Cut sharing for multistage stochastic linear programs with interstage dependency

Infanger, Gerd; Morton, David P.

doi:10.1007/bf02592154

Cited by 131 publications

(77 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Such cuts can be shared between nodes of the same stage. For an interstage dependent process with affine functions h tm , this was first observed in [8]. However, when each component (ξ t (m)) is a generalized autoregressive process (of form (8) below), the formulas we obtain for the cuts in Corollary 2.5 can be in some cases (depending on the application) more economic (in terms of memory allocation) compared to those in [8].…”

Section: Introductionmentioning

confidence: 69%

“…For an interstage dependent process with affine functions h tm , this was first observed in [8]. However, when each component (ξ t (m)) is a generalized autoregressive process (of form (8) below), the formulas we obtain for the cuts in Corollary 2.5 can be in some cases (depending on the application) more economic (in terms of memory allocation) compared to those in [8]. Moreover, since we do not assume relatively complete recourse, we also provide formulas for feasibility cuts that are needed to build sequences of feasible states in the forward pass of the algorithm.…”

Section: Introductionmentioning

confidence: 85%

“…We mention some differences between the optimality cuts derived in [8] and those written in the above corollary. In [8], the affine model is written in the vectorial form:…”

Section: Matricesmentioning

confidence: 99%

See 2 more Smart Citations

SDDP for some interstage dependent risk-averse problems and application to hydro-thermal planning

Guigues

2013

Comput Optim Appl

View full text Add to dashboard Cite

Abstract. We consider interstage dependent stochastic linear programs where both the random right-hand side and the model of the underlying stochastic process have a special structure. Namely, for equality constraints (resp. inequality constraints) the right-hand side is an affine function (resp. a given function bt) of the process value for the current time step t. As for m-th component of the process at time step t, it depends on previous values of the process through a function htm.For this type of problem, to obtain an approximate policy under some assumptions for functions bt and htm, we detail a stochastic dual dynamic programming algorithm. Our analysis includes some enhancements of this algorithm such as the definition of a state vector of minimal size, the computation of feasibility cuts without the assumption of relatively complete recourse, as well as efficient formulas for sharing optimality and feasibility cuts between nodes of the same stage. The algorithm is given for both a non-risk-averse and a risk-averse model. We finally provide preliminary results comparing the performances of the recourse functions corresponding to these two models for a real-life application.

show abstract

Section: Introductionmentioning

confidence: 69%

Section: Introductionmentioning

confidence: 85%

See 1 more Smart Citation

SDDP for some interstage dependent risk-averse problems and application to hydro-thermal planning

Guigues

2013

Comput Optim Appl

View full text Add to dashboard Cite

show abstract

“…where X is a vector of decision variables, and A(t), B(t), and C(t) are sets with random elements defined on a probability space T, t ʦ T 29,30 . CCP solves the above model by converting it into a deterministic version through (1) fixing a certain level of probability q i (q i ʦ [0,1]) for uncertain constraint i, which represents the admissible risk of violating constraint i; and (2) imposing the condition that the constraint should be satisfied with at least a probability level of 1 Ϫ q i .…”

Section: Methodsmentioning

confidence: 99%

Modeling Municipal Solid Waste Management System under Uncertainty

Huang

2010

Journal of the Air & Waste Management Association

View full text Add to dashboard Cite

In this study, a dynamic inexact waste management (DIWM) model is developed for identifying optimal waste-flow-allocation and facility-capacity-expansion strategies under uncertainty and is based on an inexact scenario-based probabilistic programming (ISPP) approach. The DIWM model can handle uncertainties presented as interval values and probability distributions, and it can support assessing the risk of violating system constraints. Several violation levels for facility-capacity and waste-diversion constraints are examined. Solutions associated with different risks of constraint violation were generated. The modeling results are valuable for supporting the planning of the study city's municipal solid waste (MSW) management practices, the long-term capacity expansion for waste management system, and the identification of desired policies regarding waste diversion. Sensitivity analyses are also undertaken to demonstrate that the violations of different constraints have varied effects on the planning of waste-flow allocation, facility expansion, and waste management cost.

show abstract

“…The ability to share cuts under some speci…c forms of stagewise dependency as discussed by Infanger and Morton [8] is now included in most commercial implementations of the SDDP algorithm. Monte Carlo sampling is also used in estimating bounds.…”

Section: Introductionmentioning

confidence: 99%

Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion

Philpott

Matos

2012

European Journal of Operational Research

179

115

View full text Add to dashboard Cite

We consider the incorporation of a time-consistent coherent risk measure into a multi-stage stochastic programming model, so that the model can be solved using a SDDP-type algorithm. We describe the implementation of this algorithm, and study the solutions it gives for an application of hydro-thermal scheduling in the New Zealand electricity system. The performance of policies using this risk measure at di¤erent levels of risk aversion is compared with the risk-neutral policy.

show abstract

Cut sharing for multistage stochastic linear programs with interstage dependency

Cited by 131 publications

References 19 publications

SDDP for some interstage dependent risk-averse problems and application to hydro-thermal planning

SDDP for some interstage dependent risk-averse problems and application to hydro-thermal planning

Modeling Municipal Solid Waste Management System under Uncertainty

Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion

Contact Info

Product

Resources

About