A posterior preference articulation approach to multiresponse surface optimization

In multiresponse surface optimization (MRSO), responses are often in conflict. To obtain a satisfactory compromise, the preference information of a decision maker (DM) on the tradeoffs among the responses should be incorporated into the problem. In most existing work, the DM expresses a subjective judgment on the responses through a preference parameter before the problem-solving process, after which a single solution is obtained. In this study, we propose a posterior preference articulation approach to MRSO. The approach initially finds a set of nondominated solutions without the DM’s preference information, and then allows the DM to select the best solution from among the nondominated solutions. An interactive selection method based on pairwise comparisons made by the DM is adopted in our method to facilitate the DM’s selection process. The proposed method does not require that the preference information be specified in advance. It is easy and effective in that a satisfactory compromise can be obtained through a series of pairwise comparisons, regardless of the type of the DM’s utility function.     

Cross-efficiency aggregation in DEA models using the evidential-reasoning approach

Cross-efficiency in data envelopment analysis (DEA) models is an effective way to rank decision-making units (DMUs). The common methods to aggregate cross-efficiency do not consider the preference structure of the decision maker (DM). When a DM’s preference structure does not satisfy the “additive independence” condition, a new aggregation method must be proposed. This paper uses the evidential-reasoning (ER) approach to aggregate the cross-efficiencies obtained from cross-evaluation through the transformation of the cross-efficiency matrix to pieces of evidence. This paper provides a new method for cross-efficiency aggregation and a new way for DEA models to reflect a DM’s preference or value judgments. Additionally, this paper presents examples that demonstrate the features of cross-efficiency aggregation using the ER approach, including an empirical example of the evaluation practice of 16 basic research institutes in Chinese Academy of Sciences (CAS) in 2010 that illustrates how the ER approach can be used to aggregate the cross-efficiency matrix produced from DEA models.     

Target setting in the general combined-oriented CCR model using an interactive MOLP method

The traditional data envelopment analysis (DEA) model does not include a decision maker’s (DM) preference structure while measuring relative efficiency, with no or minimal input from the DM. To incorporate DM’s preference information in DEA, various techniques have been proposed. An interesting method to incorporate preference information, without necessary prior judgment, is the use of an interactive decision making technique that encompasses both DEA and multi-objective linear programming (MOLP). In this paper, we will use Zionts-Wallenius (Z-W) method to reflecting the DM’s preferences in the process of assessing efficiency in the general combined-oriented CCR model. A case study will conducted to illustrate how combined-oriented efficiency analysis can be conducted using the MOLP method.     

Non-additive robust ordinal regression: A multiple criteria decision model based on the Choquet integral

Within the multicriteria aggregation–disaggregation framework, ordinal regression aims at inducing the parameters of a decision model, for example those of a utility function, which have to represent some holistic preference comparisons of a Decision Maker (DM). Usually, among the many utility functions representing the DM’s preference information, only one utility function is selected. Since such a choice is arbitrary to some extent, recently robust ordinal regression has been proposed with the purpose of taking into account all the sets of parameters compatible with the DM’s preference information. Until now, robust ordinal regression has been implemented to additive utility functions under the assumption of criteria independence. In this paper we propose a non-additive robust ordinal regression on a set of alternatives A, whose utility is evaluated in terms of the Choquet integral which permits to represent the interaction among criteria, modelled by the fuzzy measures, parameterizing our approach.     

Multiple criteria sorting with a set of additive value functions

We present a new multiple criteria sorting method that aims at assigning actions evaluated on multiple criteria to p pre-defined and ordered classes. The preference information supplied by the decision maker (DM) is a set of assignment examples on a subset of actions relatively well known to the DM. These actions are called reference actions. Each assignment example specifies a desired assignment of a corresponding reference action to one or several contiguous classes. The set of assignment examples is used to build a preference model of the DM represented by a set of general additive value functions compatible with the assignment examples. For each action a, the method computes two kinds of assignments to classes, concordant with the DM’s preference model: the necessary assignment and the possible assignment. The necessary assignment specifies the range of classes to which the action can be assigned considering all compatible value functions simultaneously. The possible assignment specifies, in turn, the range of classes to which the action can be assigned considering any compatible value function individually. The compatible value functions and the necessary and possible assignments are computed through the resolution of linear programs.     

