Expected Value Criterion Research Articles

Optimal Control for Parabolic Uncertain System Based on Wavelet Transformation

In this paper, we study a new type of optimal control problem subject to a parabolic uncertain partial differential equation where the expected value criterion is adopted in the objective function. The basic idea of Haar wavelet transformation is to transform the proposed problem into an approximate uncertain optimal control problem with arbitrary accuracy because the dimension of Haar basis tends to infinity. The relative convergence theorem is proved. An application to an optimal control problem with an uncertain heat equation is dealt with to illustrate the efficiency of the proposed method.

A Novel Tent-Levy Fireworks Algorithm for the UAV Task Allocation Problem Under Uncertain Environment

Recently, unmanned aerial vehicle (UAV) task allocation is a hot topic both in the civilian and military, while the research of considering uncertainty and multi-objective is still in its infancy. Firstly, based on the uncertainty theory, a mathematical model of the uncertain multi-objective UAV task allocation problem with uncertain variables in both objective function and constraint conditions is established. The expected value criterion and opportunity constraint are introduced to transform the model into a deterministic optimization model. Furthermore, because traditional fireworks algorithm (FWA) has the shortcomings of low solution accuracy and slow convergence speed in solving the UAV task allocation problem, a novel Tent-Levy FWA (TLFWA) based on discrete update process is designed by introducing integer coding, Tent chaotic mapping and Levy variation. Experimental results show that the mean cost calculated by TLFWA is 8.17% and 13.73% lower than that of FWA and particle swarm optimization algorithm respectively, which proves the effectiveness of TLFWA. This study provides a new way to solve multi-objective and uncertain decision-making problems.

A fixed charge transportation problem with damageable items under uncertain environment

An uncertain mathematical model for a fixed charge transportation problem is created in this paper. To make it closer to actuality, item damage during the transportation is considered. Besides, as some indeterministic factors may appear in the problem because of the incompletion of historical data, several parameters in this model such as purchasing price, supplies, demands and so on are regarded as uncertain variables based on uncertainty theory. After that, the original model is analyzed in two criteria of expected value criterion and chance-constrained one, and two kinds of uncertain models as well as their corresponding deterministic forms are constructed. Then, two intelligent algorithms like the genetic algorithm (GA) and the particle swarm optimization algorithm (PSO) are employed to figure out the equivalent forms of the models. Finally, the applications of the models are displayed via several numerical examples.

A novel approach for solving stochastic problems with multiple objective functions

In this paper we suggest an approach for solving a multiobjective stochastic linear programming problem with normal multivariate distributions. Our approach is a combination between a multiobjective method and a nonconvex technique. The problem is first transformed into a deterministic multiobjective problem introducing the expected value criterion and an utility function that represents the decision makers preferences. The obtained problem is reduced to a mono-objective quadratic problem using a weighting method. This last problem is solved by DC (Difference of Convex) programming and DC algorithm. A numerical example is included for illustration.

The Core of Uncertain Coalitional Game Based on Hurwicz Criterion with Application to Cyber Security Information Sharing

The coalitional game focuses on how people share the payoffs of collaboration when they form coalitions. However, we cannot accurately obtain the different coalitions’ payoffs because of the actual situation’s limitation or economic and technical factors. Therefore, we have to rely on experts in the field to estimate the likelihood of various events and give their belief degrees. To deal with the belief degrees, scholars of uncertainty theory suppose the transferable payoffs to be uncertain variables and propose the uncertain coalitional game. Many expected and optimistic solution concepts have been put forward in the literature, even though the expected value criterion does not consider the decision-maker’s attitude to risk, and the optimistic value criterion is too extreme. To better describe the different subjective judgments of decision-makers, the Hurwicz criterion is applied to the uncertain coalitional game, in which the players intend to maximize their Hurwicz payoffs. Besides, the method to discover the Hurwicz-core is provided, and the condition that the core is nonempty is proved. What’s more, the Hurwicz–Shapley value is mathematically proven to be in the Hurwicz-core in a convex uncertain coalitional game. An application in cyber security information sharing is provided.

