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MATHEMATICAL FOUNDATIONS OF DISTRIBUTIONALLY ROBUST MULTISTAGE OPTIMIZATION

SIAM JOURNAL ON OPTIMIZATION 2021年第4期31卷 3044-3067页

作者： Pichler, Alois Shapiro, Alexander Tech Univ Chemnitz Fak Math D-09111 Chemnitz Germany Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA

Distributionally robust optimization involves various probability measures in its problem formulation. They can be bundled to constitute a risk functional. For this equivalence, risk functionals constitute a fundamental building block in distributionally robust stochastic programming. Multistage programming requires conditional versions of risk functionals to reassess future risk after partial realizations and after preceding decisions. This paper discusses a construction of the conditional counterpart of a risk functional by passing its genuine characteristics to its conditional counterparts. It turns out that the conditional risk functionals could be different from the nested analogues of the original (law invariant) risk measure. We also discuss an implication to formulations of distributionally robust stochastic programming and a relation to stochastic games.

关键词： multistage stochastic programming distributional robustness conditional risk measures dynamic equations stochastic games rectangularity

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Time (in)consistency of multistage distributionally robust inventory models with moment constraints

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2021年第3期289卷 1127-1141页

作者： Xin, Linwei Goldberg, David A. Univ Chicago Booth Sch Business Chicago IL 60637 USA Cornell Univ Operat Res & Informat Engn Ithaca NY 14850 USA

Recently, there has been a growing interest in developing inventory control policies which are robust to model misspecification. One approach is to posit that nature selects a worst-case distribution for any relevant stochastic primitives from some pre-specified family. Several communities have observed that a subtle phenomena known as time inconsistency can arise in this framework. In particular, it becomes possible that a policy which is optimal at time zero may not be optimal for the associated optimization problem in which the decision-maker recomputes her policy at each point in time, which has implications for implementability. If there exists a policy which is optimal for both formulations, we say that the policy is time consistent, and the problem is weakly time consistent. If every optimal policy is time consistent, we say that the problem is strongly time consistent. We study these phenomena in the context of managing an inventory over time, when only the mean, variance, and support are known for the demand at each stage. We provide several illustrative examples showing that here the question of time consistency can be quite subtle. We complement these observations by providing simple sufficient conditions for weak and strong time consistency. Although a similar phenomena was previously identified by Shapiro for the setting in which only the mean and support of the demand are known, here our model is rich enough to exhibit a variety of additional interesting behaviors. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Supply chain management Inventory News vendor Multistage distributionally robust optimization rectangularity Moment constraints Time consistency Dynamic programming Base-stock policy

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Distributionally robust Optimal Control and MDP modeling

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OPERATIONS RESEARCH LETTERS 2021年第5期49卷 809-814页

作者： Shapiro, Alexander Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA

In this paper we discuss Optimal Control and Markov Decision Process (MDP) formulations of multistage optimization problems when the involved probability distributions are not known exactly, but rather are assumed to belong to specified ambiguity families. The aim of this paper is to clarify a connection between such distributionally robust approaches to multistage stochastic optimization. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Markov Decision Process Bellman equations Distributional robustness Stochastic games Risk measures rectangularity

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A Machine Vision Based Automated Quality Control System for Product Dimensional Analysis

A Machine Vision Based Automated Quality Control System for ...

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Complex Adaptive Systems Conference on Big Data, IoT, and AI for a Smarter Future

作者： Akundi, Aditya Reyna, Mark Dept Mfg & Ind Engn Brownsville TX 78520 USA Dept Elect & Comp Engn Brownsville TX USA Univ Texas Rio Grande Valley Texas Complex Engn Syst Lab Brownsville TX 78520 USA

