A comparison of multi-objective spatial dispersion models for managing critical assets in urban areas A comparison of multi-objective spatial dispersion models for managing critical assets in urban areas Advisor : Professor Frank Y. S. Lin Presented by: Tuan-Chun Chen Presentation date: May 29, 2012

Outline Introduction Background on critical asset vulnerability and protection Multi-objective spatial modeling for siting critical assets Methods Multi-objective models Study area and data Computational Results Discussion and Conclusions

Outline Introduction Background on critical asset vulnerability and protection Multi-objective spatial modeling for siting critical assets Methods Multi-objective models Study area and data Computational Results Discussion and Conclusions

Introduction Major disasters have prompted concern about homeland security. Prominent issue  How to properly manage critical assets? ◦ Critical assets are the key infrastructure components crucial for the continuity of supplies, services, and communications. ◦ The need for developing strategies for effectively managing critical assets and their location. Especially in the case of possible human sabotage.

Introduction Past researches : ◦ Methods for identifying critical infrastructure vulnerabilities and fortifying infrastructure networks. ◦ Models to minimize loss of both supply facilities and population demands in the context of natural disasters. ◦ Resilience-based research such as disaster relief management. ( objectives commonly involve locating and allocating emergency supplies for critical of vulnerable demands)

Introduction This paper focus on protect critical assets by dispersing them from each other. ◦ The p-dispersion model locates p critical facilities to maximize the minimum distance separating and pair of vulnerability. ◦ Clustering of like facilities increases vulnerability to system failure.  Dispersing facilities protects them by lessening the chance that a single attack or disaster will disable two neighboring facilities simultaneously. Problems !?

Introduction Planners and managers are unlikely to use the p- dispersion model as the sole criteria fro planning a network for critical assets. ◦ Deals only with distances between the facilities themselves. p-dispersion has been proposed as a secondary objective in a multi-objective model. ◦ But it lacks a systematic exploration of the trade-offs between dispersion and conflicting objectives (coverage, service efficiency, equity…etc)

Introduction The p-dispersion model is well-known to be computationally difficult to solve for medium and large networks.  It is important to understand how fast multi-objective models solve when the p-dispersion model is combined with other objectives.

Introduction In this paper, Multi-objective spatial dispersion models are developed and tested  Explore and compare the spatial trade-offs and other relevant objectives. Integrate the p-dispersion problem with ： ◦ the maximal covering problem ◦ the p-median problem ◦ the p-center problem ◦ a variant of the p-maxian problem

Introduction Goal ： ◦ These models have potential to aid in the management and siting of critical assets. ◦ Comparing different multi-objective models’ resulting trade-off curves and computational efficiencies may help decision-makers using these models.

Outline Introduction Background on critical asset vulnerability and protection Multi-objective spatial modeling for siting critical assets Methods Multi-objective models Study area and data Computational Results Discussion and Conclusions

Background on critical asset vulnerability and protection Critical infrastructure vulnerability analysis is not limited to connectivity of linkages. Indeed, Some of the most important components are nodes. Locational properties of nodes are important aspects of vulnerability analysis. ◦ An asset’s vulnerability is partly a function of its possible exposure to harm.

Background on critical asset vulnerability and protection Many researchers have developed methods for protecting critical infrastructures, including allocating resources to critical assets. There are two schools of thoughts in allocating resources to critical assets. ◦ Allocating fortification resources to protect critical assets against attack. ◦ Allocating emergency response units in support of critical assets resilience.

Background on critical asset vulnerability and protection The vast majority of studies developing formal mathematical strategies for critical infrastructure protection ignore asset dispersion as a potential strategy for the protection of critical assets. Yet, many researchers have identified dispersion to be an important aspect of increasing the security of critical assets. ◦ Geographical concentration ◦ Dense urban are more vulnerable to terrorist attacks.

Background on critical asset vulnerability and protection Geographical dispersion has been suggested as a strategy toward more resilient infrastructures. But as a formal modeling strategy for protecting critical assets has not been afforded the attention it deserves.

Outline Introduction Background on critical asset vulnerability and protection Multi-objective spatial modeling for siting critical assets Methods Multi-objective models Study area and data Computational Results Discussion and Conclusions

Multi-objective problems simultaneously optimize a set of objectives and provide a set of alternative solutions. The most direct way of solving multi-objective problems is by using the weighting method. This allow for multiple objectives to be combined into a single objective. The result of this problem is a set of Pareto-optimal solutions that form a Pareto-optimal trade-off curve. Multi-objective spatial modeling for siting critical assets

Multi-objective models have been developed for siting facilities surrounding populations. ◦ Risk sharing model (Ratick and White 1988) ◦ Hybrid location model (Church, Gerrard, and Tsai 1998) ◦ Spatial optimization model (Maliszewski and Horner 2010) However, their model ignores inter-facility dispersion as an objective. Multi-objective spatial modeling for siting critical assets

A fundamental spatial issue with managing critical assets  Concentration of resources in urban areas benefits society through agglomeration economies while simultaneously increasing the vulnerability of those resources due to over- concentration. Thus, maximizing accessibility has been operationalized with : ◦ the p-median model ◦ the set-covering model ◦ the max covering model ◦ the p-center problem Multi-objective spatial modeling for siting critical assets

the p-median model  minimizing weighted distance from nodes to their closest facilities. the set-covering model  covering model for covering all nodes within a specified distance standard with the minimum number of facilities. Multi-objective spatial modeling for siting critical assets

the max covering model  maximizing demand coverage within a given distance by a specified number of facilities. the p-center problem  minimizing the maximum distance from any population node to its closest facility. Multi-objective spatial modeling for siting critical assets