Multistage Uncertain Random Linear Quadratic Optimal Control

In this paper, linear quadratic (LQ) optimal control problems are investigated for two types of uncertain random systems which consider the coefficient of the perturbed term as a constant vector or a vector-valued function of state vector and control vector. First, the uncertain random optimal control model is established under expected value criterion. Second, based on Bellman’s principle, recurrence equations are presented for settling such problem. Then by applying the recurrence equations and chance theory, the analytical expressions of the optimal results for the LQ problems are derived. Furthermore, some examples and an application are given to show the effectiveness of our results.

Optimal control for uncertain discrete-time singular systems under expected value criterion

Optimal control problems governed by two different types of uncertain discrete-time singular systems are investigated under expected value criterion. The objective function including uncertain variables is optimized with the help of expected value method provided that the singular systems are both regular and impulse-free. At first, based on the principle of dynamic programming, a recurrence equation is derived to simplify an optimal control model for a class of uncertain discrete-time singular systems. After that, according to uncertainty theory and the recurrence equation, two kinds of optimal control problems subject to an uncertain linear singular system and an uncertain singular system with quadratic input variables are considered in order, and the optimal solutions are both presented by accurate expressions. A numerical example and a dynamic input-output model are settled to illustrate the effectiveness of the results obtained.

Selecting a Strategy for Determining the Combine Harvester Parameter Settings

Introduction.The article deals with adjusting the parameter settings of a combine harvester working bodies. For adjustment of complex hierarchical multilevel systems, the intellectual methods based on fuzzy expert information are used. The incoming quantitative, qualitative and evaluation information is analyzed when adjusting the combine harvester. The different types of uncertainty in considering semantic spaces of external environment factors and regulated parameters of the machine cause the application of logical and linguistic approach and mathematical apparatus of fuzzy logic for determining the optimal initial settings. The complex system of interrelations between parameters, indicators of quality of harvest, and factors of external environment causes the necessity to adjust the parameters of combine working elements in the process of harvesting. This function is performed by the correction unit in the intelligent decision support system. In the present article, the questions of creating a knowledge base for correcting adjustment parameters in cases when there are deviations of values of harvesting quality indicators from normative values are considered in detail. Materials and Methods. Interrelations between performance indicators and regulated parameters are established by empirical rules obtained through the collection and analysis of expert information. To optimize the mechanism of intellectual information system output and reduce the time of decision making, there is a necessity to establish the relevance of used knowledge base rules. To solve this problem, theoretical and game approaches are used, concepts of the matrix of performance indicators and the matrix of risks of making an inefficient decision are used. Results. An example of choosing a strategy of searching for an adequate response to the fault of the harvesting indices in the form of “losses of feeble grain with chaff” has been given. The choice of fault response strategies on the basis of Laplace criterion, expectedvalue criterion, and Savage test used for decision-making in “games with nature” has been considered. The method of the decision-making process in the problem under consideration with the application of the mentioned criteria were illustrated, the analysis of the obtained results was carried out. Discussion and Conclusion. The suggested approach substantially increases performance of the unit of intelligent system updating. It allows structuring the expert knowledge base and establishing an optimal sequence of application of production rules; this provides efficiency of the updating process of the adjustable harvester parameters and also reduces the time for decision-making. This approach can be used while solving the problems of updating technological adjustments in different technical systems and devices.

Stochastic supply chain, transportation models: implementations and benefits

To transport the commodities in minimum time with maximum safety, the difficulties arise due to mutiny, territory slide, bad road and crashed communication systems, etc. and to overcome these kind of problems, the stochastic solid transportation models with safety and time objective functions under essential constraints are formulated. Taking expected value criterion, Chance-constrained programming technique, uniform distribution $$ {\mathfrak{U}}\left( {a,b} \right) $$ , exponential distribution $$ {\mathcal{E}\mathcal{X}\mathcal{P}}\left( \beta \right) $$ and normal distribution $$ {\mathcal{N}}\left( {\mu ,\sigma^{2} } \right) $$ , four new de-randomization processes are proposed to handle the stochastic programming problem. Finally, the deterministic form of the model is solved using generalized reduced gradient techniques (LINGO.13.0 optimization software). Finally, an enlarge comparison of the proposed concept with the earlier concept are presented and the nature of the solutions is discussed.

