Stochastic Linear Programming

Kall, Peter

doi:10.1007/978-3-642-66252-2

Cited by 237 publications

(30 citation statements)

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“…Now, the only further assumptions one must impose to achieve the stability asserted in theorem 2.4 are that /* ~..r ~) and that q'(t*) is nonempty and bounded. Indeed, assumptions (2) and (3) in theorem 2.4 are both consequences of well-known facts in linear parametric programming (consult [16] for (2) and lemma 3.2 in [36] for (3)). …”

Section: Remark 26mentioning

confidence: 99%

Stability analysis for stochastic programs

Römisch

Schultz

1991

Ann Oper Res

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For stochastic programs with recourse and with (several joint) probabilistic constraints, respectively, we derive quantitative continuity properties of the relevant expectation functionals and constraint set mappings. This leads to qualitative and quantitative stability results for optimal values and optimal solutions with respect to perturbations of the underlying 9 probability distributions. Earlier stability results for stochastic programs with recourse and for those with probabilistic constraints are refined and extended, respectively. Emphasis is placed on equipping sets of probability measures with metrics that one can handle in specific situations. To illustrate the general stability results we present possible consequences when estimating the original probability measure via empirical ones.

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Section: Remark 26mentioning

confidence: 99%

Stability analysis for stochastic programs

Römisch

Schultz

1991

Ann Oper Res

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“…It is therefore, relevant to know when a deterministic counterpart of   D  is convex. The following four propositions; the proofs of which may be found in [72], provide some insights to this issue. …”

Section: Related Mathematical Resultsmentioning

confidence: 98%

Multiobjective Stochastic Linear Programming: An Overview

Adeyefa¹,

Luhandjula²

2011

AJOR

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Many Optimization problems in engineering and economics involve the challenging task of pondering both conflicting goals and random data. In this paper, we give an up-to-date overview of how important ideas from optimization, probability theory and multicriteria decision analysis are interwoven to address situations where the presence of several objective functions and the stochastic nature of data are under one roof in a linear optimization context. In this way users of these models are not bound to caricature their problems by arbitrarily squeezing different objective functions into one and by blindly accepting fixed values in lieu of imprecise ones.

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“…and the log-concavity assumption of the distribution, it follows that the set X s,k is convex when non-empty for all δ x,j ∈ (0, 1) in most distribution functions (Kall and Mayer, 2005). For some particular distributions, e.g., Gaussian, convexity is retained for δ x,j ∈ (0, 0.5].…”

Section: Safety Stock Allocation Policymentioning

confidence: 99%

Reliability–based economic model predictive control for generalised flow–based networks including actuators’ health–aware capabilities

Grosso

Ocampo‐Martínez

Puig

2016

International Journal of Applied Mathematics and Computer Science

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This paper proposes a reliability-based economic model predictive control (MPC) strategy for the management of generalised flow-based networks, integrating some ideas on network service reliability, dynamic safety stock planning, and degradation of equipment health. The proposed strategy is based on a single-layer economic optimisation problem with dynamic constraints, which includes two enhancements with respect to existing approaches. The first enhancement considers chance-constraint programming to compute an optimal inventory replenishment policy based on a desired risk acceptability level, leading to dynamical allocation of safety stocks in flow-based networks to satisfy non-stationary flow demands. The second enhancement computes a smart distribution of the control effort and maximises actuators' availability by estimating their degradation and reliability. The proposed approach is illustrated with an application of water transport networks using the Barcelona network as the case study considered.

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Stochastic Linear Programming

Cited by 237 publications

References 0 publications

Stability analysis for stochastic programs

Stability analysis for stochastic programs

Multiobjective Stochastic Linear Programming: An Overview

Reliability–based economic model predictive control for generalised flow–based networks including actuators’ health–aware capabilities

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