Maciej Nowak

Preference and veto thresholds in multicriteria analysis based on stochastic dominance

Abstract In the paper, a discrete stochastic multiattribute problem is considered. It is assumed that the performance probability distribution for each alternative on each attribute is known. Stochastic dominance approach is employed in comparing evaluations of alternatives with respect to attributes. The concept of pseudo-criteria is employed. We assume that three situations can be considered when preferences are modeled with respect to single attribute: strict preference, weak preference and indifference. Preference threshold is used to distinguish situations of strict and weak preference. ELECTRE-III distillation procedures are employed in construction of multiattribute ranking. The approach could be an appropriate method, e.g. in finance, insurance and production process control.

Aspiration level approach in stochastic MCDM problems

The paper considers a discrete stochastic multiple criteria decision making problem. This problem is defined by a finite set of actions A, a set of attributes X and a set of evaluations of actions with respect to attributes E. In stochastic case the evaluation of each action with respect to each attribute takes form of a probability distribution. Thus, the comparison of two actions leads to the comparison of two vectors of probability distributions. In the paper a new procedure for solving this problem is proposed. It is based on three concepts: stochastic dominance, interactive approach, and preference threshold. The idea of the procedure comes from the interactive multiple objective goal programming approach. The set of actions is progressively reduced as the decision maker specifies additional requirements. At the beginning the decision maker is asked to define preference threshold for each attribute. Next, at each iteration the decision maker is confronted with the set of considered actions. If the decision maker is able to make a final choice then the procedure ends, otherwise he/she is asked to specify aspiration level. A didactical example is presented to illustrate the proposed technique.

INSDECM--an interactive procedure for stochastic multicriteria decision problems

Abstract A new interactive technique for a discrete stochastic multiattribute decision making problem is proposed in this paper. It is assumed that performance probability distribution for each action on each attribute is known. Two concepts are combined in the procedure: stochastic dominance and interactive approach. The first one is employed for generating efficient actions and constructing rankings of actions with respect to attributes. The second concept is used when the communication between the DM and the model is conducted. It is assumed that decision maker’s restrictions are defined by specifying minimal or maximal values of scalar criteria measuring either expected outcome or variability of outcomes. As such restrictions are, in general, not consistent with stochastic dominance rules, we suggest verifying this consistency and asking the decision maker to redefine inconsistent restrictions.

Interactive Multicriteria Decision Aiding Under Risk—Methods and Applications

In the paper a discrete multicriteria decision making problem under risk is considered. It is assumed that the set of alternatives consists of a finite number of elements that are explicitly described. The evaluations of alternatives with respect to criteria are represented by distribution functions. The decision maker tries to find a solution preferred to all other solutions. To solve the problem one has to analyze the decision makers preferences. In the study interactive approach is used. Three interactive methods and its applications in operations management are presented.

Trade-Off Analysis in Discrete Decision Making Problems Under Risk

The paper considers a discrete stochastic multi-attribute decision making problem. This problem is defined by a finite set of alternatives A, a set of attributes X and a set E of evaluations of alternatives with respect to the attributes. In the stochastic case the evaluation of each alternative with respect to each attribute is characterized by a random variable. Thus, the comparison of two alternatives leads to the comparison of two vectors of probability distributions. In the paper a new interactive procedure for solving this problem is proposed. At each iteration a candidate alternative is proposed to the decision maker. If he/she is satisfied with the proposal, the procedure ends. Otherwise, the decision maker is asked to select the attribute to be improved and the attributes that can be decreased, ordered lexicographically starting with the one to be decreased first. The relations between distributions of trade-offs are used to generate a new proposal. An example is presented to illustrate the proposed technique.

Inverse Stochastic Dominance and its Application in Production Process Control

We are considering the problem of production process control in a firm, where a point to point type of production organisation is applied and production process control is held according to the Just-in-Time rule. In our paper we propose to solve the problem of production process control as a multiattribute problem. The algorithm, which we are proposing is built on a concept of outranking relation and inverse stochastic dominance. The multiattribute analysis, based on stochastic dominance, applies the utility theory to individual attributes in order to determinate a concordance level among them.

Solving a Multicriteria Decision Tree Problem Using Interactive Approach

Making decisions involves prediction of future outcomes. In the real world, however, predictions are not known with certainty. Moreover, in serious problems multiple criteria must be taken into account. Various techniques for multicriteria decision-making problems under risk are proposed. Most of them assume that the decision process can be reduced to a single act of choice. However, real-world decision problems are often dynamic, which means that a series of choices must be made. In the paper, a new technique for a dynamic multicriteria decision-making problem under risk is proposed. The method uses a decision tree and interactive approach. A real-world example is presented to show applicability of the procedure.

Scheduling non-critical activities using multicriteria approach

In many projects the problem of selecting the start time of a non-critical activity arises. Usually it is possible to use the “as soon as possible” or “as late as possible” rules. In some situations, however, the result of such a decision depends on external factors such as exchange rate. This leads to an approach in which the problem of scheduling non-critical activities is solved using an expanded Cox–Ross–Rubinstein (CRR) binomial tree method. In the paper a bi-criteria problem of determining the start time of a non-critical activity is considered. We assume that the early start and the late start of the activity have been identified using Critical Path Method, but the project manager is free to select the time when the activity will actually be started. This decision cannot, however, be changed later, as it is associated with the allocation of key resources. Two main criteria are considered: cost and risk. While cost depends on exchange rate, risk increases with the delay of the start of the activity. The problem can be described as a dynamic process. We propose a new interactive technique for solving such a bi-criteria decision making problem under risk. The procedure uses trade-offs to identify a candidate solution. The CRR binomial method is applied to evaluate the cost of the activity.

Optimal and Near-Optimal Strategies in Discrete Stochastic Multiobjective Quasi-hierarchical Dynamic Problems

Multi-stage, multi-criteria discrete decision processes under risk are considered and Bellmans principle of optimality is applied. Quasi-hierarchy of multi-period criteria is determined by the decision maker. The aim of the paper is to propose an algorithm to solve quasi-hierarchical problem according to decision maker’s requirements. The process of obtaining the final solution is interactive.

Hybrid MCDM Model for the Value Evaluation of the Restoration of Historical Objects

As time goes by, every historic object dilapidates and wears out. As the result, the values that it used to represent become obliterated and its effete on the public is weakened. Conservation and restoration of art works aim at preserving the extant matter and, if possible, at bringing the antiques to their former glory in historical value; the more so that the historical value of the objects also increases with time. Conservators’ work, independently of their special fields of interest, should be preceded by research whose goal is the determination of the guidelines for the conservation efforts and the selection of the best methods of action in interdependence and feedback among dimensions and criteria. A thorough analysis determines several possibility methods of action, emphasizing various groups of values. In this study, a hybrid Multiple Criteria Decision Making (MCDM) model based on DNP (DEMATEL-based ANP) is used to assess the historical objects relative values viewed by different groups of experts in inter-relationship problem of real world. The procedures provide a reference guide of improvement directions and efficient art work reservation of historical objects for achieving the aspiration levels.