Optimal design of the auto parts supply chain for JIT operations: Sequential bifurcation factor screening and multi-response surface methodology

This research proposes a solution framework based on discrete-event simulation, sequential bifurcation (SB) and response surface methodology (RSM) to address a multi-response optimization problem inherent in an auto parts supply chain. The objective is to identify the most efficient operating setting that would maximize the logistics performance after the expansion of the assembly plant’s capacity due to market growth. In the proposed framework, we first construct a comprehensive simulation as a platform to model the physical flow of the auto parts operations. We then apply the SB to identify the most important factors that influence system performance. To determine the optimal levels of these key factors, we employ RSM to develop metamodels that best describe the relationship between key decision variables and the multiple system responses. We adapt the Derringer–Suich’s desirability function to find the optimal solution of the metamodels. Computational study shows that our method enables the greatest improvement on system performance. The proposed method helps the case firm develop insights into system dynamics and to optimize the operating condition. It realizes the performance objective of the auto parts supply chain without the need for additional fiscal investment.     

Stochastic multiobjective acceptability analysis for the Choquet integral preference model and the scale construction problem

The Choquet integral preference model is adopted in Multiple Criteria Decision Aiding (MCDA) to deal with interactions between criteria, while the Stochastic Multiobjective Acceptability Analysis (SMAA) is an MCDA methodology considered to take into account uncertainty or imprecision on the considered data and preference parameters. In this paper, we propose to combine the Choquet integral preference model with the SMAA methodology in order to get robust recommendations taking into account all parameters compatible with the preference information provided by the Decision Maker (DM). In case the criteria are on a common scale, one has to elicit only a set of non-additive weights, technically a capacity, compatible with the DM’s preference information. Instead, if the criteria are on different scales, besides the capacity, one has to elicit also a common scale compatible with the preferences given by the DM. Our approach permits to explore the whole space of capacities and common scales compatible with the DM’s preference information.     

Multi-objective stochastic programming for portfolio selection

Generally, in the portfolio selection problem the Decision Maker (DM) considers simultaneously conflicting objectives such as rate of return, liquidity and risk. Multi-objective programming techniques such as goal programming (GP) and compromise programming (CP) are used to choose the portfolio best satisfying the DM’s aspirations and preferences. In this article, we assume that the parameters associated with the objectives are random and normally distributed. We propose a chance constrained compromise programming model (CCCP) as a deterministic transformation to multi-objective stochastic programming portfolio model. CCCP is based on CP and chance constrained programming (CCP) models. The proposed program is illustrated by means of a portfolio selection problem from the Tunisian stock exchange market.     

A lexicographical compromise method for multiple criteria group decision problems with imprecise information

This paper addresses multiple criteria group decision making problems where each group member offers imprecise information on his/her preferences about the criteria. In particular we study the inclusion of this partial information in the decision problem when the individuals’ preferences do not provide a vector of common criteria weights and a compromise preference vector of weights has to be determined as part of the decision process in order to evaluate a finite set of alternatives. We present a method where the compromise is defined by the lexicographical minimization of the maximum disagreement between the value assigned to the alternatives by the group members and the evaluation induced by the compromise weights.     

求解物流运输网络SUM-MIN双目标路径问题的扩展标号法

研究了物流运输网络SUM-MIN双目标路径问题. 基于模糊规划方法提出了一种求解SUM-MIN双目标路径问题的目标函数集成方法,以及集成后目标函数的扩展标号法. 在将双目标转化为单目标时,综合考虑了每个目标的边缘评价和两个目标的整体评价因素,通过对每个目标分配的权重将决策者的偏好充分体现到决策过程中,采用广义的模糊目标集成算子形成了相应的折衷规划模型. 最后,通过实例对所提方法进行了说明.     

