Extending Algebraic Modelling Languages for Stochastic Programming

Valente, Christian; Mitra, Gautam; Sadki, Mustapha; Fourer, Robert

doi:10.1287/ijoc.1080.0282

Cited by 33 publications

(14 citation statements)

References 22 publications

(16 reference statements)

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“…The necessary model transformations, including the addition of any auxiliary variables and constraints, as well as transformation into a multilevel form in the cases of non-time-consistent risk measure systems, could then in principle be automated. Ideally, such facilities should be integrated into a modeling environment tailored to the efficient expression of stochastic programming problems; see for example Colombo et al (2009) and Valente et al (2009).…”

Section: Modeling Considerations and Concluding Remarksmentioning

confidence: 99%

Multilevel Optimization Modeling for Risk-Averse Stochastic Programming

Eckstein

Eskandani

Fan

2016

INFORMS Journal on Computing

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Abstract. Coherent risk measures have become a popular tool for incorporating risk aversion into stochastic optimization models. For dynamic models in which uncertainty is resolved at more than one stage, however, using coherent risk measures within a standard single-level optimization framework becomes problematic. To avoid severe time-consistency difficulties, the current state of the art is to employ risk measures of a specific nested form, which unfortunately have some undesirable and somewhat counterintuitive modeling properties. For one thing, this technique requires increasing risk aversion as risks and reward recede in time. Further, it produces objective functions that cannot be law invariant with respect to the total incurred costs and rewards, meaning that two solutions with identical probability distributions of final wealth may be assigned different levels of risk, and the nested form of the objective function cannot be simplified. These properties deter practical acceptance of such models, and are particularly undesirable for situations with close final time horizons. This paper summarizes these issues and then presents an alternative multilevel optimization modeling approach that enforces a form of time consistency through constraints rather than by restricting the modeler's choice of objective function. This technique leads to models that are time-consistent even while using time-inconsistent risk measures, and can easily be formulated to be law invariant with respect to the final wealth if so desired. We argue that this approach should be the starting point for all multistage optimization modeling. When used with time-consistent objective functions, we show its multilevel optimization constraints become redundant and the associated models thus simplify to a more familiar single-objective form. Unfortunately, this paper also shows that its proposed approach leads to N Phard models, even in the simplest imaginable setting in which it would be needed: three-stage linear problems on a finite probability space, using the standard meansemideviation and average-value-at-risk measures. Finally, we show that for a simple but reasonably realistic test application, that the kind of models we propose, while being drawn from an N P-hard family and certainly more time consuming to solve than those obtained from the nested-objective approach, are readily solvable to global optimality using a standard commercial MILP solver. Therefore, there seems some promise of the modeling approach being useful despite its computational complexity properties.Acknowledgements: This work was supported by a grant from the Air Force Office of Scientific Research, award FA9550-11-1-0164. The authors would like to thank Andrzej Ruszczyński for his assistance and support.Note: Sections 4-7 of this report essentially duplicate material presented in the earlier reports RRR 7-2013 and (using different notation) RRR 17-2012. The remaining sections contain extensive new material and results.

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Section: Modeling Considerations and Concluding Remarksmentioning

confidence: 99%

Multilevel Optimization Modeling for Risk-Averse Stochastic Programming

Eckstein

Eskandani

Fan

2016

INFORMS Journal on Computing

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“…These constraints are needed to take into account the timewise structure of decisions with respect to the given scenario tree. Often, non-anticipativity is taken into account implicitly by the solution algorithm (e.g., by the sampling method given by Wu and Sen 2000) or the modeling environment (e.g., see the SPInE environment by Valente, Mitra, Sadki, and Fourer 2009). We state some exemplary non-anticipativity constraints for the model instance that is analyzed in our case example in section 4 in the Appendix of this paper.…”

Section: Option Contractsmentioning

confidence: 99%

Integrated Strategic Planning of Global Production Networks and Financial Hedging under Uncertain Demands and Exchange Rates

Koberstein

Lukas

Naumann

2013

Bus Res

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte.

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“…A survey of XML-based representations can be found in Valente and Mitra (2007). New developments in algebraic modeling languages include extensions for constraint programming (Fourer and Gay 2002), and extensions for stochastic programming (Valente et al 2009). The formal analysis of the semantics of typed modeling languages is in Bhargava, Krishnan, and Piela (1997).…”

Section: Model Management-imentioning

confidence: 99%

Machine Learning

2013

Encyclopedia of Operations Research and Management Science

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A term used in the artificial intelligence community to indicate automated improvement based on experience or empirical data in accomplishing a given task such as optimizing an objective function. MaintenanceMaintenance is the support of successful system operation during long periods of usage by means of: (1) regular or sample check-ups; (2) planned or preventive replacement of the system's units; (3) failure diagnosis; and/or (4) spare units supply. Operations research models for a system maintenance analysis are represented mainly by optimization models for the improvement of system and equipment reliability.For (1) and (2), one usually uses methods of controlled stochastic processes. For (3), one uses special methods based on mathematical logic, while (4) is considered in the scope of optimal redundancy and inventory control. IntroductionManpower (or, human resource) planning is concerned with the quantitative aspects of the supply of and demand for people in employment. At one extreme this might include the whole working population of a country, but it has been most successful when applied to smaller, more homogeneous systems like individual firms or professions. The term manpower planning appears to date from the 1960s though many of the ideas can be traced back much further. In recent years terms such as Workforce Panning and Personnel Planning have been used in the same sense. A history of the subject up to the 1980s,from a U.K. perspective, will be found in Smith and Bartholomew (1988). The literature of the subject is very scattered reflecting the diverse disciplinary origins of the practitioners, but most of the technical material is to be found in the journals of operations research, probability, and statistics. There was an initial surge of publication in the late 1960s and early 1970s and since then book length treatments include Grinold and Marshall (1977), Vajda (1978), and Bennison and Casson (1984). Bartholomew, Forbes and McClean (1991) gives a thorough coverage of the technical material and contains an extensive bibliography. Since then there has been a period of consolidation. The earlier theoretical work has largely proved adequate for practical needs, though there have been developments in closely related areas. See, for example, Kalamatianou and McLean (2003). The essence of manpower planning is summed up in the aphorism that its aim is to have the right numbers of people of the right kinds in the right places at the right time. The basic approach is first to classify the members of a system in relevant ways. These will often be on the basis of such things as grade, salary level, sex, qualifications, and job title. The state of the system at any point in time can then be described by the numbers in these categories, often referred to as the stocks. Over time, changes occur as individuals join, leave the system or move within it. The numbers making these transitions are called the flows. The factors giving rise to change may be predictable or unpredictable but will include such things ...

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Extending Algebraic Modelling Languages for Stochastic Programming

Cited by 33 publications

References 22 publications

Multilevel Optimization Modeling for Risk-Averse Stochastic Programming

Multilevel Optimization Modeling for Risk-Averse Stochastic Programming

Integrated Strategic Planning of Global Production Networks and Financial Hedging under Uncertain Demands and Exchange Rates

Machine Learning

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