A novel uncertain bimatrix game with Hurwicz criterion

In an uncertain bimatrix game, different uncertain equilibrium strategies have been proposed based on different criterions, such as expected value criterion, optimistic value criterion and uncertain measure criterion. This paper further presents an uncertain bimatrix game with Hurwicz criterion and defines a new solution concept Hurwicz Nash equilibrium. Furthermore, its existence theorem is also proved, and a sufficient and necessary condition is presented to find the Hurwicz Nash equilibrium. Finally, an example is provided for illustrating the usefulness of Hurwicz Nash equilibrium.

Can advisors eliminate the outcome bias in judgements and outcome-based emotions?

PurposeAn outcome bias occurs when performance is evaluated based upon the outcome of the decision rather than upon the quality of the decision itself. The purpose of this paper is to test experimentally whether advisors eliminating the uncertainty in the quality of decisions as a potential driver of the outcome bias can eliminate this bias in judgements. Additionally, the paper analyses whether such advisors can attenuate the emotional experience after decisions’ outcomes by supporting the cognitive understanding of these outcomes.Design/methodology/approachThe paper employs a between-subject experimental setting where decision makers are asked to make investment decisions. The two variables manipulated were advice (receiving advice vs deciding without an advice) and state (loss vs neutral vs gain state). Participants were randomly assigned to each group. One group completed all tasks while receiving advice before making a final decision. Another group completed all tasks without any advice. After completing each investment task, participants were randomly assigned to one of three possible states that determine their payoff.FindingsThe results reveal that advisors eliminating the uncertainty in the quality of decision can eliminate the outcome bias in the judgements of decision quality, especially after bad outcomes. Nevertheless, after controlling for the perceived quality of the decisions, advised individuals show a greater emotional sensitivity to bad outcomes than non-advised decision makers. These observations suggest that advisors eliminating the uncertainty in the decision quality can improve the understanding that good decisions can lead to bad outcomes just by chance, but they are not able to prevent affective reactions after bad outcomes; on the contrary, they may even reinforce them.Research limitations/implicationsThe observation that, after bad outcomes, advised decision makers are less willing to decide the same way than non-advised decision makers is consistent with empirical findings on the risk-taking behaviour of self-directed and mutual fund investors. Self-directed investors are less likely to revise their decision and sell an investment at a loss than mutual fund investors (Chang et al., 2016). While investors might sell funds because they are unable to observe the decision process of the manager and use the outcome to judge the manager’s skills, this study shows that such learning from decision outcomes is not necessary for observing the risk-taking behaviour of the investors. Even if the decision process of the advisor is observable (as in this study), the decision makers’ willingness to decide the same way is influenced by the losses – an effect that goes beyond the assessed quality of advice as the results of this study show.Practical implicationsThe results of this study have important implications for advisors aiming to maintain a positive relationship with their clients. Convincing clients that an advice is optimal supports their understanding that a good advice can have bad outcomes. However, this understanding may not prevent affective reactions after bad outcomes. On the contrary, the affective response after bad outcomes is even stronger with the advice than without it. Hence, advisors should address not only issues related to the quality of the provided advice, but also emotional aspects, which could be related to what clients expect from following the advice.Originality/valueThis study is one of the few that account for the possibility that the outcome bias may arise because there is uncertainty regarding the optimal choice. In particular, this paper uses a much more powerful criterion to define an optimal choice than the expected value criterion used in previous studies. The criterion represents a minimal requirement for rational behaviour in expected utility theory and many non-expected utility theories.

Hybrid Vigor

The ecological approach to rationality involves evaluating choice processes instead of choices themselves, and there are good reasons for doing this. Proponents of the ecological approach insist that objective performance criteria (such as monetary gains) replace axiomatic criteria, but this claim is highly contentious. This paper investigates these issues through a case study: 12 risky choice processes are simulated, and their performance records are compared. The first criterion is conformity to the Expected Utility axioms; the Priority Heuristic stands out for frequently violating Transitivity. Next, the Expected Value criterion is applied. Minimax performs especially poorly—despite never violating an axiom—highlighting the tension between axiomatic (coherence) and objective (correspondence) criteria. Finally, I show that axiom violations carry high costs in terms of expected value. Accordingly, coherence does not guarantee objectively high performance, but incoherence does guarantee diminished performance.

