Repair strategies in an uncertain environment: Markov decision process approach

This paper deals with repair strategies that maximize the time until a catastrophic event, that is, when there is a vital need for equipment, and the equipment fails to function. We examine the case where the need for the equipment varies over time according to a Markov chain. This means that the environment can be in different states, each with their own probability of the initiating event occurring. We model the form of the optimal policy for repair under this uncertain environment by Markov decision processes.     

Maximal elements in noncompact spaces with application to equilibria

A new maximal theorem for -majorized correspondences in noncompact spaces is presented and applied to obtain an equilibrium existence theorem for noncompact abstract economies. The corresponding results of Borglin and Keiding (1976), Yannelis and Prabhakar (1983), Ding and Tan (1993), Yuan and Tarafdar (1996), and Ding and Yuan (1998) are generalized by our results.

     

A Hartman-Grobman result for retarded functional differential equations with an application to the numerics around hyperbolic equilibria

A weak form of the Hartman-Grobman theorem for retarded functional differential equations around hyperbolic equilibria is presented. Orbits on a center-unstable manifold are compared to orbits on a center-unstable subspace of the linearized equation. The result is applied to obtain a conjugacy between the semidynamical system generated by the functional differential equation and its numerical approximation. A version of the Hartman-Grobman theorem around hyperbolic periodic orbits of functional differential equations is also given.     

Comparing hiring strategies in a committee with similarity biases

We present an organizational model that develops organizational expertise and socialization with a hiring process informed by the inherent biases of individuals. We present factors that we believe critically impact candidate selection, literature related to these factors, and our resulting equations. We discuss the model, and present two virtual experiments. The first virtual experiment was used to validate the new model by comparing the implementation with an existing reference implementation—we found similar patterns—which established relational equivalence. The second virtual experiment compared organizations with and without a stochastic selection process and with various selection strategies. Organizations that stressed socialization tended to need to review more (otherwise equally qualified) applicants than organizations that did not, and organizations that were able to deliberate more thoroughly found turnover less effective at maintaining organizational performance. Larger committees reduced the number of applicants that needed to be reviewed in firms that valued diversity, but offered no particular benefit to other organizations.     

Incentive strategies and equilibria for dynamic games with delayed information

The construction of time-lag incentive strategies for continuous time convex problems is considered. The strategies are affine in the data available and they are represented by means of Stieltjes measures. It is shown how incentive strategies can be used as equilibrium strategies in symmetric games where the decision makers are cooperative.This work was supported by the Research Council for Technology of the Academy of Finland and by the Emil Aaltonen Foundation.     

Strong equilibria of a repeated game with randomized strategies

A version of Aumann's (1976) model of a repeated game with randomized strategies is studied. The pure strategy set of each player is assumed to be a compact metric spacnd complexities due to the information structures are explicitly handled. It is shown that one can extend Aumann's argument to this setup and still prove the Aumann Proposition on equivalence of the β-core of a one-shot game with correlated strategies and the strong equilibrium utility allocations of the associated repeated game with randomized strategies. To this extended version of the Aumann Proposition, the author's theorem for nonemptiness of the β-core with correlated strategies is applicable, so this version is non-vacuous.     

On truncations and perturbations of Markov decision problems with an application to queueing network overflow control

Conditions are provided to derive error bounds on the effect of truncations and perturbations in Markov decision problems. Both the average and finite horizon case are studied. As an application, an explicit error bound is obtained for a truncation of a Jacksonian queueing network with overflow control.     

An innovative unification process for probabilistic hesitant fuzzy elements and its application to decision making

Fuzzy Optimization and Decision Making - The probabilistic hesitant fuzzy element (PHFE) is a worthwhile extension of hesitant fuzzy element (HFE) which is a means of allowing the decision makers...     

On the application of TRIMAP to problems with multiple decision makers

In this paper the potentialities of TRIMAP to provide decision support in multiobjective problems with multiple decision makers are exploited. TRIMAP is an interactive three-objective linear programming package which enables a progressive and selective learning of the nondominated solution set. The aim is to aid the opposing parties in exploring their own preferences and to explore the dynamic nature of the negotiation process.     

Periodic switching strategies for an isoperimetric control problem with application to nonlinear chemical reactions

This paper deals with an isoperimetric optimal control problem for nonlinear control-affine systems with periodic boundary conditions. As it was shown previously, the candidates for optimal controls for this problem can be obtained within the class of bang-bang input functions. We consider a parametrization of these inputs in terms of switching times. The control-affine system under consideration is transformed into a driftless system by assuming that the controls possess properties of a partition of unity. Then the problem of constructing periodic trajectories is studied analytically by applying the Fliess series expansion over a small time horizon. We propose analytical results concerning the relation between the boundary conditions and switching parameters for an arbitrary number of switchings. These analytical results are applied to a mathematical model of non-isothermal chemical reactions. It is shown that the proposed control strategies can be exploited to improve the reaction performance in comparison to the steady-state operation mode.     

Measuring consensus in decision making: an application to maritime command and control

An important component of maritime command and control is the information that has value to Royal Navy commanders in making campaign decisions. Studies aimed at identifying information requirements generally do so in a wargame context with several test subjects assuming command roles. An important adjunct to this work then is the assessment of how closely the subjects agree that the proposed information set is indeed valuable. In this paper, we focus on assessing the degree to which the test subjects participating in a MoD sponsored maritime command and control study agreed to a proposed set of information elements deemed valuable to taking combat decisions. The methodology involves the simulation of naval combat. The participants (former Royal Navy Captains and Admirals) are asked to choose a course of action that best accomplishes a stated mission. Information is provided on request. Each pair of participants is characterized by its set of information requirements. The objectives are (1) to define an overall information set that minimizes disagreement among the participants in some way; and (2) to develop a metric that assesses the amount of disagreement among the participants. Two metrics are presented: a mean consensus and a median consensus.     

