Abstract
We present a specialization of the Unified Modeling Language (UML) to help diverse stakeholders in an organization collaborate on the development of Stochastic Optimization Models. Our language describes, at an abstraction level distinct from that possible through algebraic notation, the relationships between decisions and parameters, the dynamics of information acquisition, and the requirements for model input and output. This paper describes the formal language and provides a few illustrative examples.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
(2003) OMG Unified Modeling Language Specification. Object Management Group, version 1.5
Alonso-Ayuso A, Escudero LF, GarÃn A, M T Ortu n, Pérez G (2003) An approach for strategic supply chain planning under uncertainty based on stochastic 0-1 programming. J of Global Optimization 26(1):97–124, DOI http://dx.doi.org/10. 1023/A:1023071216923
Ariyawansa KA, Felt AJ (2001) On a new collection of stochastic linear programming test problems. Tech. Rep. 4, Department of Mathematics, Washington State University, Pullman, WA 99164
Beraldi P, Conforti D, Violi A (2008) A two-stage stochastic programming model for electric energy producers. Comput Oper Res 35(10):3360–3370, DOI http://dx.doi.org/10.1016/j.cor.2007.03.008
Birge JR, Louveaux F (1997) Introduction to Stochastic Programming. Springer-Verlag
Bock C (2006) SysML and UML 2 Support for Activity Modeling. Systems Engineering 9(2):160–186
Brooke A, Kendrick D, Meeraus A (1988) GAMS A User's Guide. The Scientific Press
Cajori F (1993) History of Mathematical Notations. Dover Publications, Inc.
Checkland P (2000) Soft systems methodology: a thirty year retrospective. Systems Research and Behavioral Science
Choobineh J (1991) A diagramming technique for representation of linear programming models. Omega
Collaud G, Pasquier-Boltuck J (1994) glps: A graphical tool for the definition and manipulation of linear problems. European Journal of Operations Research
DeMarco T (1979) Structured analysis and system specification. Yourdon Press Upper Saddle River, NJ, USA
Felfernig A, Friedrich G, Jannach D, Zanker M (2002) Configuration knowledge representation using uml/ocl. LNCS
Fourer R, Lopes L (2008) StAMPL: A Filtration-Oriented Modeling Tool for Stochastic Programming, upcoming in INFORMS Journal on Computing
Fourer R, Gay DM, Kernighan BW (2002) AMPL A Modeling Language For Mathematical Programming, 2nd edn. Duxbury Press
Gassmann HI (1989) Optimzal harvest of a forest in the presence of uncertainty. Canadian Journal of Forest Research 19:1267–1274
Geoffrion AM (1987) An introduction to structured modeling. Management Science
Greenberg H (1993) A Computer-Assisted Analysis System for Mathematical Programming Models and Solutions: A User's Guide for ANALYZE. Kluwer Academic Publishers
Greenberg HJ (1996) A bibliography for the development of an intelligent mathematical programming system. ITORMS
Heikkinen VP (2003) Timber harvesting as a part of the portfolio management: A multiperiod stochastic optimisation approach. Manage Sci 49(1):131–142, DOI http://dx.doi.org/10.1287/mnsc.49.1.131.12752
Jackson M (1983) Systems Development. Prentice-Hall
Jones CV (1990) An introduction to graph-based modeling systems, part i: Overview. ORSA Jorunal on Computing
Jones CV (1991) An introduction to graph-based modeling systems, part ii: Graph-grammars and the implementation. ORSA Jorunal on Computing
Jones CV (1996a) Mimi/g: A graphical environment for mathematical programming and modeling. Interfaces
Jones CV (1996b) Visualization and Optimization. Operations Research/Computer Science Interface Series, Kluwer Academic Publishers
Jrjens J (2002) Umlsec: Extending uml for secure systems development. LNCS
Louveaux FV, Smeers Y (1998) Optimal investments for electricity generation: A stochastic model and a test-problem. In: Numerical Techniques for Stochastic Optimization, SpringerVerlag, chap 24, pp 445–453
Luján-Mora S, Trujillo J, Song IY (2002) Extending the uml for multidimensional modeling. LNCS
Ma P, F H Murphy, E A Stohr (1996) An Implementation of LPFORM. INFORMS Journal on Computing
Midler JL, Wollmer RD (1969) Stochastic programming models for scheduling airlift operations. Naval Research Logistics Quarterly 16:315–330
Neftci SN (2000) An Introduction to the MAthematics of Financial Derivatives. Academic Press
Powell SG (1997) The teachers' forum: From intelligent consumer to active modeler, two mba success stories. INTERFACES
Rosenhead J (1996) What's the problem? an introduction to problem structuring methods. Interfaces
Rubart J, Dawabi P (2002) Towards uml-g: A uml profile for modeling groupware. LNCS
Schrage L (2002) Optimization Modeling with Lingo, 4th edn. LINDO Systems Inc.
Sen S, Yu L, Genc T (2006) A stochastic programming approach to power portfolio optimization. Oper Res 54(1):55–72, DOI http://dx.doi.org/10.1287/opre.1050.0264
Sodhi MS, Tang CS (2008) The or/ms ecosystem: Strengths,weaknesses, opportunities and threats. Operations Research 56(2):267–277
Yu LY, Ji XD, Wang SY (2003) Stochastic programming models in financial optimization: A survey. AMO — Advanced Modeling and Optimization 5(1), URL citeseer.ist.psu.edu/yu03stochastic.html
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media, LLC
About this paper
Cite this paper
Lopes, L., Fourer, R. (2009). Object Oriented Modeling of Multistage Stochastic Linear Programs. In: Chinneck, J.W., Kristjansson, B., Saltzman, M.J. (eds) Operations Research and Cyber-Infrastructure. Operations Research/Computer Science Interfaces, vol 47. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-88843-9_2
Download citation
DOI: https://doi.org/10.1007/978-0-387-88843-9_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-88842-2
Online ISBN: 978-0-387-88843-9
eBook Packages: Computer ScienceComputer Science (R0)