Modeling and optimization of a road–rail intermodal transport system under uncertain information

A realistic road–rail intermodal transport system can be suitably modeled as a hub-and-spoke (H&S) network for which the parameters are subject to fuzzy uncertainty: demand, cost and time. For modeling uncertainty, we present a bi-objective optimization formulation for the hub-and-spoke based road–rail intermodal transportation (HS-RRIT) network design problem by taking into account the expected value criterion and the critical value criterion. Using the weighted sum method, we reformulate a single-objective mixed-integer linear programming (MILP) model to solve the equivalent HS-RRIT network design problem. Given the inherent complexity for solving this problem, we develop a memetic algorithm (MA) to obtain high quality solutions. This algorithm utilizes a genetic search method to explore the search space and two different local search strategies called shift and exchange to exploit information in the search region. Finally, we conduct computational analysis over the Turkish network data set to demonstrate the applicability of proposed model and the effectiveness of solution method.

Decision Criterion and Value of Information Analysis: Optimal Aspirin Dosage for Secondary Prevention of Cardiovascular Events.

In value of information (VOI) calculations, such as the expected value of perfect information (EVPI), partial perfect information (EVPPI), sample information (EVSI) or implementation (EVIM), the maximum expected value criterion defines the decision making criterion for the adoption of decisions for treatments. However, because decision makers are often risk averse, the uncertainty that accompanies a decision problem may influence adoption decisions. VOI estimates were studied based on 2 alternate decision making criteria: 1) maximum expected value and 2) 95% credible intervals. These criteria were applied to a probabilistic minimal lifetime model of incident cardiovascular events and mortality among target patients comparing 2 daily doses of aspirin (81 mg and 325 mg). Model parameters were based on literature reviews and data analyses. Expected life-years under 81 v. 325 mg of aspirin were estimated to be 14.86 (SE, 0.10) and 14.72 (0.31) respectively, with a difference of 0.14 (0.29). The probability that 81 mg was optimal was estimated to be 67%. Under Decision Criterion 1, EVIM and EVPI were about 233-thousand and 411-thousand years, respectively. Under Criterion 2, EVIM was undefined, as there remains ambiguity about what to implement. Consequently, EVPI becomes the entire 644-thousand years. Also, under Criterion 1, EVSI reaches an asymptote at a sample size of 10,000 per arm, with minimal gains in value beyond a 5,000 person per arm trial. With Criterion 2, a sample size of 10,000 per arm or higher is substantially more valuable than lower sample sizes. Alternative decision criteria for treatment adoption change the VOI. Decision criteria should be justified for VOI analyses. If multiple criteria may be relevant, analysts should complete VOI estimates using multiple criteria.

A three-echelon supply chain with asymmetric information under uncertainty

This paper investigates a three-echelon supply chain problem in which multiple suppliers, a single manufacturer and a single retailer are participants. The manufacturer selects suppliers and estimates quantity of defective components purchased from the suppliers, but the quality information is unavailable for the manufacture due to asymmetric information. In addition, customers’ demands could not be predicated accurately either. Under this circumstance, quantity of defective components and demands of customers are all characterized as uncertain variables according to real trade. Based on uncertainty theory, three models under different criteria such as expected value criterion, chance-constrained one and measure-chance one are constructed for the problem and corresponding solution approach is proposed as well under uncertain environment. Finally, some numerical examples are given to show the applications of the problem.