Spacing of facilities can be accomplished in two general forms : 1.Minimum closeness can be incorporated as a pairwise constraint that requires the distance between any two facilities to be greater or equal to some user-specified critical distance.  Pros : do not alter the formulation of the objective function.  Cons: the distances between facilities are not determined through a model’s output, but by user-specified distance. Multi-objective spatial modeling for siting critical assets

Spacing of facilities can be accomplished in two general forms : 2.Modeled as its own objective where by there minimum inter- facility distance between any two facilities is maximized. This type of objective can be formulated in discrete network space as the p-dispersion problem.

Despite many additional works in the facility dispersion literature, only a few published works have considered the p-dispersion problem with respect to accessibility objectives or other relevant objectives for siting critical assets Thus, analyzing dispersion with other objectives relevant for placing critical assets would be useful. Multi-objective spatial modeling for siting critical assets

Outline Introduction Background on critical asset vulnerability and protection Multi-objective spatial modeling for siting critical assets Methods Multi-objective models Study area and data Computational Results Discussion and Conclusions

Methods This Research employs the p-dispersion model, which maximizes the distances between facilities, in a multi- objective model in combination with several desirable- facility objectives. The p-dispersion problem formulation : (1)

Methods (2) (3) (4)

Methods Compare the trade-offs and computational efficiencies of four different bi-objective models. ◦ the p-median model ◦ the p-center problem ◦ the max covering model ◦ the p-maxian problem

Methods The p-median problem : (5) (6) (7) (8)

Methods The max covering problem : (9) (10) (11)

Methods The p-center problem : (12) (13) Plus constraint (2), (4), (6)~(8)

Methods The p-maxian problem : (14) Subject to constraint (2), (4) vjvj Number of potential targets

Outline Introduction Background on critical asset vulnerability and protection Multi-objective spatial modeling for siting critical assets Methods Multi-objective models Study area and data Computational Results Discussion and Conclusions

Multi-objective models Each of the multi-objective models explored are constructed using the weighting method of multi- objective programming. The p-median and the p-dispersion Subject to constraint (2), (4), (6)~(8) (15)

Multi-objective models The max covering problem and the p-dispersion : Subject to constraint (2), (4), (10)~(11) (16)

Multi-objective models The p-center problem and the p-dispersion : Subject to constraint (2), (4), (6)~(8), and (13) (17)

Multi-objective models A variant of the p-maxian problem and the p-dispersion : Subject to constraint (2), (4) (17)

Outline Introduction Background on critical asset vulnerability and protection Multi-objective spatial modeling for siting critical assets Methods Multi-objective models Study area and data Computational Results Discussion and Conclusions

Study area and data The study area for this research is the city of Orlando Florida. The data set consists of a network of 268 nodes representing census tract centroids. (taken from 2000 Census)

filtered from InfoUSA 2007 (using Standard industrial classification (SIC) code) Number of occupants > 25 Dollar assets and income > $1million square footage > 10,000

Study area and data Measure the separation between demands and potential facility sites by : ◦ Network distances ◦ Euclidean distances

Outline Introduction Background on critical asset vulnerability and protection Multi-objective spatial modeling for siting critical assets Methods Multi-objective models Study area and data Computational Results Discussion and Conclusions

Computational Results Parameters : Algorithm : Branch and bound  lower bound : D ≧ D LB where D from the initial or previous run is set as D LB to prune unnecessary branches. Weights (w)0.01, 0.1, 0.2~1 Coverage (p)5 (miles)

(a) p-median/p-dispersion (b) Max-cover/p-dispersion

(c) p-center/p-dispersion (d) p-maxian/p-dispersion

Outline Introduction Background on critical asset vulnerability and protection Multi-objective spatial modeling for siting critical assets Methods Multi-objective models Study area and data Computational Results Discussion and Conclusions

Multi-objective modeling can provide conspicuous trade-off gains among conflicting spatial objectives, but very time consuming (at least NP-hard problem). Single-objective models are perhaps too simplistic for actual siting situations, and computers are fast enough to solve multi-objective problems (but it can be a large in real world). Therefore, it is important for policy maker or analysts to understand more about multi-objective spatial model for critical asset location management.

Discussion and Conclusions Some multi-objective dispersion problems provide more L-shape trade-offs than others. In terms of computational performance, the p-center was the slowest. In terms of trade-off gains between dispersion and competing, the max-cover had the most linear trade-off curve. The trade-off curves for the p-median variant performed the best in terms of the trade-off curve, and also solved relatively fast.

Discussion and Conclusions This paper compared and assessed the computational efficiencies of four different multi-objective models for spatially managing critical assets. It also illustrated the potential use of several multi- multi-objective spatial models for the management of critical assets and has highlighted both the trade-offs of different conflicting goals. Although multi-objective facility location models in the context of siting critical assets are computationally intensive, they are feasible with a reasonable number of candidate facility sites.

Discussion and Conclusions There are a number of opportunities for future research : ◦ Look in more detail at ways of differentiating critical infrastructure facilities. (type of targets or supplies) ◦ Build in uncertainty regarding road network availability in the event of a disaster.

Thanks for your attention !!!