A robust desirability function method for multi-response surface optimization considering model uncertainty

A robust desirability function approach to simultaneously optimizing multiple responses is proposed. The approach considers the uncertainty associated with the fitted response surface model. The uniqueness of the proposed method is that it takes account of all values in the confidence interval rather than a single predicted value for each response and then defines the robustness measure for the traditional desirability function using the worst case strategy. A hybrid genetic algorithm is developed to find the robust optima. The presented method is compared with its conventional counterpart through an illustrated example from the literature.     

Building a set of additive value functions representing a reference preorder and intensities of preference: GRIP method

We present a method called Generalized Regression with Intensities of Preference (GRIP) for ranking a finite set of actions evaluated on multiple criteria. GRIP builds a set of additive value functions compatible with preference information composed of a partial preorder and required intensities of preference on a subset of actions, called reference actions. It constructs not only the preference relation in the considered set of actions, but it also gives information about intensities of preference for pairs of actions from this set for a given decision maker (DM). Distinguishing necessary and possible consequences of preference information on the considered set of actions, GRIP answers questions of robustness analysis. The proposed methodology can be seen as an extension of the UTA method based on ordinal regression. GRIP can also be compared to the AHP method, which requires pairwise comparison of all actions and criteria, and yields a priority ranking of actions. As for the preference information being used, GRIP can be compared, moreover, to the MACBETH method which also takes into account a preference order of actions and intensity of preference for pairs of actions. The preference information used in GRIP does not need, however, to be complete: the DM is asked to provide comparisons of only those pairs of reference actions on particular criteria for which his/her judgment is sufficiently certain. This is an important advantage comparing to methods which, instead, require comparison of all possible pairs of actions on all the considered criteria. Moreover, GRIP works with a set of general additive value functions compatible with the preference information, while other methods use a single and less general value function, such as the weighted-sum.     

On Method for Uncertain Multiple Attribute Decision Making Problems with Uncertain Multiplicative Preference Information on Alternatives

The uncertain multiple attribute decision making (UMADM) problems are investigated, in which the information about attribute weights is known partly and the attribute values take the form of interval numbers, and the decision maker (DM) has uncertain multiplicative preference information on alternatives. We make the decision information uniform by using a transformation formula, and then establish an objective-programming model. The attribute weights can be determined by solving the developed model. The concept of interval positive ideal point of alternatives (IPIPA) is introduced, and an approach based on IPIPA and projection to ranking alternatives is proposed. The method can avoid comparing and ranking interval numbers, and can reflect both the objective information and the DMs subjective preferences.     

Comparing influence theories in voting games under locally generated measures of dissatisfaction

The Isbell desirability relation (I), the Shapley?CShubik index (SS) and the Banzhaf?CColeman index (BC) are power theories that grasp the notion of individual influence in a yes?Cno voting rule. Also, a yes?Cno voting rule is often used as a tool for aggregating individual preferences over any given finite set of alternatives into a collective preference. In this second context, Diffo Lambo and Moulen (DM) have introduced a power relation which ranks the voters with respect to how ably they influence the collective preference. However, DM relies on the metric d that measures closeness between preference relations. Our concern in this work is: do I, SS, BC and DM agree when the same yes?Cno voting rule is the basis for collective decision making? We provide a concrete and intuitive class of metrics called locally generated (LG). We give a characterization of the LG metrics d for which I, SS, BC and DM agree on ranking the voters.     

