Modifications of the Omega ratio for decision making under uncertainty

Proceedings of 6th International Scientific Conference Contemporary Issues in Business, Management and Economics Engineering ‘2

2019

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Purpose – scenario planning is very helpful when the decision maker deals with uncertain issues. Probabilities are also frequently applied to such problems. In the paper, we examine the correctness of combining probabilities with scenario planning in economic decisions which are usually made under uncertainty. The goal of the article is to find and discuss cases where the use of probabilities in scenario planning is appropriate and cases where such an approach is not desira-ble. Research methodology – in order to achieve this target, we first make a concise literature review of existing approaches concerning the application of probabilities to scenario planning. Then, we investigate and compare diverse decision mak-ing circumstances presented by means of numerical examples and differing from each other with regard to the nature of the decision problem (way of payoff estimation, novelty degree of the problem, access to historical data etc.) and the de-cision maker’s objectives and preferences (one-shot or multi-shots decisions, attitude towards risk). We explore the newsvendor problem, the spare parts quantity problem, the project selection problem and the project time management with scenario-based decision project graphs. Findings – the work contains both recommendations already described in the literature and suggestions formulated by the author. We get to the point that scenario planning is unquestionable support for decision making under uncertainty, however, the use of probabilities as an accompanying tool may be necessary and justified in some specific cases only. Their significance depends for instance on (1) the number of times a given variant is supposed to be executed; (2) the de-cision maker’s knowledge about the considered problem; (3) the novelty degree of the problem; (4) the decision maker’s conviction that the probability values really reflect his/her attitude towards risk. The analysis of numerical examples leads us to the conclusion that scenario planning should not be linked with the likelihood (1) for one-shot decisions problems; (2) for decision problems related to different kinds of innovation; (3) in the case of lack of certainty which type of proba-bility definition ought to be applied to a given situation; (4) if the decision maker anticipates new future factors not in-cluded in historical data. Research limitations – in the paper we mainly analyse one-criterion problems and payoff matrices with data precisely de-fined. Further conclusions can be obtained after investigating multi-criteria cases and examples with interval payoffs. We limit our research to selected probability definitions. Nevertheless, a wider review can lead to new interesting observa-tions. Practical implications – the aforementioned findings are crucial in such domains as economic modeling and decision the-ory. The results of the research can be used in planning, management, and decision optimization. They provide valuable guidelines for each decision maker dealing with an uncertain future. Originality/Value – authors of previous papers related to this topic have already formulated many significant conclusions. However, this contribution examines the problem from a new point of view since it concentrates on novel decisions, con-cerning unique, innovative or innovation projects (products). It encourages the decision makers to treat problems usually called in the literature “stochastic problems” (i.e. with known probability distribution) as “strategic problems” (i.e. with unknown probability distribution). This is especially the case of the newsvendor problem and the spare parts quantity problem

Section: Economic Decision Problems -Numerical Examples and Analysismentioning

confidence: 99%

Role of scenario planning and probabilities in economic decision problems – literature review and new conclusions

Proceedings of 6th International Scientific Conference Contemporary Issues in Business, Management and Economics Engineering ‘2

2019

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“…These parameters belong to interval [0,1] and satisfy the condition α+β=1, where α (β) tends to 0 (1) for extreme optimists (risk-prone behavior) and is close to 1 (0) for radical pessimists (risk-averse behavior). The coefficients of pessimism and optimism have been already used in decision rules suggested for instance by [Gaspars-Wieloch, 2014b;2015a;Hurwicz, 1952;Perez et al, 2015].…”

Section: Procedures For Mdmu+sp Pure Strategies and Independent Criteriamentioning

confidence: 99%

A Decision Rule for Uncertain Multi-Criteria Pure Decision Making and Independent Criteria

2017

Optimum

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SummaryThe paper is concerned with multi-criteria decision-making under uncertainty with scenario planning. This topic has been explored by many researchers since almost all real-world decision problems contain multiple conflicting criteria and a deterministic evaluation of criteria is often impossible. We propose a procedure for uncertain multi-objective optimization which can be applied when seeking a pure strategy. A pure strategy, as opposed to a mixed strategy, allows the decision-maker to select and perform only one accessible alternative. The new approach takes into account the decision-maker's preference structure (importance of particular goals) and nature (pessimistic, moderate or optimistic attitude towards a given problem). It is designed for one-shot decisions made under uncertainty with unknown probabilities (frequencies), see decision-making under complete uncertainty or decision-making under strategic uncertainty. The novel approach can be used in the case of totally independent payoff matrices for particular targets.

“…In the case of ALT(A) and ALT(A)S at least one activity from each set has to be performed;  The number of scenarios for particular tasks may be different. Possible durations are estimated by experts;  Four types of time dependencies are possible ( where α denotes the coefficient of pessimism (α is close to 1 for extreme pessimists -risk averse behaviour, and β is close to 1 for radical optimists -risk prone behaviour);  For activities with scenarios (see sets DET(A)S and ALT(A)S) a weighted average is calculated on the basis of a hybrid of Hurwicz and Bayes rules (H+B rule) which is described in detail in (Gaspars-Wieloch 2014a, 2015a, 2015b, 2016a, 2016b. In H+B rule, in contradiction to well-known classical decision rules such as Hurwicz, Wald, Hayashi, Savage approaches (Hayashi 2008;Hurwicz 1952;Savage 1961;Wald 1950), all outcomes have an influence on the value of the final measure, which is quite advantageous for cases where alternatives contain many scenario values almost equal to extreme ones.…”

Section: Scenario-based Dpg Rule For Innovative Projects (Sb-dpg Rule)mentioning

confidence: 99%

Innovative Projects Scheduling with Scenario-Based Decision Project Graphs

Proceedings of 5th International Scientific Conference Contemporary Issues in Business, Management and Education ‘2017

2017

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Abstract. Decision project graphs -DPG are treated as a combination of deterministic and stochastic networks. They are designed for projects where at some stages at least one activity from a set of alternative activities is supposed to be performed. A given alternative task may differ from other activities belonging to this set in respect of times, costs and even sets of successors. Decision project graphs are used in project planning, scheduling and management. Due to the fact that especially in the case of innovative projects many factors are not completely known before the project execution, the DPG issue has been already investigated both under certainty and uncertainty. In this contribution we present a novel scenario-based DPG rule which takes into consideration possible scenarios, dependent activity durations, the decision-maker's attitude towards risk and the distribution of parameter values connected with particular activities. The procedure is especially designed for totally new (innovative) projects where it is complicated to estimate probabilities of particular scenarios since no historical data are available. The decision rule is assisted with an optimization model which can be easily solved with the use of diverse optimization computer tools. The model may support both reactive and proactive project management.