Abstract
Optimization models for making decisions over time in uncertain environments rely on probabilistic inputs, such as scenario trees for stochastic mathematical programs. The quality of model outputs, i.e., the solutions obtained, depends on the quality of these inputs. However, solution quality is rarely assessed in a rigorous way. The connection between validation of model inputs and quality of the resulting solution is not immediate. This chapter discusses some efforts to formulate realistic probabilistic inputs and subsequently validate them in terms of the quality of solutions they produce. These include formulating probabilistic models based on statistical descriptions understandable to decision makers; conducting statistical tests to assess the validity of stochastic process models and their discretization; and conducting re-enactments to assess the quality of the formulation in terms of solution performance against observational data. Studies of long-term capacity expansion in service industries, including electric power, and short-term scheduling of thermal electricity generating units provide motivation and illustrations. The chapter concludes with directions for future research.
This chapter is dedicated to the memory of my mother, Janice Crawford McAllister (1929-2017).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
Generally I prefer the gender-neutral term “newsvendor,” but in this book chapter I wish to emphasize that the professional problem solved by the woman may be more complicated than the one her male counterpart faces!
References
Bean JC, Higle J, Smith RL (1992) Capacity expansion under stochastic demands. Oper Res 40:S210–S216
Carøe CC, Schultz R (1999) Dual decomposition in stochastic integer programming. Oper Res Lett 24:37–45
Casimir RJ (1990) The newsboy and the flower-girl. OMEGA Int J Manag Sci 18(4):395–398
Cheung K, Gade D, Ryan S, Silva-Monroy C, Watson JP, Wets R, Woodruff D (2015) Toward scalable stochastic unit commitment - part 2: Assessing solver performance. Energy Syst 6(3):417–438. https://doi.org/10.1007/s12667-015-0148-6
Dupac̆ová J, Gröwe-Kuska N, Römisch W (2003) Scenario reduction in stochastic programming. Math Program 95(3):493–511. https://doi.org/10.1007/s10107-002-0331-0
Feng Y, Ryan SM (2013) Scenario construction and reduction applied to stochastic power generation expansion planning. Comput Oper Res 40(1):9–23
Feng Y, Ryan SM (2016) Day-ahead hourly electricity load modeling by functional regression. Appl Energy 170:455–465. https://doi.org/10.1016/j.apenergy.2016.02.118
Feng Y, Rios I, Ryan SM, Spurkel K, Watson JP, Wets RJB, Woodruff DL (2015) Toward scalable stochastic unit commitment - part 1: Load scenario generation. Energy Syst. https://doi.org/10.1007/s12667-015-0146-8
Freidenfelds J (1981) Capacity expansion: Analysis of simple models with applications. North-Holland, New York
Gade D, Hackebeil G, Ryan SM, Watson JP, Wets RJB, Woodruff DL (2016) Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs. Math Program Ser B 157(1):47–67. https://doi.org/10.1007/s10107-016-1000-z
Gneiting T, Katzfuss M (2014) Probabilistic forecasting. Annu Rev Stat Appl 1:125–151. https://doi.org/10.1146/annurev-statistics-062713-085831
Gneiting T, Raftery AE (2007) Strictly proper scoring rules, prediction, and estimation. J Am Stat Assoc 102(477):359–378. https://doi.org/10.1198/016214506000001437
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. https://doi.org/10.1016/j.orl.2015.03.008
Guo GC, Ryan SM (2017) Progressive hedging lower bounds for time consistent risk-averse multistage stochastic mixed-integer programs. URL https://works.bepress.com/sarah_m_ryan/93/
Hart WE, Laird CD, Watson JP, Woodruff DL, Hackebeil GA, Nicholson BL, Siirola JD (2017) Pyomo – optimization modeling in Python, 2nd edn. Springer
Heitsch H, Römisch W (2003) Scenario reduction algorithms in stochastic programming. Comput Optim Appl 24:187–206
Heitsch H, Römisch W (2007) A note on scenario reduction for two-stage stochastic programs. Oper Res Lett 35(6):731–738. https://doi.org/10.1016/j.orl.2006.12.008
Jin S, Ryan S, Watson JP, Woodruff D (2011) Modeling and solving a large-scale generation expansion planning problem under uncertainty. Energy Syst 2:209–242. https://doi.org/10.1007/s12667-011-0042-9. URL http://dx.doi.org/10.1007/s12667-011-0042-9
Jin S, Botterud A, Ryan SM (2014) Temporal vs. stochastic granularity in thermal generation capacity planning with wind power. IEEE Trans Power Syst 29(5):2033–2041. https://doi.org/10.1109/TPWRS.2014.2299760
Manne AS (1961) Capacity expansion and probabilistic growth. Econometrica 29(4):632–649
Marathe R, Ryan SM (2005) On the validity of the geometric Brownian motion assumption. Eng Econ 50:159–192. https://doi.org/10.1080/00137910590949904
Marathe RR, Ryan SM (2009) Capacity expansion under a service level constraint for uncertain demand with lead times. Nav Res Logist 56(3):250–263