Selection of a representative value function in robust multiple criteria ranking and choice

We introduce the concept of a representative value function in robust ordinal regression applied to multiple criteria ranking and choice problems. The proposed method can be seen as a new interactive UTA-like procedure, which extends the UTA^GMS and GRIP methods. The preference information supplied by the decision maker (DM) is composed of a partial preorder and intensities of preference on a subset of reference alternatives. Robust ordinal regression builds a set of general additive value functions which are compatible with the preference information, and returns two binary preference relations: necessary and possible. They identify recommendations which are compatible with all or at least one compatible value function, respectively. In this paper, we propose a general framework for selection of a representative value function from among the set of compatibles ones. There are a few targets which build on results of robust ordinal regression, and could be attained by a representative value function. In general, according to the interactively elicited preferences of the DM, the representative value function may emphasize the advantage of some alternatives over the others when all compatible value functions acknowledge this advantage, or reduce the ambiguity in the advantage of some alternatives over the others when some compatible value functions acknowledge an advantage and other ones acknowledge a disadvantage. The basic procedure is refined by few extensions. They enable emphasizing the advantage of alternatives that could be considered as potential best options, accounting for intensities of preference, or obtaining a desired type of the marginal value functions.     

Optimization of TQFP molding process using neuro-fuzzy-GA approach

This paper focuses on an integrated optimization problem that involves multiple qualitative and quantitative responses in the thin quad flat pack (TQFP) molding process. A fuzzy quality loss function (FQLF) is first applied to the qualitative responses, since the molding defects cannot be simply represented by the relationship between molding conditions and mathematical models. Neural network is then used to provide a nonlinear relationship between process parameters and responses. A genetic algorithm together with exponential desirability function is employed to determine the optimal parameter setting for TQFP encapsulation. The proposed method was implemented in a semiconductor assembly factory in Taiwan. The results from this study have proved the feasibility of the proposed approach.     

Learning about preferences in electronic negotiations – A volume-based measurement method

To create an integrative solution in a bargaining problem, negotiators need to have information about each other’s preferences. Empirical negotiation research therefore requires methods to measure the extent to which information about preferences is available during a negotiation. We propose such a method based on Starr’s domain criterion, which was originally developed for sensitivity analysis in decision making. Our method provides indices for the amount of preference information that can be inferred both in negotiations reaching an agreement and negotiations where an agreement was not (yet) reached. To test the external validity of our proposed measures, we conduct an empirical study which shows that the proposed measures exhibit positive relationships to the success of negotiations as well as to the efficiency of outcomes that would be expected according to negotiation theory.     

Robust optimization for multiple responses using response surface methodology

Typically in the analysis of industrial data for product/process optimization, there are many response variables that are under investigation at the same time. Robustness is also an important concept in industrial optimization. Here, robustness means that the responses are not sensitive to the small changes of the input variables. However, most of the recent work in industrial optimization has not dealt with robustness, and most practitioners follow up optimization calculations without consideration for robustness. This paper presents a strategy for dealing with robustness and optimization simultaneously for multiple responses. In this paper, we propose a robustness desirability function distinguished from the optimization desirability function and also propose an overall desirability function approach, which makes balance between robustness and optimization for multiple response problems. Simplex search method is used to search for the most robust optimal point in the feasible operating region. Finally, the proposed strategy is illustrated with an example from the literature. Copyright © 2009 John Wiley & Sons, Ltd.     

A semiparametric method for estimating nonlinear autoregressive model with dependent errors

The first-order nonlinear autoregressive model is considered and a semiparametric method is proposed to estimate regression function. In the presented model, dependent errors are defined as first-order autoregressive AR(1). The conditional least squares method is used for parametric estimation and the nonparametric kernel approach is applied to estimate regression adjustment. In this case, some asymptotic behaviors and simulated results for the semiparametric method are presented. Furthermore, the method is applied for the financial data in Iran’s Tejarat-Bank.     

基于模式搜索的渴求函数法在多响应优化中的应用

渴求函数法是处理多响应参数优化的常用方法之一,它通过最大化总体渴求值获得因子的最佳水平组合.然而,随着因子个数和响应个数的增加,渴求函数往往变得多约束、多峰分布、高度非线性,传统的基于梯度的优化算法不适用.根据因子及响应个数等问题复杂程度不同,提出了以模式搜索算法为基础,用重叠等值线图或遗传算法设定模式搜索的起始点,对总体渴求函数进行寻优的新方法.算例验证了该方法的有效性.