Sampling Scenario Set Partition Dual Bounds for Multistage Stochastic Programs

Published Online:https://doi.org/10.1287/ijoc.2018.0885

References

  • Ahmed S (2010) Two-stage stochastic integer programming: A brief introduction. Cochran JJ, Cox, Jr. LA, Keskinocak P, Kharoufeh JP, Smith JC, eds. Wiley Encyclopedia of Operations Research and Management Science (Wiley, Hoboken, NJ).Google Scholar
  • Ahmed S (2013) A scenario decomposition algorithm for 0–1 stochastic programs. Oper. Res. Lett. 41(6):565–569.CrossrefGoogle Scholar
  • Ahmed S, Garcia R (2003) Dynamic capacity acquisition and assignment under uncertainty. Ann. Oper. Res. 124(1–4):267–283.CrossrefGoogle Scholar
  • Ahmed S, Garcia R, Kong N, Ntaimo L, Parija G, Qui F, Sen S (2015) SIPLIB: A stochastic integer programming test problem library. Accessed December 21, 2015, http://www.isye.gatech.edu/∼sahmed/siplib.Google Scholar
  • Aldasoro U, Escudero LF, Merino M, Pérez G (2013) An algorithmic framework for solving large-scale multistage stochastic mixed 0–1 problems with nonsymmetric scenario trees. Part II: Parallelization. Comput. Oper. Res. 40(12):2950–2960.CrossrefGoogle Scholar
  • Beier E, Venkatachalam S, Corolli L, Ntaimo L (2015) Stage-and scenario-wise Fenchel decomposition for stochastic mixed 0-1 programs with special structure. Comput. Oper. Res. 59:94–103.CrossrefGoogle Scholar
  • Birge JR (1985) Aggregation bounds in stochastic linear programming. Math. Programming 31(1):25–41.CrossrefGoogle Scholar
  • Birge JR, Louveaux F (2011) Introduction to Stochastic Programming (Springer Science & Business Media, Berlin).CrossrefGoogle Scholar
  • Bodur M, Dash S, Günlük O, Luedtke J (2016) Strengthened benders cuts for stochastic integer programs with continuous recourse. INFORMS J. Comput. 29(1):77–91.LinkGoogle Scholar
  • Carøe CC, Schultz R (1999) Dual decomposition in stochastic integer programming. Oper. Res. Lett. 24(1–2):37–45.CrossrefGoogle Scholar
  • Cheung K, Gade D, Silva-Monroy C, Ryan SM, Watson JP, Wets RJB, Woodruff DL (2015) Toward scalable stochastic unit commitment. Energy Systems 6(3):417–438.CrossrefGoogle Scholar
  • Crainic TG, Fu X, Gendreau M, Rei W, Wallace SW (2011) Progressive hedging-based metaheuristics for stochastic network design. Networks 58(2):114–124.CrossrefGoogle Scholar
  • Erdogan SA, Gose A, Denton BT (2015) On-line appointment sequencing and scheduling. IIE Trans. 47(11):1267–1286.CrossrefGoogle Scholar
  • Escudero LF, Garín MA, Unzueta A (2016) Cluster Lagrangean decomposition in multistage stochastic optimization. Comput. Oper. Res. 67:48–62.CrossrefGoogle Scholar
  • Escudero LF, Garín MA, Merino M, Pérez G (2010) On BFC-MSMIP strategies for scenario cluster partitioning, and twin node family branching selection and bounding for multistage stochastic mixed integer programming. Comput. Oper. Res. 37(4):738–753.CrossrefGoogle Scholar
  • Escudero LF, Garín MA, Merino M, Pérez G (2012) An algorithmic framework for solving large-scale multistage stochastic mixed 0–1 problems with nonsymmetric scenario trees. Comput. Oper. Res. 39(5):1133–1144.CrossrefGoogle Scholar
  • Escudero LF, Garín MA, Pérez G, Unzueta A (2013) Scenario cluster decomposition of the Lagrangian dual in two-stage stochastic mixed 0–1 optimization. Comput. Oper. Res. 40(1):362–377.CrossrefGoogle Scholar
  • Espinoza D, Moreno E (2014) A primal-dual aggregation algorithm for minimizing conditional value-at-risk in linear programs. Comput. Optim. Appl. 59(3):617–638.CrossrefGoogle Scholar
  • Guo G, Hackebeil G, Ryan SM, Watson JP, Woodruff DL (2015) Integration of progressive hedging and dual decomposition in stochastic integer programs. Oper. Res. Lett. 43(3):311–316.CrossrefGoogle Scholar
  • Holmes D (1994) A collection of stochastic programming problems. Technical Report 94-11, Department of Operations Engineering, University of Michigan, Ann Arbor.Google Scholar