McAllister C, Ryan SM (2000) Relative risk characteristics of rolling horizon hedging heuristics for capacity expansion. Eng Econ 45(2):115–128
Muñoz FD, Hobbs BF, Ho JL, Kasina S (2014) An engineering-economic approach to transmission planning under market and regulatory uncertainties: WECC case study. IEEE Trans Power Syst 29(1):307–317
Nitsche S, Silva-Monroy C, Staid A, Watson JP, Winner S, Woodruff D (2017) Improving wind power prediction intervals using vendor-supplied probabilistic forecast information. In: IEEE Power & Energy Society General Meeting
Pflug GC (2001) Scenario tree generation for multiperiod financial optimization by optimal discretization. Math Program Ser B 89:251–271. https://doi.org/10.1007/s101070000202
Pflug GC, Pichler A (2014) Multistage stochastic optimization. Springer
Pinson P, Girard R (2012) Evaluating the quality of scenarios of short-term wind power generation. Appl Energy 96:12–20, https://doi.org/10.1016/j.apenergy.2011.11.004
Quelhas A, McCalley JD (2007) A multiperiod generalized network flow model of the U.S. integrated energy system: Part II simulation results. IEEE Trans Power Syst 22(2):837–844
Quelhas A, Gil E, McCalley JD, Ryan SM (2007) A multiperiod generalized network flow model of the U.S. integrated energy system: Part I – model description. IEEE Trans Power Syst 22(2):829–836
Rockafellar RT, Wets RJB (1991) Scenarios and policy aggregation in optimization under uncertainty. Math Oper Res 16(1):119–147
Ross S (1999) An introduction to mathematical finance. Cambridge University Press, Cambridge, UK
Royset JO, Wets RJB (2014) From data to assessments and decisions: Epi-spline technology. INFORMS Tutor Oper Res, 27–53. https://doi.org/10.1287/educ.2014.0126
Ryan SM (1988) Degeneracy in discrete infinite horizon optimization. Ph.D. dissertation, The University of Michigan
Ryan SM (1998) Forecast frequency in rolling horizon hedging heuristics for capacity expansion. Eur J Oper Res 109(3):550–558
Ryan SM (2003) Capacity expansion with lead times and correlated random demand. Nav Res Logist 50(2):167–183. https://doi.org/10.1002/nav.10055
Ryan SM (2004) Capacity expansion for random exponential demand growth with lead times. Manag Sci 50(6):740–748. https://doi.org/10.1287/mnsc.1030.0187
Ryan SM, Bean JC (1989) Degeneracy in infinite horizon optimization. Math Program 43:305–316
Ryan SM, Bean JC, Smith RL (1992) A tie-breaking rule for discrete infinite horizon optimization. Oper Res 40(Supplement 1):S117–S126
Ryan SM, McCalley JD, Woodruff D (2011) Long term resource planning for electric power systems under uncertainty. In: Eto JH, Thomas RJ (eds) Computational needs for the next generation electric grid, U.S. Department of Energy, pp 6–1–41. URL http://energy.gov/sites/prod/files/FINAL_CompNeeds_Proceedings2011.pdf
Sarı D, Ryan SM (2016). MTDrh: Mass transportation distance rank histogram. URL https://cran.r-project.org/package=MTDrh
Sarı D, Ryan SM (2017) Statistical reliability of wind power scenarios and stochastic unit commitment cost. Energy Syst https://doi.org/10.1007/s12667-017-0255-7
Sarı D, Lee Y, Ryan S, Woodruff D (2016) Statistical metrics for assessing the quality of wind power scenarios for stochastic unit commitment. Wind Energy 19:873–893. https://doi.org/10.1002/we.1872
Sarı Ay D, Ryan SM (2018) Observational data-based quality assessment of scenario generation for stochastic programs. Comput Manag Sci https://works.bepress.com/sarah_m_ryan/94/
Staid A, Watson JP, Wets RJB, Woodruff DL (2017) Generating short-term probabilistic wind power scenarios via nonparametric forecast error density estimators. Wind Energy 20(12):1911–1925. https://doi.org/10.1002/we.2129
Székely GJ, Rizzo ML (2013) Energy statistics: A class of statistics based on distances. J Statist Plann Inference 143(8):1249–1272. https://doi.org/10.1016/j.jspi.2013.03.018
Wang Y (2010) Scenario reduction heuristics for a rolling stochastic programming simulation of bulk energy flows with uncertain fuel costs. Ph.D. dissertation, Iowa State University, URL http://search.proquest.com/docview/848503163
Wang Y, Ryan SM (2010) Effects of uncertain fuel costs on optimal energy flows in the U.S. Energy Syst 1:209–243
Wilks DS (2004) The minimum spanning tree histogram as a verification tool for multidimensional ensemble forecasts. Mon Weather Rev 132:1329–1340
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Ryan, S.M. (2020). Specifying and Validating Probabilistic Inputs for Prescriptive Models of Decision Making over Time. In: Smith, A. (eds) Women in Industrial and Systems Engineering. Women in Engineering and Science. Springer, Cham. https://doi.org/10.1007/978-3-030-11866-2_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-11866-2_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-11865-5
Online ISBN: 978-3-030-11866-2
eBook Packages: EngineeringEngineering (R0)