The decision rule approach to optimization under uncertainty: methodology and applications

An Y, Zeng B, Zhang Y, Zhao L (2014) Reliable $$p$$ p -median facility location problem: two-stage robust models and algorithms. Transp Res B 64:54–72

Ardestani-Jaafari A, Delage E (2016) Robust optimization of sums of piecewise linear functions with application to inventory problems. Oper Res 64(2):474–494

Atamtürk A, Zhang M (2007) Two-stage robust network flow and design under demand uncertainty. Oper Res 55(4):662–673

Ayoub J, Poss M (2016) Decomposition for adjustable robust linear optimization subject to uncertainty polytope. Comput Manag Sci 13(2):219–239

Bandi C, Trichakis N, Vayanos P (2017) Robust multiclass queuing theory for wait time estimation in resource allocation systems. Manag Sci (forthcoming)

Ben-Tal A, Goryashko A, Guslitzer E, Nemirovski A (2004) Adjustable robust solutions of uncertain linear programs. Math Program 99(2):351–376

Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust optimization. Princeton University Press, Princeton

Bertsekas DP (2001) Dynamic programming and optimal control. Athena Scientific, Belmont

Bertsimas D, Caramanis C (2010) Finite adaptibility in multistage linear optimization. IEEE Trans Automat Contr 55(12):2751–2766

Bertsimas D, Georghiou A (2015) Design of near optimal decision rules in multistage adaptive mixed-integer optimization. Oper Res 63(3):610–627

Bertsimas D, Georghiou A (2018) Binary decision rules for multistage adaptive mixed-integer optimization. Math Program 167(2):395–433

Bertsimas D, Goyal V (2010) On the power of robust solutions in two-stage stochastic and adaptive optimization problems. Math Oper Res 35(2):284–305

Bertsimas D, Goyal V (2012) On the power and limitations of affine policies in two-stage adaptive optimization. Math Program 134(2):491–531

Bertsimas D, de Ruiter FJCT (2016) Duality in two-stage adaptive linear optimization: faster computation and stronger bounds. INFORMS J Comput 28(3):500–511

Bertsimas D, Iancu DA, Parrilo PA (2010) Optimality of affine policies in multi-stage robust optimization. Math Oper Res 35(2):363–394

Bertsimas D, Brown DB, Caramanis C (2011) Theory and applications of robust optimization. SIAM Rev 53(3):464–501

Bertsimas D, Goyal V, Sun XA (2011) A geometric characterization of the power of finite adaptability in multistage stochastic and adaptive optimization. Math Oper Res 36(1):24–54

Bertsimas D, Iancu DA, Parrilo PA (2011) A hierarchy of near-optimal policies for multistage adaptive optimization. IEEE Trans Automat Contr 56(12):2809–2824

Bertsimas D, Thiele A (2006) Robust and data-driven optimization: modern decision making under uncertainty. In: INFORMS TutoRials in operations research: models, methods, and applications for innovative decision making, pp 95–122

Bertsimas D, Vayanos P (2017) Data-driven learning in dynamic pricing using adaptive optimization. Optimization Online

Birge JR, Louveaux F (1997) Introduction to stochastic programming. Springer, New York

Campi MC, Garatti S (2011) A sampling-and-discarding approach to chance-constrained optimization: feasibility and optimality. J Optim Theory Appl 148(2):257–280

Charnes A, Cooper WW (1959) Chance-constrained programming. Manag Sci 6(1):73–79

Charnes A, Cooper WW, Symonds GH (1958) Cost horizons and certainty equivalents: an approach to stochastic programming of heating oil. Manag Sci 4(3):235–263

Chen X, Zhang Y (2009) Uncertain linear programs: extended affinely adjustable robust counterparts. Oper Res 57(6):1469–1482

Chen P, Papageorgiou LG, Pinto JM (2008) Medium-term planning of single-stage single-unit multiproduct plants using a hybrid discrete/continuous-time MILP model. Ind Eng Chem Res 47(6):1925–1934

Chen X, Sim M, Sun P, Zhang J (2008) A linear decision-based approximation approach to stochastic programming. Oper Res 56(2):344–357

