A two-stage robust model for a reliable p-center facility location problem

Abstract

We propose a two-stage robust model for reliable facility location when some facilities can be disrupted, for instance by a natural disaster. A reliable network is designed in a "proactive" planning phase, and when a facility is disrupted, its original clients can be reallocated to another available facility in a "reactive" phase. When demand and cost are uncertain, the initial design is also robust against the realizations (scenarios) of these parameters, which will only be revealed post-disruption. Based on the p-center location model, which attempts to optimize the worst-case performance of the network, our model is concerned with the reliability for every client. Three solution methods have been implemented and tested to solve the model, namely, a linear reformulation, a Benders dual cutting plane method, and a column-and-constraint generation method. We present an extensive numerical study to compare the performance of these methods. We find that, depending on the size of the instance (as given by the number of client sites and scenarios), either the Benders dual cutting plane method or column-and-constraint generation performs best. The effectiveness of our model is also examined in comparison with alternative facility location models.

Peer Review #2 of "Development of a coded suite of models to explore relevant problems in logistics (v0.1)"

“…• Problem Modeling: within this context the following extensions can be mentioned: k- Demands (Alizadeh M et al, 2015), p-Center FLP with Disruption (Du B et al, 2020), and MFLP Models for Waste Management (Adeleke OJ and Olukanni DO, 2020).…”

Wildfire burn scar encapsulation

“…The problem of subsetting a subdomain around a given location or set of points, appears to be similar to several canonical problems treated in the realm of optimization. Among the relevant applications we found the topics of set covering problems [1], shape and object packing problems (both regular and irregular) [2,7,15,19,20,27], location problems [8,16,21,28] and districting problems [10,17,29] to relate very closely to the general aspects of our specific domain subsetting needs. Even though a wide variety of literature was found within the last 7 years concerning the aforementioned applications, in this section we cover only the most relevant papers that explore diverse methods for solving problems directly comparable or applicable to our domain subsetting problem.…”

A MILP facility location model with distance value adjustments for demand fulfillment using Google Maps

“…However, the facility location is required to be at least a given distance from demand points because it is "obnoxious" to them. Another example is the study of Du, Zhou, & Leus (2020), where a two-stage robust model is designed based on the p-center location model for reliable facility location when some facilities can be disrupted. Thus, a reliable network is constructed in a "proactive" planning phase, and when a facility is disrupted, its original clients can be reallocated to another available facility in a "reactive" phase.…”