Adjustable Robust Optimization Reformulations of Two-Stage Worst-Case Regret Minimization Problems
References
- (2009) Min-max and min-max regret versions of combinatorial optimization problems: A survey. Eur. J. Oper. Res. 197(2):427–438.Crossref, Google Scholar
- (2016) Robust optimization of sums of piecewise linear functions with application to inventory problems. Oper. Res. 64(2):474–494.Link, Google Scholar
- (2020) Linearized robust counterparts of two-stage robust optimization problems with applications in operations management. INFORMS J. Comput. 33(3):1138–1161.Google Scholar
- (2008a) Min-max regret robust optimization approach on interval data uncertainty. J. Optim. Theory Appl. 137(2):297–316.Crossref, Google Scholar
- (2008b) Scenario relaxation algorithm for finite scenario-based min-max regret and min-max relative regret robust optimization. Comput. Oper. Res. 35(6):2093–2102.Crossref, Google Scholar
- (2004) Minmax regret linear resource allocation problems. Oper. Res. Lett. 32(2):174–180.Crossref, Google Scholar
- (2005) On the complexity of minmax regret linear programming. Eur. J. Oper. Res. 160(1):227–231.Crossref, Google Scholar
- (2016) Decomposition for adjustable robust linear optimization subject to uncertainty polytope. Comput. Management Sci. 13(2):219–239.Crossref, Google Scholar
- (2009) Robust Optimization (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
- (2004) Adjustable robust solutions of uncertain linear programs. Math. Programming 99(2):351–376.Crossref, Google Scholar
- (2016) Duality in two-stage adaptive linear optimization: Faster computation and stronger bounds. INFORMS J. Comput. 28(3):500–511.Link, Google Scholar
- (2020) Relative robust and adaptive optimization. INFORMS J. Comput. 32(2):408–427.Abstract, Google Scholar
- (2012) On the power and limitations of affine policies in two-stage adaptive optimization. Math. Programming 134(2):491–531.Crossref, Google Scholar
- (2004) The price of robustness. Oper. Res. 52(1):35–53.Link, Google Scholar
- (2010a) Optimality of affine policies in multistage robust optimization. Math. Oper. Res. 35(2):363–394.Link, Google Scholar
- (2011) A hierarchy of near-optimal policies for multistage adaptive optimization. IEEE Trans. Automated Control 56(12):2809–2824.Crossref, Google Scholar
- (2010b) Models for minimax stochastic linear optimization problems with risk aversion. Math. Oper. Res. 35(3):580–602.Link, Google Scholar
- (2010) A quantitative measurement of regret theory. Management Sci. 56(1):161–175.Link, Google Scholar
- (2005) Online Computation and Competitive Analysis (Cambridge University Press, Cambridge, UK).Google Scholar
- (2017) Intertemporal pricing under minimax regret. Oper. Res. 65(1):104–129.Link, Google Scholar
- (2009) Uncertain linear programs: Extended affinely adjustable robust counterparts. Oper. Res. 57(6):1469–1482.Link, Google Scholar
- (2008) A linear decision-based approximation approach to stochastic programming. Oper. Res. 56(2):344–357.Link, Google Scholar
- (2014) Robust optimization for transmission expansion planning: Minimax cost vs. minimax regret. IEEE Trans. Power Systems 29(6):3069–3077.Crossref, Google Scholar
- (2005) On the complexity of the continuous unbounded knapsack problem with uncertain coefficients. Oper. Res. Lett. 33(5):481–485.Crossref, Google Scholar
- (2015) Robust multistage decision making. Aleman DM, Thiele AC, eds. The Operations Research Revolution. INFORMS TutORials in Operations Research (INFORMS, Catonsville, MD), 20–46.Google Scholar
- (2017) JuMP: A modeling language for mathematical optimization. SIAM Rev. 59(2):295–320.Crossref, Google Scholar
- (2010) Robustness and duality in linear programming. J. Oper. Res. Soc. 61(8):1288–1296.Crossref, Google Scholar
- (2011) Robust optimization made easy with ROME. Oper. Res. 59(4):973–985.Link, Google Scholar
- (2002) Uncertainty-immunized solutions in linear programming. MS thesis, Technion, Israeli Institute of Technology, Haifa, Israel.Google Scholar
- (2011) A scenario approach for estimating the suboptimality of linear decision rules in two-stage robust optimization. Proc. 50th IEEE Conf. on Decision and Control and European Control Conf. (IEEE, Piscataway, NJ), 7386–7391.Google Scholar
- (2018) Conic programming reformulations of two-stage distributionally robust linear programs over wasserstein balls. Oper. Res. 66(3):849–869.Link, Google Scholar
- (2014) Pareto efficiency in robust optimization. Management Sci. 60(1):130–147.Link, Google Scholar
- (1995) Minimax regret solution to linear programming problems with an interval objective function. Eur. J. Oper. Res. 86(3):526–536.Crossref, Google Scholar
- (1996) Maximum regret analysis in linear programs with an interval objective function. Proc. Internat. Workshop on Soft Computing in Industry, 308–317.Google Scholar