Quality control (QC) in manufacturing processes is critical to ensuring consumers receive products with proper functionality and reliability. Faulty products can lead to additional costs for the manufacturer and damage trust in a brand. A growing trend in QC is the use of machine vision (MV) systems because of their noncontact inspection, high repeatability, and relatively low cost. This paper presents a robust MV system developed to perform comparative dimensional inspection on diversely shaped samples, including additive manufacturing products. The algorithm used performs dimensional inspection on a base product considered to have acceptable dimensions. The perimeter, area, rectangularity, and circularity of the base product are determined using blob analysis on a calibrated camera. These parameters are then used as the standard with which to judge additional products. Each product following is similarly inspected and compared to the base product parameters. A likeness score is calculated for each product, which provides a single value tracking all parameter differences. Finally, the likeness score is considered on whether it is within a threshold, and the product is considered to be acceptable or defective. The proposed MV system has achieved satisfactory results, as discussed in the results section, that would allow it to serve as a dependable and accurate QC inspection system in industrial settings. (c) 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://***/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the Complex Adaptive Systems Conference, June 2021.

关键词： Machine Vision Quality Control Dimensional Analysis Digital Quality rectangularity Circularity Production Manufacturing

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Effects of tree spacing on branch-size development during early growth of an experimental plantation of Eucalyptus pilularis in subtropical Australia

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AUSTRALIAN FORESTRY 2020年第1期83卷 39-45页

作者： West, P. W. Smith, R. G. B. Southern Cross Univ Forest Res Ctr Lismore NSW 2480 Australia

Branch development in trees 1.6-5.7 years after planting was studied in a plantation experiment involving Eucalyptus pilularis in subtropical eastern Australia. The experiment compared stocking densities at planting in the range of 816-1667 stems ha(-1) and rectangularities of tree spacing in the range of 1-6. Branch diameters at their bases were measured on the lowest 5 m of the stems of trees judged likely to yield sawn timber of high quality at final harvest. Neither stocking density nor rectangularity had substantial effects on branch numbers or diameters. Particular interest was paid to the presence of branches with diameters in excess of 2.5 cm that might produce knots large enough to degrade the quality of sawn timber. Such branches developed on lower stems between 2-4 years of age. An average of nearly five such branches was found on more widely spaced trees, reducing to 2-3 on more closely spaced trees. The results confirmed other work suggesting that pruning of high-quality eucalypt plantations should start near 2-3 years of age to both limit the development of large branches and restrict the size of knotty cores in logs. There was no evidence that changing the rectangularity of spacing to 3 or a little more, from the more normal practice of close to square, would affect such pruning regimes: increasing the distance between rows can reduce establishment and harvest costs and allow easier access for silvicultural operations.

关键词： branching spacing rectangularity Eucalyptus pilularis pruning

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Objective rationality and recursive multiple priors

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JOURNAL OF MATHEMATICAL ECONOMICS 2022年 102卷 1页

作者： Ceron, Federica Vergopoulos, Vassili UJM St Etienne Univ Lyon GATE UMR 5824 F-42023 St Etienne France Univ Paris 2 Pantheon Assas LEMMA 4 Rue Blaise Desgoffe F-75006 Paris France

We provide an axiomatic characterization of recursive MaxMin preferences that stem from a (possibly) incomplete relation representing preference judgements that are justified by objective probabilistic information. To ensure that her choice behavior be informed by objective information, dynamically consistent, and ambiguity averse, the decision-maker evaluates alternatives by their minimal expected value over the rectangular hull of the objective information set. The characterization builds upon two axioms that naturally combine the three requirements in a behavioral way. Our main result suggests a principled justification for the use of recursive MaxMin preferences in applications to dynamic choice problems.(c) 2022 Elsevier B.V. All rights reserved.

关键词： MaxMin expected utility rectangularity Unanimity rule Dynamic consistency Prior-by-prior updating Mental and behavioral preferences

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Real options, ambiguity, and dynamic consistency - A technical note

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2020年 229卷 107772-107772页

作者： Schroder, David Univ London Birkbeck Coll Malet St London WC1E 7HX England

Recent research on real options does not only consider optimal investment decisions under risk, but also under ambiguity. However, most models that allow for ambiguity are generally not dynamically consistent. Examples are, among others, the a-MEU model, the imprecision aversion model, or the NMEU model. Dynamic consistency is however required to solve optimal stopping real options problems analytically or in closed-form. This paper highlights the resulting difficulties, which are often overlooked, exemplarily for the NMEU model.

