to minimize iF fi + jD(c(j),j + tj), where tj is the time taken to reach (j) along path P. We call this the minimum latency uncapacitated facility location (MLU...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Deeparnab Chakrabarty, Chaitanya Swamy
• Keywords: Approximation Guarantees, CORR 2010, Education, Facility Location, Minimum Latency