A theory of motivation and satisfaction with application to decision support

The paper deals with optimization of allocation of human resources among different activities. It is assumed that an individual is characterized by a risk averse and constant return to scale utility function of two variables: motivation to perform and reward following the performance. The individual is trying to maximize the utility by the best allocation of his time resources among the activities and by selecting the best portfolio of activities. Motivations are regarded, generally, as the product of the individual's preferences (i.e. subjective choice probabilities), productivities of time, output prices, performance and access probabilities, etc., while the rewards are profits or salaries connected with each activity. Satisfaction is defined as the maximum of utility attained for the optimum allocation and selection strategies. It is shown that for the given equitable reward rate, the optimum allocation and portfolio selection strategies can be derived explicitly and the derivation does not require the explicit knowledge of the individual's utility function.     

On the concept of decision aiding process: an operational perspective

The paper presents the concept of decision aiding process as an extension of the decision process. The aim of the paper is to analyse the type of activities occurring between a “client” and an “analyst” both engaged in a decision process. The decision aiding process is analysed both under a cognitive point of view and an operational point of view: i.e. considering the “products”, or cognitive artifacts the process will deliver at the end. Finally the decision aiding process is considered as a reasoning process for which the update and revision problems hold.     

Fractional Liu process with application to finance

As a fuzzy counterpart of Brownian motion, Liu process has attracted more and more attention in the recent literature. In this paper, the concept of fractional Liu process is proposed as an extension of Liu process. Furthermore, we obtain the expressions of the membership functions, expected values and variances of arithmetic and geometric fractional Liu processes for each fixed time. As an application, geometric fractional Liu process is assumed to characterize the stock price, which formulates a new fuzzy stock model. Based on this proposed model, European option pricing formulas are gained and two numerical examples are given with different parameters.     

Finite horizon semi-Markov decision processes with application to maintenance systems

This paper investigates finite horizon semi-Markov decision processes with denumerable states. The optimality is over the class of all randomized history-dependent policies which include states and also planning horizons, and the cost rate function is assumed to be bounded below. Under suitable conditions, we show that the value function is a minimum nonnegative solution to the optimality equation and there exists an optimal policy. Moreover, we develop an effective algorithm for computing optimal policies, derive some properties of optimal policies, and in addition, illustrate our main results with a maintenance system.     

Local decision making and decision fusion in hierarchical levels

Hierarchical problem solving is preferred when the problem is overwhelmingly complicated. In such a case, the problem should better be analyzed in hierarchical levels. At each level, some temporary solutions are obtained; then a suitable decision fusion technique is used to merge the temporary solutions for the next level. The hierarchical framework proposed in this study depends on reutilization or elimination of previous level local agents that together perform the decisions due to a decision-fusion technique: a performance criterion is set for local agents. The criterion checks the success of agents in their local regions. An agent satisfying this criterion is reutilized in the next level, whereas an agent not successful enough is removed from the agent pool in the next level. In place of a removed agent, a number of new local agents are developed. This framework is applied on a fault detection problem.      

A queue with instantaneous tri-route decision process

This paper focuses on the study of several random processes associated with M/G1 queue with instantaneous tri-route decision process. The stationary distribution of the output process is derived. Some particular queues with feedback and without feedback are also analysed. Some operating characteristics are studied for this queue. Optimum service rate is obtained. A numerical study is carried out to test the feasibility of the queueing model.     

Extremal equilibria for monotone semigroups in ordered spaces with application to evolutionary equations

We consider monotone semigroups in ordered spaces and give general results concerning the existence of extremal equilibria and global attractors. We then show some applications of the abstract scheme to various evolutionary problems, from ODEs and retarded functional differential equations to parabolic and hyperbolic PDEs. In particular, we exhibit the dynamical properties of semigroups defined by semilinear parabolic equations in RN with nonlinearities depending on the gradient of the solution. We consider as well systems of reaction-diffusion equations in RN and provide some results concerning extremal equilibria of the semigroups corresponding to damped wave problems in bounded domains or in RN. We further discuss some nonlocal and quasilinear problems, as well as the fourth order Cahn-Hilliard equation.     

A soft multi-criteria decision analysis model with application to the European Union enlargement

This paper proposes a new multi-criteria decision analysis (MCDA) model that uses a series of existing intuitive and analytical methods to systematically capture both objective and subjective beliefs and preferences from a group of decision makers (DMs). A defuzzification method that combines entropy and the theory of displaced ideal synthesizes crisp values from the DMs’ subjective judgments. This approach assists the DMs in their selection process by plotting alternatives in a four quadrant graph and considering their Euclidean distance from the “ideal” choice. A pilot study illustrates the details of the proposed method. The DMs were a group of graduate students from the University of Paderborn in Germany. The pilot study concerned the addition of new members into the European Union (EU), a decision that has profound economic and political effects on both the entering and existing members of the Union. The DMs were required to consider a large number of internal strengths and weaknesses and external opportunities and threats in assessing the decision to enlarge the EU. Although the pilot study was not performed by actual DMs from the EU, it was an excellent platform for testing the proposed model.