关键词： Ambiguity Dynamic consistency Real options NMEU preferences rectangularity Optimal stopping

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Quantifying ambiguity bounds via time-consistent sets of indistinguishable models

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SYSTEMS & CONTROL LETTERS 2021年 149卷 104877-104877页

作者： Balter, Anne G. Pelsser, Antoon Tilburg Univ Tilburg Netherlands Netspar Tilburg Netherlands Maastricht Univ Maastricht Netherlands Univ Amsterdam Amsterdam Netherlands Dept Econometr & Operat Res Warandelaan 2 NL-5037 AB Tilburg Netherlands Tongersestr 53 NL-6211 LM Maastricht Netherlands

Models can be wrong and recognising their limitations is important in financial and economic decision making under uncertainty. Robust strategies, which are least sensitive to perturbations of the underlying model, take uncertainty into account. Interpreting the explicit set of alternative models surrounding the baseline model has been difficult so far. We specify alternative models via a time-consistent set of equivalent probability measures and derive a quantitative bound on the uncertainty set. We find an explicit ex ante relation between the size of this set, and the Type I and II error probabilities on the statistical test that is hypothetically performed to investigate whether the alternative model specification could be rejected at a future test horizon. The hypothetical test is constructed to obtain all alternative models that are indistinguishable from the baseline model. We also link the ambiguity bound, which is now a function of interpretable variables, to numerical values on several divergence measures and illustrate our methodology on a robust investment problem. (C) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).

关键词： Model uncertainty Robustness Stochastic control Divergence rectangularity

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A Machine Vision Based Automated Quality Control System for Product Dimensional Analysis

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Procedia Computer Science 2021年 185卷 127-134页

作者： Aditya Akundi Mark Reyna Department of Manufacturing and Indsutrial Engineering The University of Texas Rio Grande Valley Texas 78520 United States Complex Engineering System Laboratory The University of Texas Rio Grande Valley Texas 78520 United States Department of Electrical and Computer Engineering The University of Texas Rio Grande Valley Texas 78520 United States

关键词： Machine Vision Quality Control Dimensional Analysis Digital Quality rectangularity Circularity Production Manufacturing

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Biogeographic differentiation between two morphotypes of the Southern Ocean diatom Fragilariopsis kerguelensis

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POLAR BIOLOGY 2019年第7期42卷 1369-1376页

作者： Glemser, Barbara Kloster, Michael Esper, Oliver Eggers, Sarah Lena Kauer, Gerhard Beszteri, Bank Helmholtz Ctr Polar & Marine Res Alfred Wegener Inst Handelshafen 12 D-27570 Bremerhaven Germany Univ Appl Sci Emden Leer Constantiapl 4 D-26723 Emden Germany Univ Duisburg Essen Univ Str 5 D-45141 Essen Germany

Fragilariopsiskerguelensis (O' Meara) Hust. is a ubiquitous diatom of the Southern Ocean. Its thick frustules are the numerically dominant component of the siliceous sediment layer covering large parts of the seafloor beneath. Morphometric variability of frustules of this diatom has been of interest for paleoenvironmental reconstructions. Recently, two morphotypes differentiated by the morphometric descriptor rectangularity were described from a Southern Ocean sediment core, the relative abundance of which correlated with reconstructed paleotemperatures. In the present study, we use semi-automated microscopic and image analysis methods to answer whether these morphotypes also appear in recent assemblages, and if yes, do their distributions reflect geographic location or environmental factors. Three transects from the water column, sampled along the Greenwich meridian with hand nets, and one sediment surface transect from the South Pacific, were analyzed. In each of these transects, both morphotypes were detected, and annual mean sea surface temperatures (SST) were found to be a good predictor of their relative abundances. The transition between dominance of one or the other morphotype appeared roughly between the Antarctic Polar Front and the Southern Boundary of the Antarctic Circumpolar Current. Although more extensive circumpolar sampling will be needed to confirm the generality of our conclusions, the observed morphometric cline is a novel aspect of the biology of this species and can in the future potentially be used for further developing paleoproxies especially for highly ***-dominated sediment in the Southern Ocean.

关键词： Fragilariopsiskerguelensis rectangularity Morphometrics Biogeography

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