  • Holmes D (2018) A (PO)rtable (S)tochastic programming (T)est (S)et (POSTS). Accessed February 10, 2018, http://users.iems.northwestern.edu/∼jrbirge/html/dholmes/post.html.Google Scholar
  • Huang K, Ahmed S (2009) The value of multistage stochastic programming in capacity planning under uncertainty. Oper. Res. 57(4):893–904.LinkGoogle Scholar
  • Kim K, Zavala VM (2018) Algorithmic innovations and software for the dual decomposition method applied to stochastic mixed-integer programsMath. Programming Comput.10(2):225–266.CrossrefGoogle Scholar
  • Klein Haneveld WK, van der Vlerk MH (1999) Stochastic integer programming: General models and algorithms. Ann. Oper. Res. 85(0):39–57.CrossrefGoogle Scholar
  • Klein Haneveld WK, Stougie L, van der Vlerk MH (2006) Simple integer recourse models: Convexity and convex approximations. Math. Programming 108(2–3):435–473.CrossrefGoogle Scholar
  • Kleywegt AJ, Shapiro A, Homem-de Mello T (2002) The sample average approximation method for stochastic discrete optimization. SIAM J. Optim. 12(2):479–502.CrossrefGoogle Scholar
  • Løkketangen A, Woodruff DL (1996) Progressive hedging and tabu search applied to mixed integer (0, 1) multistage stochastic programming. J. Heuristics 2(2):111–128.CrossrefGoogle Scholar
  • Louveaux FV (1986) Discrete stochastic location models. Ann. Oper. Res. 6(2):21–34.CrossrefGoogle Scholar
  • Lubin M, Martin K, Petra CG, Sandıkçı B (2013) On parallelizing dual decomposition in stochastic integer programming. Oper. Res. Lett. 41(3):252–258.CrossrefGoogle Scholar
  • Maggioni F, Pflug GC (2016) Bounds and approximations for multistage stochastic programs. SIAM J. Optim. 26(1):831–855.CrossrefGoogle Scholar
  • Maggioni F, Allevi E, Bertocchi M (2014) Bounds in multistage linear stochastic programming. J. Optim. Theory Appl. 163(1):200–229.CrossrefGoogle Scholar
  • Maggioni F, Allevi E, Bertocchi M (2016) Monotonic bounds in multistage mixed-integer linear stochastic programming. Comput. Management Sci. 13(3):423–457.CrossrefGoogle Scholar
  • Mak W-K, Morton DP, Wood RK (1999) Monte Carlo bounding techniques for determining solution quality in stochastic programs. Oper. Res. Lett. 24(1–2):47–56.CrossrefGoogle Scholar
  • Norkin VI, Pflug GC, Ruszczyński A (1998) A branch and bound method for stochastic global optimization. Math. Programming 83(1–3):425–450.CrossrefGoogle Scholar
  • Nowak MP, Schultz R, Westphalen M (2005) A stochastic integer programming model for incorporating day-ahead trading of electricity into hydro-thermal unit commitment. Optim. Engrg. 6(2):163–176.CrossrefGoogle Scholar
  • Ntaimo L, Sen S (2005) The million-variable “march” for stochastic combinatorial optimization. J. Global Optim. 32(3):385–400.CrossrefGoogle Scholar
  • Ntaimo L, Sen S (2008) A comparative study of decomposition algorithms for stochastic combinatorial optimization. Comput. Optim. Appl. 40(3):299–319.CrossrefGoogle Scholar
  • Özaltin OY, Prokopyev OA, Schaefer AJ, Roberts MS (2011) Optimizing the societal benefits of the annual influenza vaccine: A stochastic programming approach. Oper. Res. 59(5):1131–1143.LinkGoogle Scholar
  • Powell WB (2007) Approximate Dynamic Programming: Solving the Curses of Dimensionality (Wiley, New York).CrossrefGoogle Scholar
  • Powell WB (2014) Clearing the jungle of stochastic optimization. INFORMS TutORials in Operations Research, 109–137.Google Scholar
  • Powell WB, Topaloglu H (2003) Stochastic programming in transportation and logistics. Ruszczynski A, Shapiro A, eds. Stochastic Programming. Handbooks in Operations Research and Management Science, vol. 10 (Elsevier, Amsterdam), 555–635.Google Scholar
  • Rockafellar RT, Wets RJB (1991) Scenarios and policy aggregation in optimization under uncertainty. Math. Oper. Res. 16(1):119–147.LinkGoogle Scholar
