Risk aversion in multistage stochastic programming: A modeling and algorithmic perspective

Homem-de-Mello, Tito; Pagnoncelli, Bernardo K.

doi:10.1016/j.ejor.2015.05.048

Cited by 97 publications

(35 citation statements)

References 45 publications

(57 reference statements)

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“…Although each

F

is a single‐period risk measure of the type discussed in Section 3.3, the nested formulation of the cost‐to‐go function V creates a conditional risk mapping . However, our since our framework allows the single‐stage risk measures to differ between nodes, one can model expected conditional risk measures , and end‐of‐horizon risk measures by dynamically changing the single‐period risk measures in each subproblem . Moreover, because the risk measure is applied locally to each node in a nested fashion, the property of time consistency naturally arises.…”

Section: Policy Graphsmentioning

confidence: 99%

“…Moreover, because the risk measure is applied locally to each node in a nested fashion, the property of time consistency naturally arises. (A proper discussion on time‐consistency is out‐of‐scope for the current paper, see, e.g., .) Finally, note that the nonanticipative constraints usually associated with multistage stochastic programming are satisfied by our recursive definition of a policy.…”

Section: Policy Graphsmentioning

confidence: 99%

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The policy graph decomposition of multistage stochastic programming problems

Dowson

2020

Networks

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We propose the policy graph as a structured way of formulating a general class of multistage stochastic programming problems in a way that leads to a natural decomposition. We also propose an extension to the stochastic dual dynamic programming algorithm to solve a subset of problems formulated as a policy graph. This subset includes discrete-time, convex, infinite-horizon, multistage stochastic programming problems with continuous state and control variables. To demonstrate the utility of our algorithm, we solve an existing multistage stochastic programming problem from the literature based on pastoral dairy farming. We show that the finite-horizon model in the literature suffers from end-of-horizon effects, which we are able to overcome with an infinite-horizon model. KEYWORDSinfinite horizon, multistage, policy graph, stochastic programming Networks. 2020;76:3-23. wileyonlinelibrary.com/journal/net © 2020 Wiley Periodicals, Inc. 3 4 DOWSONto solve a subset of problems formulated as a policy graph. Finally, in Section 5 we demonstrate the utility of considering the infinite-horizon formulation of a problem arising from pastoral agriculture. TERMINOLOGY Basic definitionsFirst, let us define the stage in multistage. Definition.A stage is a discrete moment in time in which the agent chooses a decision and any uncertainty is revealed.Therefore, multistage refers to a problem that can be decomposed into a sequence of stages. This requires the assumption that time can be discretized. Second, the stochastic component of multistage stochastic programming refers to problems with uncertainty. In this paper, we differentiate between two types of uncertainty; the first of which we term a noise. (We shall describe the second type in the next section, but it relates to how the problem transitions between stages.) Definition.A noise is a stagewise-independent random variable in stage t.In stage t, we denote a single observation of the noise with the lowercase t , and the sample space from which it is drawn by the uppercase Ω t . Ω t can be continuous or discrete, although in this paper we only consider the discrete case. Furthermore, we use the term stagewise-independent to refer to the fact that the distribution of the noise in stage t is independent of the noise in other time periods 1, 2, …, t − 1, t + 1, t + 2, ….Next we define a state, modifying slightly the definition from Powell [40]. Definition.A state is a function of history that captures all the information we need to model a system from some point in time onward.Expressed a different way, a state is the smallest piece of information that is necessary to pass between stage t and t + 1 so that the optimal decision-making in stage t + 1 onward can be made independently from the decisions that were made in stages 1 to t. Each dimension of the state is represented by a state variable. State variables can be continuous or discrete.We denote the state variable at the start of stage t by the lowercase x t . We refer to x t as the incoming state variable. Then, during the ...

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“…Although each

F

Section: Policy Graphsmentioning

confidence: 99%

Section: Policy Graphsmentioning

confidence: 99%

The policy graph decomposition of multistage stochastic programming problems

Dowson

2020

Networks

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“…Alternatively, risk preferences can be captured by introducing a risk utility function [75], controlling for conditional value-at-risk [76], or applying the concept of stochastic dominance [77]. Any option requires making additional assumptions, including choice of a risk measure [77,78,79], and might significantly affect computational efficiency. [20] Social discount rate (% y -1 ) 0.00 [69] Note: *data is based on own assumptions (Appendix A).…”

Section: Case Study and Datamentioning

confidence: 99%

Policy analysis of perennial energy crop cultivation at the farm level: Short rotation coppice (SRC) in Germany

Spiegel

Britz

Djanibekov

et al. 2018

Biomass and Bioenergy

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“…The rationale behind it is that the solution of any node and its successor node set in the scenario tree should not consider the data, constraints and variables that belong to scenarios that cannot occur from that point. So, ECSD belongs to the type of risk averse measures that have the time consistency property as presented in [36]. 4.…”

Section: Main Contributions Of This Work In Stscp Problem Solvingmentioning

confidence: 99%

“…In other words, TSD satisfies the properties: translation invariance, positive homogeneity, monotonicity and convexity. In addition, it can also be shown [36] that the time-consistency of TSD, as defined below, depends on the bounds e p and θ p . The tighter these bounds are, the lower the consistency probability of TSD.…”

Section: Time-inconsistent Tsd Measurementioning

confidence: 99%