A comparison of multi-objective spatial dispersion models for managing critical assets in urban areas Paul J. Maliszewski a,⇑ , Michael J. Kuby a , Mark W. Horner b a School of Geographical Sciences and Urban Planning, Arizona State University, AZ 85287, USA b Department of Geography, Florida State University, FL 32306, USA article info Article history: Received 21 July 2011 Received in revised form 20 December 2011 Accepted 20 December 2011 Available online 9 January 2012 Keywords: Critical infrastructure protection Dispersion Facility location abstract A diverse array of spatial optimization models dealing with protection, service, coverage, equity, and risk can potentially aid with the effective placement of critical assets. Protection of assets can be enhanced using the p-dispersion model, which locates facilities to maximize the minimum distance between any two. Dispersion, however, is rarely the only objective for a system of facilities, and the p-dispersion model is known to be difficult to solve. Therefore, this paper analyzes the trade-offs and computational times of four multi-objective models that combine the p-dispersion model with other facility location objectives relevant to siting critical assets, such as the p-median, max-cover, p-center, and p-maxian models. The multi-objective models are tested on a case study of Orlando, Florida. The dispersion/center model pro- duced the most gradual trade-off curve, while the dispersion/maxian trade-off curve had the most pro- nounced ‘‘elbow.’’ The center and median multi-objective models were far more computationally demanding than the models using max cover and p-maxian. These findings may inform decision-makers and researchers in deciding what type of multi-objective models to use for planning dispersed networks of critical assets. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Over the past decade, major disasters in the United States such as the 9/11 attacks, hurricane Katrina, and the H1N1 pandemic have prompted concern about homeland security. One of the most prom- inent issues in the homeland security community is how to prop- erly manage critical assets (Critical Infrastructure Protection Program, 2006; The White House, 2001). Critical assets are the key infrastructure components that are crucial for the continuity of supplies, services, and communications. These assets are critical because their loss would have potentially devastating effects on society (Chopra & Sodhi, 2004). Consequently, the need for develop- ing strategies for effectively managing critical assets and their loca- tions has garnered the attention of policy makers and researchers, especially in the case of possible human sabotage (Parfomak, 2007). In recent years, many researchers have explored methods for identifying critical infrastructure vulnerabilities and fortifying infrastructure networks (Akgun, Kandakoglu, & Ozok, 2010; Church, Scaparra, & Middleton, 2004; Li et al., 2009; Murray, Mat- isziw, & Grubesic, 2008; Nagurney & Qiang, 2008; Snyder, Scaparra, Daskin, & Church, 2006; Taylor, Sekhar, & D’Este, 2006). Models have been developed to minimize loss of both supply facilities and population demands in the context of natural disasters (Galin- do & Batta, 2010; Rawls & Turnquist, 2010). In resilience-based research such as disaster relief management, objectives commonly involve locating and allocating emergency supplies for critical or vulnerable demands (Horner & Downs, 2010; Sathe & Miller- Hooks, 2005; Widener & Horner, 2011). One strategy for protecting critical assets involves fortifying, or allocating retrofitting resources to vulnerable components of various infrastructures (Daskin, 2008; Qiao et al., 2007; Scaparra & Church, 2008; Snyder et al., 2006). This paper focuses on an alternative strategy, which aims to protect critical assets by dispersing them from each other (Kim & O’Kelly, 2009). Specifically, the p-dispersion model locates p critical facilities to maximize the minimum distance separating any pair of facilities (Kuby, 1987). Clustering of like facilities in- creases vulnerability to system failure (Erkut, 1990; Goodman, Kirk, & Kirk, 2007; Larson, 2005; Li, Rosenwald, Jung, & Liu, 2005; Liu, Jung, Heytd, Vittal, & Phadke, 2000; Lovins & Lovins, 1982). Therefore, dispersing facilities protects them by lessening the chance that a single attack or disaster will disable two neighboring facilities simultaneously. Planners and managers, however, are unlikely to use the p- dispersion model as the sole criteria for planning a network of crit- ical assets because it deals only with the distances between the facilities themselves, and not with distances from facilities to the 0198-9715/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compenvurbsys.2011.12.006 ⇑ Corresponding author. Address: School of Geographical Sciences and Urban Planning, Arizona State University, Coor Hall, 975 S. Myrtle Ave., Fifth Floor, P.O. Box 875302, Tempe, AZ 85287-5302, USA. Tel.: +1 850 345 1713. E-mail addresses: paul.maliszewski@asu.edu (P.J. Maliszewski), Mikekuby@ asu.edu (M.J. Kuby), mhorner@fsu.edu (M.W. Horner). Computers, Environment and Urban Systems 36 (2012) 331–341 Contents lists available at SciVerse ScienceDirect Computers, Environment and Urban Systems journal homepage: www.elsevier.com/locate/compenvurbsys