A generalized maximin decision model for managing risk and measurable uncertainty

ABSTRACTWe propose an innovative approach to probabilistic decision making, in which the optimal selection is made both for a decision alternative to manage risk and for a collection of measurable events to simultaneously manage uncertainty as measured by information entropy. The resulting generalized maximin model is a combinatorial optimization problem for maximizing the expected value of a random variable, defined as the minimum return in a given event, over all measurable events in a discrete sample space. The collection of measurable events and applicable probability measure are endogenously determined by a partition of the sample space and optimized for a given index that specifies the number of constituent events. The modeling approach is very general, encompassing as a special case the maximin decision criterion and providing an equivalent solution to the expected value criterion with other cases representing trade-offs between these criteria. A dynamic programming algorithm for solving the non-diversified model in polynomial time is developed. Diversification of the decisions results in a nonlinear integer optimization model that is transformed to an easily solvable mixed-integer linear model. Publicly available data of 79 investments over 10 periods are used to compare the model with mean–variance, conditional value-at-risk, and constrained maximin models.

Uncertain extensive game with application to resource allocation of national security

Uncertain theory is a powerful tool for describing human uncertainty, especially in social economic studies. In this paper, we consider finite extensive games with payoffs being uncertain variables. We introduce three different criteria: the expected value criterion, the optimistic value criterion and the pessimistic value criterion to describe players’ behaviors in different decision-making situations. Accordingly, three types of uncertain equilibria and uncertain subgame perfect equilibria for the uncertain extensive game are proposed. Moreover, we provide theorems to prove the existence of uncertain equilibria and uncertain subgame perfect equilibria. Finally, the resource allocation problem for national security is formulated and analyzed using the uncertain extensive game. Results show that different decision criteria may lead to different subgame perfect equilibria, demonstrating the significance of introducing different uncertain subgame perfect equilibria.

Pricing and effort decisions for a supply chain with uncertain information

This paper analyses the pricing and effort decisions of a supply chain with single manufacturer and single retailer. The manufacturer produces a kind of product and then wholesales the product to the retailer, who in turn retails it to customers over a single selling season. The retailer can influence demand through her sales effort. This research depicts the consumer demand, the manufacturing cost and the sales effort cost as uncertain variables. Considering the demand expansion effectiveness of sales effort, one centralised and three decentralised game models are built on the basis of the expected value criterion, and the equilibrium solutions are obtained. We investigate the effects of the parameters’ uncertainty degrees on the pricing and effort decisions. The results indicate that the manufacturer benefits from improvement in demand and cost uncertainties when he has at least bargaining power in the supply chain. The results also imply that the uncertainty degree of sales effort elasticity has an outstanding influence on the pricing and effort decisions, whereas the uncertainty degree of price elasticity has a modest impact on these decisions. We also study the effects of the parameters’ uncertainty degrees on the supply chain from the consumers’ perspective. The results suggest that with a power retailer, the retail price should always be on the high end. Consequently, consumers do not necessarily benefit from a power retailer. When the manufacturer and the retailer have equal bargaining power, consumers do not necessarily benefit from the supply chain, either.

Multi-product newsvendor problem with hybrid demand and its applications to ordering pharmaceutical reference standard materials

Uncertainty is inherent in the newsvendor problem. Most of the existing literature is devoted to characterizing the uncertainty either by randomness or by fuzziness. However, in many cases, randomness and fuzziness simultaneously appear in the same problem. Motivated by this observation, we investigate the multi-product newsvendor problem by considering the demands as hybrid variables which are proposed to describe quantities with double uncertainties. According to the expected value criterion, we formulate an expected profit maximization model and convert it to a deterministic form when the chance distributions are given. We discuss two special cases of hybrid variable demands and give their chance distributions. Then we design hybrid simulation to estimate the chance distribution and use genetic algorithm to solve the proposed models. Finally, we proceed to present numerical examples of purchasing pharmaceutical reference standard materials to illustrate the applicability of our methodology and the effectiveness of genetic algorithm.

Half-full or half-empty? A model of decision making under risk

We propose a descriptive model of decision making under risk, inspired by the “half-full, half-empty” glass metaphor, that explains well-known paradoxes identified by Allais (1953), Kahneman and Tversky (1979), and Birnbaum (2008). The model is intuitive in that it is closely related to the expected value criterion and its parameters have a clear behavioral interpretation, and parsimonious in that it provides an approach to modeling behavior based on only two parameters.