Pre-disaster investment decisions for strengthening a highway network

• Published in: Computers & operations research Vol. 37; no. 10; pp. 1708 - 1719
• Main Authors: Peeta, Srinivas, Sibel Salman, F., Gunnec, Dilek, Viswanath, Kannan
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.10.2010; Elsevier; Pergamon Press Inc
• Subjects: Applied sciences; Decision making models; Decision theory. Utility theory; Decision-dependent probability distribution; Disasters; Earthquake mitigation; Emergency preparedness; Exact sciences and technology; Failure; Financing; Flows in networks. Combinatorial problems; Ground, air and sea transportation, marine construction; Highways; Investment; Knapsack problem; Links; Mathematical analysis; Mathematical models; Mathematical programming; Networks; Operational research and scientific management; Operational research. Management science; Random link failures; Retrofitting highways; Road transportation and traffic; Roads & highways; Stochastic models; Studies; Two-stage stochastic program; Istanbul Turkey; Turkey; Earthquake mitigation; Decision-dependent probability distribution; Networks; Two-stage stochastic program; Retrofitting highways; Random link failures; Costs; Disaster; Modeling; Earthquakes; Freeway; Budget; Survival probability; Monotonic function; Probabilistic approach; Decision making; Local optimum; Highway; Rupture; Road network; Failures; Knapsack problem; Stochastic programming; Multilinear function; Objective function; Planning; Reliability; Investment
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2009.12.006

We address a pre-disaster planning problem that seeks to strengthen a highway network whose links are subject to random failures due to a disaster. Each link may be either operational or non-functional after the disaster. The link failure probabilities are assumed to be known a priori, and investment decreases the likelihood of failure. The planning problem seeks connectivity for first responders between various origin–destination (O–D) pairs and hence focuses on uncapacitated road conditions. The decision-maker's goal is to select the links to invest in under a limited budget with the objective of maximizing the post-disaster connectivity and minimizing traversal costs between the origin and destination nodes. The problem is modeled as a two-stage stochastic program in which the investment decisions in the first stage alter the survival probabilities of the corresponding links. We restructure the objective function into a monotonic non-increasing multilinear function and show that using the first order terms of this function leads to a knapsack problem whose solution is a local optimum to the original problem. Numerical experiments on real-world data related to strengthening Istanbul's urban highway system against earthquake risk illustrate the tractability of the method and provide practical insights for decision-makers.