The paper presents a new scenario-based decision rule for the classical version of the newsvendor problem (NP) under complete uncertainty (i.e. uncertainty with unknown probabilities). So far, NP has been analyzed under uncertainty with known probabilities or under uncertainty with partial information (probabilities known incompletely). The novel approach is designed for the sale of new, innovative products, where it is quite complicated to define probabilities or even probability-like quantities, because there are no data available for forecasting the upcoming demand via statistical analysis. The new procedure described in the contribution is based on a hybrid of Hurwicz and Bayes decision rules. It takes into account the decision maker’s attitude towards risk (measured by coefficients of optimism and pessimism) and the dispersion (asymmetry, range, frequency of extremes values) of payoffs connected with particular order quantities. It does not require any information about the probability distribution.
The Hurwicz's criterion is one of the classical decision rules applied in decision making under uncertainty as a tool enabling to find an optimal pure strategy both for interval and scenarios uncertainty. The interval uncertainty occurs when the decision maker knows the range of payoffs for each alternative and all values belonging to this interval are theoretically probable (the distribution of payoffs is continuous). The scenarios uncertainty takes place when the result of a decision depends on the state of nature that will finally occur and the number of possible states of nature is known and limited (the distribution of payoffs is discrete). In some specific cases the use of the Hurwicz's criterion in the scenarios uncertainty may lead to quite illogical and unexpected results. Therefore, the author presents two new procedures combining the Hurwicz's pessimism-optimism index with the Laplace's approach and using an additional parameter allowing to set an appropriate width for the ranges of relatively good and bad payoffs related to a given decision. The author demonstrates both methods on the basis of an example concerning the choice of an investment project. The methods described may be used in each decision making process within which each alternative (decision, strategy) is characterized by only one criterion (or one synthetic measure).
The paper contains a description of a new approach (called the SF + AS method, i.e. the scenario forecasting + alternative selection method) that can be used in decision making under uncertainty when pure optimal strategies are sought-after. This procedure takes into consideration the level of decision maker's coefficient of optimism (or coefficient of pessimism) and consists of two stages: the true scenario forecasting (on the basis of the decision maker's preferences) and the appropriate alternative selection by taking into account the payoffs of the appointed true scenario or the most probable scenarios. In contradiction to existing decision rules, this procedure assumes that the decision making process should involve only a part of the payoff matrix because only one state of nature will occur in the end. The second essential difference between the SF + AS method and other decision rules is that in the first one there is an attempt to appoint globally the best and the worst scenario (regardless the alternative considered). Meanwhile, other procedures determine the status of a given event depending on the decision.
The paper contains a description of a possible modification of the original Net Present Value which allows one to evaluate projects under uncertainty with unknown probabilities (understood mainly as frequencies). Cash flows are usually uncertain since both incomes and expenditure related to the project concern the future. Additionally, probabilities of particular scenarios may be unknown due to many factors (e.g. the diversity of definitions for probability, lack of historical data, lack of sufficient knowledge about possible states of nature). The novel approach is based on a hybrid of Hurwicz and Bayes decision rules and is supported by a sensitivity analysis. The new method applies scenario planning and takes into account the decision maker's attitude towards a given decision problem (measured by coefficients of pessimism and optimism). The procedure can be used even in the case of asymmetric distributions of net cash flows at particular periods since it considers the frequency of each value. The modification of the Net Present Value may support any uncertain multi-period economic decision.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.