- (1997a) An achievement rate approach to linear programming problems with an interval objective function. J. Oper. Res. Soc. 48(1):25–33.Crossref, Google Scholar
- (1997b) Minimax regret solution algorithms for linear program with convex polyhedral objective coefficients. Proc. 2nd Eur. Workshop Fuzzy Decision Anal. Neural Networks Management Planning Optim. (Dortmund, Germany), 116–125.Google Scholar
- (1994) Minimax regret in linear programming problems with an interval objective function. Tzeng GH, Wang HF, Wen UP, Yu PL, eds. Multiple Criteria Decision Making (Springer, New York), 65–74.Crossref, Google Scholar
- (2001) On computation methods for a minimax regret solution based on outer approximation and cutting hyperplanes. Internat. J. Fuzzy Systems 3(4):548–557.Google Scholar
- (1999) On computation methods of the minimax regret solution for linear programming problems with uncertain objective function coefficients. Proc. IEEE Internat. Conf. on Systems, Man, and Cybernetics, vol. 3. 979–984.Google Scholar
- (2013) Two-stage minimax regret robust unit commitment. IEEE Trans. Power Systems 28(3):2271–2282.Crossref, Google Scholar
- (2017) Affinely adjustable robust model for multiperiod production planning under uncertainty. IEEE Trans. Engrg. Management 64(4):505–514.Crossref, Google Scholar
- (1996) Robust Discrete Optimization and Its Applications (Springer, New York).Google Scholar
- (2011) Primal and dual linear decision rules in stochastic and robust optimization. Math. Programming 130(1):177–209.Crossref, Google Scholar
- (1982) Regret theory: An alternative theory of rational choice under uncertainty. Econom. J. (London) 92(368):805–824.Google Scholar
- (1998) A new mixed integer formulation for the maximum regret problem. Internat. Trans. Oper. Res. 5(5):389–403.Crossref, Google Scholar
- (1999a) A heuristic to minimax absolute regret for linear programs with interval objective function coefficients. Eur. J. Oper. Res. 117(1):157–174.Crossref, Google Scholar
- (1999b) Minimising the maximum relative regret for linear programmes with interval objective function coefficients. J. Oper. Res. Soc. 50(10):1063–1070.Crossref, Google Scholar
- (2016) On the average performance of the adjustable RO and its use as an offline tool for multi-period production planning under uncertainty. Comput. Management Sci. 13(2):1–23.Crossref, Google Scholar
- (1954) Games against nature. Thrall RM, Coombs CH, Davis RL, eds. Decision Processes (Wiley, New York), 49–59.Google Scholar
- (2009) On robust maximum flow with polyhedral uncertainty sets. Optim. Lett. 3(3):367–376.Crossref, Google Scholar
- (2014) A probabilistic model for minmax regret in combinatorial optimization. Oper. Res. 62(1):160–181.Link, Google Scholar
- (2013) Robust regret for uncertain linear programs with application to co-production models. Eur. J. Oper. Res. 227(3):483–493.Crossref, Google Scholar
- (2018) Adaptive robust optimization with minimax regret criterion: Multiobjective optimization framework and computational algorithm for planning and scheduling under uncertainty. Comput. Chemical Engrg. 108:425–447.Crossref, Google Scholar
- (2008) Regret in the newsvendor model with partial information. Oper. Res. 56(1):188–203.Link, Google Scholar
- (1988) Lot-size models with backlogging: Strong reformulations and cutting planes. Math. Programming 40(1-3):317–335.Crossref, Google Scholar
- (1951) The theory of statistical decision. J. Amer. Statist. Assoc. 46(253):55–67.Crossref, Google Scholar
- (2019) Designing response supply chain against bioattacks. Oper. Res. 67(5):1246–1268.Link, Google Scholar
- (2011) Statistical decisions under ambiguity. Theory Decision 70(2):129–148.Crossref, Google Scholar
- (2000) Robust multi-item newsboy models with a budget constraint. Internat. J. Production Econom. 66(3):213–226.Crossref, Google Scholar
- (2018) A copositive approach for two-stage adjustable robust optimization with uncertain right-hand sides. Comput. Optim. Appl. 70(1):33–59.Crossref, Google Scholar
- (2019) A survey of adjustable robust optimization. Eur. J. Oper. Res. 277(3):799–813.Google Scholar
- (2006) Expected value of distribution information for the newsvendor problem. Oper. Res. 54(6):1128–1136.Link, Google Scholar
- (2013) Solving two-stage robust optimization problems using a column-and-constraint generation method. Oper. Res. Lett. 41(5):457–461.Crossref, Google Scholar
- (2011) Two-stage minimax regret robust uncapacitated lot-sizing problems with demand uncertainty. Oper. Res. Lett. 39(5):342–345.Crossref, Google Scholar
- (2018) Adjustable robust optimization via Fourier-motzkin elimination. Oper. Res. 66(4):1086–1100.Link, Google Scholar
- (2013) Newsvendor optimization with limited distribution information. Optim. Methods Software 28(3):640–667.Crossref, Google Scholar

