The budget constrained r-interdiction median problem with capacity expansion

Deniz Aksen (), Nuray Piyade () and Necati Aras ()

Central European Journal of Operations Research, 2010, vol. 18, issue 3, 269-291

Abstract: In this article, we elaborate on a budget constrained extension of the r-interdiction median problem with fortification (RIMF). The objective in the RIMF is to find the optimal allocation of protection resources to a given service system consisting of p facilities so that the disruptive effects of r possible attacks to the system are minimized. The defender of the system needs to fortify q facilities of the present system to offset the worst-case loss of r non-fortified facilities due to an interdiction in which the attacker’s objective is to cause the maximum possible disruption in the service level of the system. The defender-attacker relationship fits a bilevel integer programming (BIP) formulation where the defender and attacker take on the respective roles of the leader and the follower. We adopt this BIP formulation and augment it with a budget constraint instead of a predetermined number of facilities to be fortified. In addition, we also assume that each facility has a flexible service capacity, which can be expanded at a unit cost to accommodate the demand of customers who were serviced by some other interdicted facility before the attack. First, we provide a discrete optimization model for this new facility protection planning scenario with a novel set of closest assignment constraints. Then, to tackle this BIP problem we use an implicit enumeration algorithm performed on a binary tree. For each node representing a different fortification scheme, the attacker’s problem is solved to optimality using Cplex 11. We report computational results obtained on a test bed of 96 randomly generated instances. The article concludes with suggestions for future research. Copyright Springer-Verlag 2010

Keywords: Mixed-integer bilevel programming; Interdiction median problem with fortification; Facility protection; Binary enumeration tree (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (24)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10100-009-0110-6 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:cejnor:v:18:y:2010:i:3:p:269-291

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10100

DOI: 10.1007/s10100-009-0110-6

Access Statistics for this article

Central European Journal of Operations Research is currently edited by Ulrike Leopold-Wildburger

More articles in Central European Journal of Operations Research from Springer, Slovak Society for Operations Research, Hungarian Operational Research Society, Czech Society for Operations Research, Österr. Gesellschaft für Operations Research (ÖGOR), Slovenian Society Informatika - Section for Operational Research, Croatian Operational Research Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().