Optimal Allocation of Risk-Reduction Resources in Event Trees

• Published in: Management science Vol. 54; no. 7; pp. 1313 - 1321
• Main Authors: Sherali, Hanif D, Desai, Jitamitra, Glickman, Theodore S
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01-07-2008; Institute for Operations Research and the Management Sciences
• Series: Management Science
• Subjects: Algorithms; Analysis; Applied sciences; Branch & bound algorithms; branch-and-bound; Budgetary resources; Business management; Business studies; Conditional probabilities; Decision theory. Utility theory; Decision trees; event trees; Exact sciences and technology; factorable programming; Failure analysis; Fault trees; global optimization; Investment analysis; Investment strategies; Linear programming; Management science; Mathematical programming; Nuclear energy; Objective functions; Operational research and scientific management; Operational research. Management science; Optimal solutions; Programming; Resource allocation; Risk management; risk reduction; Risk theory. Actuarial science; Strategic planning; Strategic planning (Business); Studies; system safety; risk reduction; Tree(graph); Strategic planning; Modeling; factorable programming; Optimization; Prevention; event trees; Optimal allocation; Quantitative analysis; Script; system safety; Branch and bound method; Decision making; Global optimum; Linear programming; Risk analysis; global optimization; Safety systems; branch-and-bound; Objective function; Reliability; Risk management; Probability measure; Non convex analysis
• ISSN: 0025-1909; 1526-5501
• DOI: 10.1287/mnsc.1070.0844

In this paper, we present a novel quantitative analysis for the strategic planning decision problem of allocating certain available prevention and protection resources to, respectively, reduce the failure probabilities of system safety measures and the total expected loss from a sequence of events. Using an event tree optimization approach, the resulting risk-reduction scenario problem is modeled and then reformulated as a specially structured nonconvex factorable program. We derive a tight linear programming relaxation along with related theoretical insights that serve to lay the foundation for designing a tailored branch-and-bound algorithm that is proven to converge to a global optimum. Computational experience is reported for a hypothetical case study, as well as for several realistic simulated test cases, based on different parameter settings. The results on the simulated test cases demonstrate that the proposed approach dominates the commercial software BARON v7.5 when the latter is applied to solve the original model by more robustly yielding provable optimal solutions that are at an average of 16.6% better in terms of objective function value; and it performs competitively when both models are used to solve the reformulated problem, particularly for larger test instances.