Chance-Constrained Programming Models and Approximations for General Stochastic Bottleneck Spanning Tree Problems

References

• Ahuja RK, Magnanti TL, Orlin JB (1993) Network Flows: Theory, Algorithms, and Applications (Prentice Hall, Upper Saddle River, NJ).Google Scholar
• Bapat RB, Beg MI (1989) Order statistics for nonidentically distributed variables and permanents. The Indian J. Statist.: Ser. A 51:79–93.Google Scholar
• Beale EML, Forrest JJH (1976) Global optimization using special ordered sets. Math. Programming 10:52–69.Crossref, Google Scholar
• Beale EML, Tomlin JA (1970) Special facilities in a general mathematical programming system for non-convex problems using ordered sets of variables. Proc. Fifth IFORS Conf., Vol. 69 (Tavistock, London & Wiley, New York), 447–454.Google Scholar
• Birge JR, Louveaux FV (2011) Introduction to Stochastic Programming (Springer-Verlag, New York).Crossref, Google Scholar
• Cheng X, Narahari B, Simha R, Cheng MX, Liu D (2003) Strong minimum energy topology in wireless sensor networks: NP-completeness and heuristics. IEEE Trans. Mobile Comput. 2:248–256.Crossref, Google Scholar
• Dentcheva D, Prékopa A, Ruszczyński A (2002) Bounds for probabilistic integer programming problems. Discrete Appl. Math. 124:55–65.Crossref, Google Scholar
• Forrest JJH, Hirst JPH, Tomlin JA (1974) Practical solution of large mixed integer programming problems with UMPIRE. Management Sci. 20:736–773.Link, Google Scholar
• Garey MR, Johnson DS (1979) Computers and Intractability: A Guide to the Theory of NP-Completeness (W.H. Freeman and Co., New York).Google Scholar
• Ishii H, Nishida T (1983) Stochastic bottleneck spanning tree problem. Networks 13:443–449.Crossref, Google Scholar
• Ishii H, Shiode S (1995) Chance constrained bottleneck spanning tree problem. Ann. Oper. Res. 56:177–187.Crossref, Google Scholar
• Kleywegt AJ, Shapiro A, Homem-de-Mello T (2002) The sample average approximation method for stochastic discrete optimization. SIAM J. Optim. 12:479–502.Crossref, Google Scholar
• Kruskal JB (1956) On the shortest spanning subtree of a graph and the traveling salesman problem. Proc. Amer. Math. Soc. 7:48–50.Crossref, Google Scholar
• Luedtke J, Ahmed S (2008) A sample approximation approach for optimization with probabilistic constraints. SIAM J. Optim. 19:674–699.Crossref, Google Scholar
• Mak WK, Morton DP, Wood RK (1999) Monte Carlo bounding techniques for determining solution quality in stochastic programs. Oper. Res. Lett. 24:47–56.Crossref, Google Scholar
• McCormick GP (1976) Computability of global solutions to factorable nonconvex programs: Part I—Convex underestimating problems. Math. Programming 10:147–175.Crossref, Google Scholar
• Norkin VI, Pflug GC, Ruszczyński A (1998) A branch and bound method for stochastic global optimization. Math. Programming 83:425–450.Crossref, Google Scholar
• Prim RC (1957) Shortest connection networks and some generalizations. Bell System Tech. J. 36:1389–1401.Crossref, Google Scholar
• Shapiro A, Homem-de-Mello T (2000) On the rate of convergence of optimal solutions of Monte Carlo approximations of stochastic programs. SIAM J. Optim. 11:70–86.Crossref, Google Scholar
• Shapiro A, Dentcheva D, Ruszczyński A (2009) Lectures on Stochastic Programming: Modeling and Theory, Vol. 9 (SIAM, Philadelphia).Crossref, Google Scholar
• Sridhar S, Linderoth J, Luedtke J (2014) Models and solution techniques for production planning problems with increasing byproducts. J. Global Optim. 59(2-3):597–631.Crossref, Google Scholar
• Tomlin JA (1988) Special ordered sets and an application to gas supply operations planning. Math. Programming 42:69–84.Crossref, Google Scholar