Sequential Bounding Methods for Two-Stage Stochastic Programs

References

• Al-Khayyal FA, Falk JE (1983) Jointly constrained biconvex programming. Math. Oper. Res. 8:273–286.Link, Google Scholar
• Bassok Y, Anupindi R, Akella R (1999) Single-period multiproduct inventory models with substitution. Oper. Res. 47:632–642.Link, Google Scholar
• Batun S, Denton BT, Huschka TR, Schaefer AJ (2011) Operating room pooling and parallel surgery processing under uncertainty. INFORMS J. Comput. 23:220–237.Link, Google Scholar
• Bertsimas D, Tsitsiklis JN (1997) Introduction to Linear Optimization (Athena Scientific Belmont, Belmont, MA).Google Scholar
• Bezanson J, Karpinski S, Shah VB, Edelman A (2012) Julia: A fast dynamic language for technical computing. Accessed March 24, 2016, http://arxiv.org/pdf/1209.5145v1.pdf.Google Scholar
• Birge JR (1983) Aggregation bounds in stochastic production problems. Technical Report 83-13, Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI.Google Scholar
• Birge JR (1985) Aggregation bounds in stochastic linear programming. Math. Programming 31:25–41.Crossref, Google Scholar
• Birge JR, Louveaux F (1997) Introduction to Stochastic Programming (Springer, New York).Google Scholar
• Birge JR, Wets RJ-B (1986) Designing approximation schemes for stochastic optimization problems. Math. Programming Study 27:54–102.Crossref, Google Scholar
• Chan WKV, Schruben L (2008) Optimization models of discrete-event system dynamics. Oper. Res. 56:1218–1237.Link, Google Scholar
• Dantzig G, Glynn P (1990) Parallel processors for planning under uncertainty. Ann. Oper. Res. 22:1–21.Crossref, Google Scholar
• Dattorro J (2005) Convex Optimization and Euclidean Distance Geometry (Meboo Publishing, Palo Alto, CA).Google Scholar
• Denton B, Gupta D (2003) A sequential bounding approach for optimal appointment scheduling. IIE Trans. 35:1003–1016.Crossref, Google Scholar
• Erdogan SA, Gose AH, Denton BT (2015) Online appointment sequencing and scheduling. IIE Trans. 47:1267–1286.Crossref, Google Scholar
• Forrest J, de la Nuez D, Lougee-Heimer R (2004) CLP user guide. Accessed March 24, 2016, http://www.coin-or.org/Clp/userguide/clpuserguide.html.Google Scholar
• Glynn PW, Infanger G (2013) Simulation-based confidence bounds for two-stage stochastic programs. Math. Programming 138:15–42.Crossref, Google Scholar
• Huang CC, Ziemba WT, Ben-Tal A (1977) Bounds on the expectation of a convex function of a random variable: With applications to stochastic programming. Oper. Res. 25:315–325.Link, 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
• Korf LA (2004) Stochastic programming duality: ℒ∞ multipliers for unbounded constraints with an application to mathematical finance. Math. Programming 99:241–259.Crossref, Google Scholar
• Lubin M, Dunning I (2015) Computing in operations research using Julia. INFORMS J. Comput. 27:238–248.Link, Google Scholar
• Madansky A (1959) Bounds on the expectation of a convex function of a multivariate random variable. Annals Math. Statistics 30:743–746.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
• Morton DP, Popova E (2004) A Bayesian stochastic programming approach to an employee scheduling problem. IIE Trans. 36:155–167.Crossref, Google Scholar
• Morton DP, Wood RK (1999) Restricted-recourse bounds for stochastic linear programming. Oper. Res. 47:943–956.Link, Google Scholar
• Nahmias S (2001) Production and Operations Analysis, 4th ed. (McGraw-Hill, Boston).Google Scholar
• Pennanen T (2009) Epi-convergent discretizations of multistage stochastic programs via integration quadratures. Math. Programming 116:461–479.Crossref, Google Scholar
• Rao US, Swaminathan JM, Zhang J (2004) Multi-product inventory planning with downward substitution, stochastic demand and setup costs. IIE Trans. 36:59–71.Crossref, Google Scholar
• Rockafellar RT, Wets RJ-B (1976a) Stochastic convex programming: Basic duality. Pacific J. Math. 62:173–195.Crossref, Google Scholar
• Rockafellar RT, Wets RJ-B (1976b) Stochastic convex programming: Relatively complete recourse and induced feasibility. SIAM J. Control Optim. 14:507–522.Crossref, Google Scholar
• Santoso T, Ahmed S, Goetschalckx M, Shapiro A (2005) A stochastic programming approach for supply chain network design under uncertainty. Eur. J. Oper. Res. 167:96–115.Crossref, Google Scholar
• Shapiro A, Homem de Mello T (1998) A simulation-based approach to two-stage stochastic programming with recourse. Math. Programming 81:301–325.Crossref, Google Scholar
• Sherali HD, Adams WP (1998) A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems, Vol. 31 (Springer, New York).Google Scholar
• Wets RJ-B (1983) Solving stochastic programs with simple recourse. Stochastics: An Internat. J. Probab. Stochastic Processes 10:219–242.Google Scholar
• Wright SE (1994) Primal-dual aggregation and disaggregation for stochastic linear programs. Math. Oper. Res. 19:893–908.Link, Google Scholar
• Zipkin PH (1980a) Bounds for row-aggregation in linear programming. Oper. Res. 28:903–916.Link, Google Scholar
• Zipkin PH (1980b) Bounds on the effect of aggregating variables in linear programs. Oper. Res. 28:403–418.Link, Google Scholar