Chvátal V (1983) Linear programming. WH Freeman, New York

Daskin MS, Snyder LV, Berger RT (2005) Logistics systems: design and optimization. In: Langevin A, Riopel D (eds) Facility location in supply chain design. Springer, New York, pp 39–65

Delage E, Iancu DA (2015) Robust multistage decision making. In: The operations research revolution. INFORMS TutORials in operations research: models, methods, and applications for innovative decision making, pp 20–46

Dupačová J, Consigli G, Wallace S (2000) Scenarios for multistage stochastic programs. Annal Oper Res 100(1):25–53

Eisner M, Olsen P (1975) Duality for stochastic programming interpreted as L.P. in $${L}_p$$ L p -space. SIAM J Appl Math 28(4):779–792

Floudas CA, Lin X (2005) Mixed integer linear programming in process scheduling: modeling, algorithms, and applications. Annal Oper Res 139(1):131–162

Gabrel V, Murat C, Thiele A (2014) Recent advances in robust optimization: an overview. Eur J Oper Res 235(3):471–483

Garstka SJ, Wets RJB (1974) On decision rules in stochastic programming. Math Program 7(1):117–143

Georghiou A, Wiesemann W, Kuhn D (2015) Generalized decision rule approximations for stochastic programming via liftings. Math Program 152(1):301–338

Georghiou A, Tsoukalas A, Wiesemann W (2017) A primal-dual lifting scheme for two-stage robust optimization. Optimization Online

Georghiou A, Tsoukalas A, Wiesemann W (2018) Robust dual dynamic programming. Oper Res (forthcoming)

Gilboa I, Schmeidler D (1989) Maxmin expected utility with non-unique prior. J Math Econ 18(2):141–153

Goh J, Sim M (2010) Distributionally robust optimization and its tractable approximations. Oper Res 58(4):902–917

Gorissen BL, Yanğkoğlu İ, den Hertog D (2015) A practical guide to robust optimization. Omega 53:124–137

Gounaris CE, Wiesemann W, Floudas CA (2013) The robust capacitated vehicle routing problem under demand uncertainty. Oper Res 61(3):677–683

Guslitser E (2002) Uncertainty-immunized solutions in linear programming. Master’s thesis, Technion

Hadjiyiannis MJ, Goulart PJ, Kuhn DA (2011) scenario approach for estimating the suboptimality of linear decision rules in two-stage robust optimization. In: Proceedings of the 50th IEEE conference on decision and control and european control conference, pp 7386–7391

Hadjiyiannis MJ, Goulart PJ, Kuhn D (2011) An efficient method to estimate the suboptimality of affine controllers. IEEE Trans Automat Contr 56(12):2841–2853

Hanasusanto GA, Kuhn D (2018) Conic programming reformulations of two-stage distributionally robust linear programs over Wasserstein balls. Oper Res 66(3):849–869

Hanasusanto GA, Kuhn D, Wiesemann W (2015) $$K$$ K -adaptability in two-stage robust binary programming. Oper Res 63(4):877–891

Hochreiter R, Pflug GC (2007) Financial scenario generation for stochastic multi-stage decision processes as facility location problems. Annal Oper Res 152(1):257–272

IBM ILOG CPLEX Homepage (2015). https://www.ibm.com/analytics/cplex-optimizer

Kall P, Wallace S (1994) Stochastic programming. Wiley, New York

Kong Q, Li S, Liu N, Teo C-P, Yan Z (2017) Robust multi-period vehicle routing under customer order uncertainty. http://www.columbia.edu/~nl2320/doc/Noshow-MS-1030c.pdf

Kuhn D, Wiesemann W, Georghiou A (2011) Primal and dual linear decision rules in stochastic and robust optimization. Math Program 130(1):177–209

Kuhn D, Parpas P, Rustem B (2008) Stochastic optimization of investment planning problems in the electric power industry. In: Georgiadis M, Kikkinides E, Pistikopoulos E (eds) Process systems engineering: volume 5: energy systems engineering, Wiley-VCH, ch. 4, pp 215–230

Lappas NH, Gounaris CE (2016) Multi-stage adjustable robust optimization for process scheduling under uncertainty. AIChE J 62(5):1646–1667

