Decision Maker's Preference Structure Research Articles

A Robust Interactive Desirability Function Approach for Multiple Response Optimization Considering Model Uncertainty

To solve multiple response optimization problems that often involve incommensurate and conflicting responses, a robust interactive desirability function approach is proposed in this article. The proposed approach consists of a parameter initialization phase and calculation and decision-making phases. It considers a decision maker's preference information regarding tradeoffs among responses and the uncertainties associated with predicted response surface models. The proposed method is the first to consider model uncertainty using an interactive desirability function approach. It allows a decision maker to adjust any of the preference parameters, including the shape, bound, and target of a modified robust function with consideration of model uncertainty in a single and integrated framework. This property of the proposed method is illustrated using a tire tread compound problem, and the robustness of the adjustments for the approach is also considered. The new method is shown to be highly effective in generating a compromise solution that is faithful to the decision maker's preference structure and robust to uncertainties associated with model predictions.

Integrating simulation and FITradeoff method for scheduling rules selection in job-shop production systems

Scheduling decisions related to due date assignment, order release and priority dispatching affect multiple performance dimensions simultaneously. Previous job-shop studies based on simulation and multiobjective optimization techniques do not explore the goals that a decision-maker (DM) wishes to reach, when assessing compensations between multiple benefits and potential impacts yielded by a combination of rules. With the aim of reflecting the DM's preference structure on scheduling decisions, this paper considers a discrete event simulation approach integrated with the Flexible and Interactive Tradeoff (FITradeoff) compensatory method to identify the best combination of due date assignment, order release and shop dispatching rules. Through discrete event simulation, the performance of different combinations of rules and inherent parameters are evaluated with regard to the attributes of total cost, production quantity, total throughput time, and tardiness. The FITradeoff method is used to compensate the disadvantage in one of the performance attributes with the advantage in other attributes, considering the DM's preferences which are elicited in a procedure that requires less information in order to make comparisions between multiple simulated consequences. A numerical application is set out using realistic data from a manufacturer of ladies' shoes so as to visualize and discuss the steps of the model and its usefulness in practice.

ADDITIVE-VETO MODELS FOR CHOICE AND RANKING MULTICRITERIA DECISION PROBLEMS

Using additive models for aggregation of criteria is an important procedure in many multicriteria decision methods. This compensatory approach, which scores the alternatives straightforwardly, may have significant drawbacks. For instance, the Decision Maker (DM) may prefer not to select alternatives which have a very low performance in whatever criterion. In contrast, such an alternative may have the best overall evaluation, since the additive model may compensate this low performance in one of the criteria as a result of high performance in other criteria. Thus, additive-veto models are proposed with a view to considering the possibility of vetoing alternatives in such situations, particularly for choice and ranking problems. A numerical application illustrates the use of such models, with a detailed discussion related to real practical problems. Moreover, the results obtained from a numerical simulation show that it is not so rare for a veto of the best alternative to occur in the additive model. This is of considerable relevance depending on the DM's preference structure.

A generalized model for data envelopment analysis with interval data

Data envelopment analysis (DEA) is a method to estimate the relative efficiency of decision-making units (DMUs) performing similar tasks in a production system that consumes multiple inputs to produce multiple outputs. So far, a number of DEA models with interval data have been developed. The CCR model with interval data, the BCC model with interval data and the FDH model with interval data are well known as basic DEA models with interval data. In this study, we suggest a model with interval data called interval generalized DEA (IGDEA) model, which can treat the stated basic DEA models with interval data in a unified way. In addition, by establishing the theoretical properties of the relationships among the IGDEA model and those DEA models with interval data, we prove that the IGDEA model makes it possible to calculate the efficiency of DMUs incorporating various preference structures of decision makers.

Fusion of artificial neural networks and genetic algorithms for multi-objective system reliability design optimization

In this work, artificial neural networks (ANNs) are used to include the decision-maker's preference structure within a genetic algorithm (GA) search of the optimal system reliability configuration. For verification, the proposed approach is applied to two literature case studies of increasing complexity concerning the optimization of the reliability design of a series system.

