Reliability Models for Facility Location: The Expected Failure Cost Case

TLDR

Facility location models such as the P‑median and uncapacitated fixed‑charge problems typically assume that chosen facilities always operate, yet in practice failures due to weather, labor, or ownership changes can force customers to use distant alternatives and raise transportation costs. The study aims to select facility locations that are both cost‑effective under traditional objectives and robust to such failures. The authors develop reliability‑augmented PMP and UFLP models and solve them with an optimal Lagrangian relaxation, producing trade‑off curves between daily operating cost and expected failure cost. This novel reliability approach demonstrates empirically that significant reliability gains can be achieved with only modest increases in operating cost.

Abstract

Classical facility location models like the P-median problem (PMP) and the uncapacitated fixed-charge location problem (UFLP) implicitly assume that, once constructed, the facilities chosen will always operate as planned. In reality, however, facilities “fail” from time to time due to poor weather, labor actions, changes of ownership, or other factors. Such failures may lead to excessive transportation costs as customers must be served from facilities much farther than their regularly assigned facilities. In this paper, we present models for choosing facility locations to minimize cost, while also taking into account the expected transportation cost after failures of facilities. The goal is to choose facility locations that are both inexpensive under traditional objective functions and also reliable. This reliability approach is new in the facility location literature. We formulate reliability models based on both the PMP and the UFLP and present an optimal Lagrangian relaxation algorithm to solve them. We discuss how to use these models to generate a trade-off curve between the day-to-day operating cost and the expected cost, taking failures into account, and we use these trade-off curves to demonstrate empirically that substantial improvements in reliability are often possible with minimal increases in operating cost.