Liebchen C, Lübbecke M, Möhring RH, Stiller S (2009) The concept of recoverable robustness, linear programming recovery, and railway applications. In: Ahuja RK, Möhring RH, Zaroliagis CD (eds) Robust and online large-scale optimization: models and techniques for transportation systems. Springer, New York, pp 1–27

Liu S, Pinto JM, Papageorgiou LG (2008) A TSP-based MILP model for medium-term planning of single-stage continuous multiproduct plants. Ind Eng Chem Res 47(20):7733–7743

Lorca A, Sun XA (2015) Adaptive robust optimization with dynamic uncertainty sets for multi-period economic dispatch under significant wind. IEEE Trans Power Syst 30(4):1702–1713

Lorca A, Sun XA (2017) Multistage robust unit commitment with dynamic uncertainty sets and energy storage. IEEE Trans Power Syst 32(3):1678–1688

Meixell MJ, Gargeya VB (2005) Global supply chain design: a literature review and critique. Transp Res E 41(6):531–550

Melo M, Nickel S, da Gama FS (2009) Facility location and supply chain management: a review. Eur J Oper Res 196(2):401–412

Min H, Zhou G (2002) Supply chain modeling: past, present and future. Comput Ind Eng 43(1–2):231–249

Nemirovski A, Shapiro A (2007) Convex approximations of chance constrained programs. SIAM J Optim 17(4):969–996

Pereira MVF, Pinto LMVG (1991) Multi-stage stochastic optimization applied to energy planning. Math Program 52(1):359–375

Pflug GC (2000) Some remarks on the value-at-risk and the conditional value-at-risk. Probabilistic constrained optimization. Springer, New York, pp 272–281

Pflug GC (2001) Scenario tree generation for multiperiod financial optimization by optimal discretization. Math Program 89(2):251–271

Pflug GC, Pichler A (2014) Multistage stochastic optimization. Springer, New York

Pflug GC, Römisch W (2007) Modeling, measuring and managing risk. World Scientific, Singapore

Rockafellar R, Uryasev S (2000) Optimization of conditional value-at-risk. J Risk 2:21–42

Ruiz C, Conejo AJ (2015) Robust transmission expansion planning. Eur J Oper Res 242(2):390–401

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(1):96–115

Shapiro A (2011) Analysis of stochastic dual dynamic programming method. Eur J Oper Res 209(1):63–72

Shapiro A, Dentcheva D, Ruszczyński A (2009) Lectures on stochastic programming: modeling and theory. SIAM

Simchi-Levi D, Wang H, Wei Y (2018) Constraint generation for two-stage robust network flow problem

Subramanyam A, Gounaris C, Wiesemann W (2017a) $$K$$ K -adaptability in two-stage mixed-integer robust optimization. Optimization Online

Subramanyam A, Mufalli F, Pinto JM, Gounaris CE (2017b) Robust multi-period vehicle routing under customer order uncertainty. Optimization Online

Tsiakis P, Shah N, Pantelides CC (2001) Design of multi-echelon supply chain networks under demand uncertainty. Ind Eng Chem Res 40(16):3585–3604

van der Vlerk MH (1996–2007) Stochastic programming bibliography. http://www.eco.rug.nl/mally/spbib.html

Vayanos P, Kuhn D, Rustem B (2012) A constraint sampling approach for multi-stage robust optimization. Automatica 48(3):459–471

Vayanos P, Kuhn D, Rustem B (2011) Decision rules for information discovery in multi-stage stochastic programming. In: Proceedings of the 50th IEEE conference on decision and control and european control conference, pp 7368–7373

Verderame PM, Elia JA, Li J, Floudas CA (2010) Planning and scheduling under uncertainty: a review across multiple sectors. Ind Eng Chem Res 49(9):3993–4017

Warrington J, Goulart P, Mariéthoz S, Morari M (2013) Policy-based reserves for power systems. IEEE Trans Power Syst 28(4):4427–4437

Xu G, Burer S (2018) A copositive approach for two-stage adjustable robust optimization with uncertain right-hand sides. Comput Optim Appl 70(1):33–59

Yanıkoğlu İ, Gorissen BL, den Hertog D (2017) Adjustable robust optimization–a survey and tutorial ResearchGate

Zeng B, Zhao L (2013) Solving two-stage robust optimization problems using a column-and-constraint generation method. Oper Res Lett 41(5):457–561