An algorithm for solving multiobjective problem with multiple Decision Makers

This article aims to develop an algorithm for solving multiobjective linear programming problems with multiple Decision Makers (DMs) which combines the interactive fuzzy method and a heuristic based on iterative computation. DMs' preference can be quantified with a membership function and a threshold which means the minimum level of acceptance of a solution. The proposed heuristic can automatically search for the best set of weights for the linear utility function. Since the global goal for the proposed heuristic is to minimise the average of all the membership value deviation from the threshold, over- as well as under-achievement in the objective function will be penalised. The algorithm is implemented with Matlab and GAMS and applied to a problem in warehouses with three different objective functions. The results illustrates that the developed algorithm is effective in providing efficient solutions with respect to different preference structures of DMs.

A generalized model in presence undesirable factors

Many production processes yield both desirable factors(input/output) and undesirable ones. Efficiency measurment is usually based on the assumption that desirable inputs and undesirable outputs have to minimized and desirable outputs and undesirable inputs have to be maximized.So far, a number of UDEA(DEA in present undesirable factors) models have been developed: The UCCR, UBCC models and the UFDH model are well known as basic UDEA model. In this paper, we suggest a model call generalized UDEA(UGDEA)model,which can treat the above stated basic DEA models in a unified way. In addition,by establishing the theoretical properties on relationship among the UGDEA model and those UDEA models, we prove that the UGDEA model make it possible to calculate the efficiency of DMU incorporating various preference structures of decision makers.

Optimal Weighting of Bias and Variance in Dual Response Surface Optimization

Dual response surface optimization simultaneously considers the mean and the standard deviation of a response. The minimization of the mean squared error (MSE) is a simple, yet effective, approach in dual response surface optimization. The bias and variance components of MSE need to be weighted properly if they are not of the same importance in the given problem situation. To date, the relative weights of bias and variance have been equally set or determined only by the data. However, the weights should be determined in accordance with the tradeoffs on various factors in quality and costs. In this paper, we propose a systematic method to determine the weights of bias and variance in accordance with a decision maker's preference structure regarding the tradeoffs.

A generalized model for data envelopment analysis

Data envelopment analysis (DEA) is a method to estimate a relative efficiency of decision making units (DMUs) performing similar tasks in a production system that consumes multiple inputs to produce multiple outputs. So far, a number of DEA models have been developed: The CCR model, the BCC model and the FDH model are well known as basic DEA models. These models based on the domination structure in primal form are characterized by how to determine the production possibility set from a viewpoint of dual form; the convex cone, the convex hull and the free disposable hull for the observed data, respectively. In this study, we suggest a model called generalized DEA (GDEA) model, which can treat the above stated basic DEA models in a unified way. In addition, by establishing the theoretical properties on relationships among the GDEA model and those DEA models, we prove that the GDEA model makes it possible to calculate the efficiency of DMU incorporating various preference structures of decision makers. Furthermore, we propose a dual approach to GDEA, GDEA D and also show that GDEA D can reveal domination relations among all DMUs.

The double role of the weight factor in the goal programming model

In Goal Programming model, the best solution is established in such a way that the sum of the weighted deviations from the goals is minimal. The weight factor of a given objective is composed of two components destined to represent two different roles. The first one is “normalization” meaning to bring all deviations to a common unit of measurement based on the degree of proximity to the goal. The second is “valorization” reflecting the decision-maker's preference structure. The weight factor related to an objective is not a simple constant but a function of the realized level of objectives. Because of this variable nature of the weights this model will be non-linear. To cope with this problem we intend to obtain an equivalent linear presentation so that the problem can be solved using standard software suitable for mixed linear programs.

Modelling a Decision Maker's Preferences with Different Assumptions about the Preference Structure: Theory Development and Initial Applications for Tourism and Hospitality Management

Understanding customers' preferences and preference structure is an important aspect of managing service applications. This paper develops a heuristic approach that includes a new preference elicitation procedure and two different value function models. The elicitation procedure makes no assumptions about the form of the preference structure of the decision maker (DM), is easy to understand, and does not take much time to complete. Then, two different models based on different assumptions about the DM's preference structure are developed to fit the elicitation procedure data. The Linear-Fractional Model assumes perfect substitution (linear indifference curves where the slopes can vary) and the Decision Utility Model assumes perfect complements (right-angled indifference curves). The paper develops the methods using an example of a park management problem. The models are tested in an exploratory experiment that demonstrates how to use the methods and techniques in a multi-criteria decision problem.