  • Ruszczynski AP, Shapiro A (2003) Stochastic Programming, Handbooks in Operations Research and Management Science, vol. 10 (Elsevier, Amsterdam).CrossrefGoogle Scholar
  • Ryan K, Rajan D, Ahmed S (2016) Scenario decomposition for 0-1 stochastic programs: Improvements and asynchronous implementation. 2016 IEEE Internat. Parallel Distributed Processing Sympos. Workshops (IPDPSW) (Institute of Electrical and Electronics Engineers Computer Society, Piscataway, NJ), 722–729.CrossrefGoogle Scholar
  • Sahinidis NV (2004) Optimization under uncertainty: State-of-the-art and opportunities. Comput. Chemical Engrg. 28(6–7):971–983.CrossrefGoogle Scholar
  • Sandıkçı B, Özaltin OY (2017) A scalable bounding method for multi-stage stochastic programs. SIAM J. Optim. 27(3):1772–1800.CrossrefGoogle Scholar
  • Sandıkçı B, Kong N, Schaefer AJ (2013) A hierarchy of bounds for stochastic mixed-integer programs. Math. Programming 138(1–2):253–272.CrossrefGoogle 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(1):96–115.CrossrefGoogle Scholar
  • Schultz R (2003) Stochastic programming with integer variables. Math. Programming 97(1–2):285–309.CrossrefGoogle Scholar
  • Sen S, Higle JL (2005) The C3 theorem and a D2 algorithm for large scale stochastic mixed-integer programming: Set convexification. Math. Programming 104(1):1–20.CrossrefGoogle Scholar
  • Sen S, Sherali HD (2006) Decomposition with branch-and-cut approaches for two-stage stochastic mixed-integer programming. Math. Programming 106(2):203–223.CrossrefGoogle Scholar
  • Sen S, Zhou Z (2014) Multistage stochastic decomposition: A bridge between stochastic programming and approximate dynamic programming. SIAM J. Optim. 24(1):127–153.CrossrefGoogle Scholar
  • Shapiro A (2006) On complexity of multistage stochastic programs. Oper. Res. Lett. 34(1):1–8.CrossrefGoogle Scholar
  • Shapiro A, Dentcheva D, Ruszczynski A (2014) Lectures on Stochastic Programming: Modeling and Theory, vol. 16 (SIAM, Philadelphia).CrossrefGoogle Scholar
  • Sims MJ (1992) Use of a stochastic capacity planning model to find the optimal level of flexibility for a manufacturing system. Working paper, Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor.Google Scholar
  • Song Y, Luedtke J (2015) An adaptive partition-based approach for solving two-stage stochastic programs with fixed recourse. SIAM J. Optim. 25(3):1344–1367.CrossrefGoogle Scholar
  • van der Vlerk MH (2007) Stochastic integer programming bibliography. Accessed February 14, 2019, http://www.eco.rug.nl/mally/biblio/sip.html.Google Scholar
  • van der Vlerk MH (2010) Convex approximations for a class of mixed-integer recourse models. Ann. Oper. Res. 177(1):139–150.CrossrefGoogle Scholar
  • Veliz FB, Watson JP, Weintraub A, Wets RJB, Woodruff DL (2015) Stochastic optimization models in forest planning: A progressive hedging solution approach. Ann. Oper. Res. 232(1):259–274.Google Scholar
  • Wallace SW, Fleten S-E (2003) Stochastic programming models in energy. Ruszczynski A, Shapiro A, eds. Stochastic Programming, Handbooks in Operations Research and Management Science, vol. 10 (Elsevier, Amsterdam), 637–677.CrossrefGoogle Scholar
  • Watson JP, Woodruff DL (2011) Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems. Comput. Management Sci. 8(4):355–370.CrossrefGoogle Scholar
  • Zenarosa GL, Prokopyev OA, Schaefer AJ (2014a) M-SMIPLIB: A multistage stochastic mixed-integer programming test set library. Accessed October 17, 2016, http://www.cs.cmu.edu/∼gzen/m-smiplib/.Google Scholar
  • Zenarosa GL, Prokopyev OA, Schaefer AJ (2014b) Scenario-tree decomposition: Bounds for multistage stochastic mixed-integer programs. Working paper, University of Pittsburgh, Pittsburgh.Google Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.