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Critical analysis of classical scenario-based decision rules for pure strategy searching

Gaspars-Wieloch Helena

Zeszyty Naukowe. Organizacja i Zarządzanie / Politechnika Śląska

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2020

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z. 149

155--165

EN

Purpose: The contribution briefly presents the essence and applications of the well-known classical decision rules designed for decision making under uncertainty with unknown probabilities and based on scenario planning. We concentrate on games against nature, pure strategy searching and one-criterion optimization. Design/methodology/approach: The main goal of this work is to analyse numerous case studies and formulate conclusions concerning the properties (in particular drawbacks and limitations) of the aforementioned strategic procedures. Findings: The paper focuses on the limited usefulness of classical decision rules in real economic decision problems. It is advised to apply them very carefully. Research limitations/implications: A similar analysis for mixed strategy searching and multi-criteria optimization should be performed within a future research. Originality/value: The work offers numerous practical guidelines modifying existing procedures and allowing decision makers to obtain logic recommendations.

2

A minimax approach to mapping partial interval uncertainties into point estimates

Romanuke Vadim

Journal of Mathematics and Applications

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2019

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Vol. 42

147--185

EN

A problem of simultaneously reducing a group of interval uncertainties is considered. The intervals are positively normalized. There is a constraint, by which the sum of any point estimates taken from those intervals is equal to 1. Hence, the last interval is suspended. For mapping the interval uncertainties into point estimates, a minimax decision-making method is suggested. The last interval’s point estimate is then tacitly found. Minimax is applied to a maximal disbalance between a real unknown amount and a guessed amount. These amounts are interpreted as aftermaths of the point estimation. According to this model, the decision-maker is granted a pure strategy, whose components are the most appropriate point estimates. Such strategy is always single. Its components are always less than the right endpoints. The best mapping case is when we obtain a totally regular strategy whose components are greater than the left endpoints. The irregular strategy’s components admitting many left endpoints are computed by special formulae. The worst strategy exists, whose single component is greater than the corresponding left endpoint. Apart from the point estimation, irregularities in the decision-maker’s optimal strategy may serve as an evidence of the intervals’ incorrectness. The irregularity of higher ranks is a criterion for correcting the intervals.

3

Alokacja zasobu w warunkach niepewności: modele decyzyjne i procedury obliczeniowe

Gaspars H.

Badania Operacyjne i Decyzje

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2007

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nr 1

5-27

PL

W literaturze można znaleźć omówienie deterministycznej i stochastycznej odmiany zagadnienia rozdziału zasobu. Celem niniejszego opracowania jest sformułowanie modeli optymalizacyjnych, mających zastosowanie w zagadnieniu alokacji zasobu w warunkach niepewności, z którą mamy do czynienia wówczas, gdy zyski wynikające ze skierowania danej ilości środka do konkretnej działalności są opisane jako zmienne losowe o nieznanym rozkładzie. Autorka przedstawia cztery modele, uwzględniające różne postawy decydentów wobec stanów natury, które mogą wystąpić. W tym celu odwołuje się do reguł Walda, Hurwicza, Bayes’a i Savage’a. Analizowane są również możliwe procedury obliczeniowe, pozwalające wyznaczyć optymalne rozwiązanie dla każdego przypadku. Oprócz ogólnej metody programowania dynamicznego, wykorzystać można również dwie metody uproszczone, stosowane w deterministycznej wersji zagadnienia, gdy decyzje podejmowane są w warunkach niepewności. Jednakże te dwie procedury wymagają spełnienia dodatkowych założeń, które częściowo różnią się od założeń sformułowanych dla deterministycznej odmiany rozpatrywanego problemu.

EN

The deterministic and stochastic versions of the resource allocation problem have already been discussed in the literature. The goal of this contribution is to formulate optimization models applicable to the problem of resource allocation under uncertainty, which signifies that profits resulting from the assignment of a quantity of resource to a given activity, are defined as random variables with unknown distribution. The author presents four models depending on the attitude of the decision-maker towards states of nature that may occur, and refers to the rules formulated by Wald, Hurwicz, Bayes and Savage to this end. Possible computational procedures, allowing finding the optimal solution for each case, are also analyzed. Apart from the dynamic programming, two simplified methods used for the deterministic version of resource allocation can also be applied when decisions are made under uncertainty. However, these two methods require that the problem fulfill additional assumptions, which are partially different from those formulated for the deterministic approach.