Multi-objective analysis of hospital delivery systems

Automation introduction in hospital applications has become increasingly important in recent years. Delivery, transportation and distribution services are examples of critical operations that can be automated. This paper examines clinical laboratory and pharmacy deliveries in middle to large size hospitals, in order to evaluate whether or not a fleet of mobile robots can replace a traditional human-based delivery system. The complexity of the problem derives from its multi-objective character, since several, often contrasting factors must be taken under consideration. The problem has common characteristics with transportation system design and automation introduction evaluation in manufacturing. The Analytic Hierarchy Process was used to build a decision problem that synthesized economic and technical performance as well as social, human and environmental factors. The technical performance measures were assessed through computer simulation. This research provides a methodology to approach automation introduction evaluation in a hospital environment. The final results enable a better understanding of the delivery and transportation requirements of middle to large size hospitals and how a fleet of mobile robots can meet these requirements. We applied our methodology to the University of Virginia Health Science Center. We show with a high overall confidence that a fleet of mobile robots can achieve better final results than a human-based transportation system according to a representative preference structure formulated by a hospital manager. An ANOVA analysis indicates that the final results were not excessively dependent on the input data of the simulation model. In addition, a sensitivity analysis indicated that the results are stable with respect to variations in the decision maker's preference structure.

Interactive multiple objective programming using Tchebycheff programs and artificial neural networks

A new interactive multiple objective programming procedure is developed that combines the strengths of the interactive weighted Tchebycheff procedure (Steuer and Choo. Mathematical Programming 1983;26(1):326–44.) and the interactive FFANN procedure (Sun, Stam and Steuer. Management Science 1996;42(6):835–49.). In this new procedure, nondominated solutions are generated by solving augmented weighted Tchebycheff programs (Steuer. Multiple criteria optimization: theory, computation and application. New York: Wiley, 1986.). The decision maker indicates preference information by assigning “values” to or by making pairwise comparisons among these solutions. The revealed preference information is then used to train a feed-forward artificial neural network. The trained feed-forward artificial neural network is used to screen new solutions for presentation to the decision maker on the next iteration. The computational experiments, comparing the current procedure with the interactive weighted Tchebycheff procedure and the interactive FFANN procedure, produced encouraging results. Scope and purpose Artificial neural networks have been shown to possess an ability to learn and represent complex mappings, and have been applied to pattern recognition problems. The authors of the current paper believe that a decision maker's preference structure may be viewed as a pattern, and thus should be amenable to artificial neural networks. In a previous work (Sun, Stam and Steuer. Mangement Science 1996;42(6):835–49.), the authors developed a neural-network-based interactive solution method for multiple objective programming problems. The current paper extends that earlier work, combining elements of traditional interactive method with neural networks. In the computational experiments, the new method produced better results for most problems than both the traditional interactive method and the earlier neural-network-based method, thus providing an attractive alternative to existing interactive multiple objective programming procedures.

A Decision Model for the Multiple Criteria Group Secretary Problem: Theoretical Considerations

A decision model is developed for solving the discrete multiple criteria group secretary problem. The model extends the single decision-maker progressive algorithm by Korhonen, Moskowitz and Wallenius to group contexts. As the original progressive algorithm, it relaxes the usual assumption of a fixed set of available decision alternatives and complete knowledge of a decision-maker's preference structure (value function). The decision-makers are requested to settle on a compromise, if possible. The model then proceeds with determining the likelihood of finding possibly/surely better settlements (compromises). Linear value functions, linear prospect theory-type value functions, and quasiconcave value functions are considered.

A Decision Model for the Multiple Criteria Group Secretary Problem: Theoretical Considerations

A decision model is developed for solving the discrete multiple criteria group secretary problem. The model extends the single decision-maker progressive algorithm by Korhonen, Moskowitz and Wallenius to group contexts. As the original progressive algorithm, it relaxes the usual assumption of a fixed set of available decision alternatives and complete knowledge of a decision-maker's preference structure (value function). The decision-makers are requested to settle on a compromise, if possible. The model then proceeds with determining the likelihood of finding possibly/surely better settlements (compromises). Linear value functions, linear prospect theory-type value functions, and quasiconcave value functions are considered.

Solving Multiple Objective Programming Problems Using Feed-Forward Artificial Neural Networks: The Interactive FFANN Procedure

In this paper, we propose a new interactive procedure for solving multiple objective programming problems. Based upon feed-forward artificial neural networks (FFANNs), the method is called the Interactive FFANN Procedure. In the procedure, the decision maker articulates preference information over representative samples from the nondominated set either by assigning preference “values” to the sample solutions or by making pairwise comparisons in a fashion similar to that in the Analytic Hierarchy Process. With this information, a FFANN is trained to represent the decision maker's preference structure. Then, using the FFANN, an optimization problem is solved to search for improved solutions. An example is given to illustrate the Interactive FFANN Procedure. Also, the procedure is compared computationally with the Tchebycheff Method (Steuer and Choo [Steuer, R. E., E.-U. Choo. 1983. An interactive weighted Tchebycheff procedure for multiple objective programming. Math. Programming 26(1) 326–344.]). The computational results indicate that the Interactive FFANN Procedure produces good solutions and is robust with regard to the neural network architecture.

Comparative Assessment of AHP and MAV in Highway Planning: Case Study

A comparative analysis is made between the analytic hierarchy process (AHP) and the multiattribute value (MAV) functions, using the MAV theory as the basis of reference, in the evaluation of transportation projects. The analysis considers three different perspectives: theoretical support, practicality, and ability to capture the decision maker's (DM) preferences. From the theoretic-behavioral standpoint, it appears that the validity of some of the assumptions of the AHP remain to be formally established, as concluded by several researchers. Secondly, the practicality of AHP was analyzed, in terms of the quantity and type of information demanded from the DM. For an even mix of ratio scale variables and nonratio scale variables the AHP requires less information than the MAV, provided the number of alternatives is less than five. Beyond this limit, the AHP requires more information than MAV. The ability to capture the decision maker's preference structure is analyzed through a case study, to which both metho...

Flowshop Scheduling of Robotic Cells with Job-dependent Transportation and Set-up Effects

In most of the approaches to the Multiobjective Stochastic Linear Programming problem that have been proposed in the literature, the notion of quality of a solution is not adequately defined. We reconsider this problem from a decision point of view, in contexts where either the decision maker's preference structure cannot be described by a utility function, or where this structure is expressed by an unknown non-decreasing utility function and the probability distribution of the random parameters is unknown. We define a fundamental set of ‘pointwise admissible’ solutions, as well as several subsets of particular interest. We discuss the relevance of these various pointwise efficient sets, their interrelations, and their practical identification.

An approach to using the analytic hierarchy process for solving multiple criteria decision making problems

In this paper we present a procedure for solving multiple criteria decision making problems. Our procedure, which is an extension of the Analytic Hierarchy Process, addresses the issue of fuzziness in the weighing information provided by the decision maker, the consequent stability of the AHP ranking of the alternatives and the sensitivity of such rankings to small perturbations. These issues are especially important when the concept of optimality incorporates parameters or weights that reflect subjective preferences. The procedure provides a consistent and systematic method for carrying out goal-seeking sensitivity analysis that captures the decision maker's preference structure using his/her indifference region.

PAHAP: A Pairwise Aggregated Hierarchical Analysis of Ratio-Scale Preferences

In this paper, we present a Pairwise Aggregated Hierarchical Analysis of Ratio-Scale Preferences (PAHAP), a new method for solving discrete alternative multicriteria decision problems. Following the Analytic Hierarchy Process (AHP), PAHAP uses pairwise preference judgments to assess the relative attractiveness of the alternatives. By first aggregating the pairwise judgment ratios of the alternatives across all criteria, and then synthesizing based on these aggregate measures, PAHAP determines overall ratio scale priorities and rankings of the alternatives which are not subject to rank reversal, provided that certain weak consistency requirements are satisfied. Hence, PAHAP can serve as a useful alternative to the original AHP if rank reversal is undesirable, for instance when the system is open and criterion scarcity does not affect the relative attractiveness of the alternatives. Moreover, the single matrix of pairwise aggregated ratings constructed in PAHAP provides useful insights into the decision maker's preference structure. PAHAP requires the same preference information as the original AHP (or, altematively, the same information as the Referenced AHP, if the criteria are compared based on average (total) value of the alternatives). As it is easier to implement and interpret than previously proposed variants of the conventional AHP which prevent rank reversal, PAHAP also appears attractive from a practitioner's viewpoint.