Monte Carlo simulation techniques for group decision making with incomplete information

In this paper we deal with group decision-making problems where several decision makers elicit their own preferences separately. The decision makers’ preferences are quantified using a decision support system, which admits incomplete information concerning the decision makers’ responses to the questions they are asked. Consequently, each decision maker proposes classes of utility functions and attribute weight intervals for the different attributes. We introduce an approach based on Monte Carlo simulation techniques for aggregating decision maker preferences that could be the starting point for a negotiation process, if necessary. The negotiation process would basically involve the decision maker tightening the imprecise component utilities and weights to output more meaningful results and achieve a consensus alternative. We focus on how attribute weights and the component utilities associated with a consequence are randomly generated in the aggregation process taking into account the decision-makers’ preferences, i.e., their respective attribute weight intervals and classes of utility functions. Finally, an application to the evaluation of intervention strategies for restoring a radionuclide contaminated lake illustrates the usefulness and flexibility of this iterative process.     

DEA models for resource reallocation and production input/output estimation

This paper discusses the “inverse” data envelopment analysis (DEA) problem with preference cone constraints. An inverse DEA model can be used for a decision making unit (DMU) to estimate its input/output levels when some or all of its input/output entities are revised, given its current DEA efficiency level. The extension of introducing additional preference cones to the previously developed inverse DEA model allows the decision makers to incorporate their preferences or important policies over inputs/outputs into the production analysis and resource allocation process. We provide the properties of the inverse DEA problem through a discussion of its related multi-objective and weighted sum single-objective programming problems. Numerical examples are presented to illustrate the application procedure of our extended inverse DEA model. In particular, we demonstrate how to apply the model to the case of a local home electrical appliance group company for its resource reallocation decisions.     

Strategy-proof location of public bads in a two-country model

We consider the joint decision of placing public bads in each of two neighboring countries, modeled by two adjacent line segments. Residents of the two countries have single-dipped preferences, determined by the distance of their dips to the nearer public bad (myopic preferences) or, lexicographically, by the distance to the nearer and the other public bad (lexmin preferences). A (social choice) rule takes a profile of reported preferences as input and assigns the location of the public bad in each country. For the case of myopic preferences, all rules satisfying strategy-proofness, country-wise Pareto optimality, non-corruptibility, and the far away condition are characterized. These rules pick only border locations. The same holds for lexmin preferences under strategy-proofness and country-wise Pareto optimality alone.     

Industrial petrochemical production planning and expansion: A multi-objective linear programming approach

This paper considers a strategic model planning for the petrochemical industry. It concerns with the expansion in a firm producing multiple products in several regions of a country. The expansion of the existing facilities and the new ones are considered. It also exists a large amount of interdependencies among the firm’s products, because the output of one particular plant can be used as an input to the production of another plant in the same or different regions and to satisfy the final demand. The decision makers involved in the planning process should identify several objectives. Then, multiple objective programming is used for making trade-offs among the economic and operational factors considered. To define the interval criteria weights into the model we utilized the Analytic Hierarchy Process to bring them closer to the decision makers preferences. This work was sponsored by the Institut National Polytechnique de Toulouse, France, when the author was Associate Professor at the Département Génie des Systèmes Industriels.     

Finding common weights based on the DM's preference information

Data Envelopment Analysis (DEA) is basically a linear programming-based technique used for measuring the relative performance of organizational units, referred to as Decision Making Units (DMUs). The flexibility in selecting the weights in standard DEA models deters the comparison among DMUs on a common base. Moreover, these weights are not suitable to measure the preferences of a decision maker (DM). For dealing with the first difficulty, the concept of common weights was proposed in the DEA literature. But, none of the common weights approaches address the second difficulty. This paper proposes an alternative approach that we term as ‘preference common weights’, which is both practical and intellectually consistent with the DEA philosophy. To do this, we introduce a multiple objective linear programming model in which objective functions are input/output variables subject to the constraints similar to the equations that define production possibility set of standard DEA models. Then by using the Zionts–Wallenius method, we can generate common weights as the DM's underlying value structure about objective functions.     

Decision maker preferences for information in complex decision making: New directions for OR intervention

Operations research models are used in many business and non-business entities to support a variety of decision making activities, primarily well-defined, operational decisions. This is due to the traditional emphasis of these models on optimal solutions to pre-specified problems. Some attempts have been made to use OR models in support of more complex, strategic decision making. Traditionally, these models have been developed without explicit consideration for the information processing abilities and limitations of the decision makers, who interact with, provide input to, and receive output from such models.Research in judgement and decision making show that human decisions are influenced by a number of factors including, but not limited to, information presentation modes; information content, modes, e.g., quantitative versus qualitative; order effects such as primacy, recency; and simultaneous versus sequential presentation of data.This article presents empirical research findings involving executive business decision makers and their preferences for information in decision making scenarios. These preference functions were evaluated using OR techniques. The results indicate that decision makers view information in different ways. Some decision makers prefer qualitative, narrative, social information, whereas other prefer quantitative, numerical, firm specific information. Results also show that decision making tasks influence the preference structure of decision makers, but that in general, the preference are relatively stable across tasks.The results imply that for OR models to be more useful in support of non-routine decision making, attention needs to be focused on the information content and presentation effects of model inputs and outputs.     

Ordered median problem with demand distribution weights

The ordered median function unifies and generalizes most common objective functions used in location theory. It is based on the ordered weighted averaging (OWA) operator with the preference weights allocated to the ordered distances. Demand weights are used in location problems to express the client demand for a service thus defining the location decision output as distances distributed according to measures defined by the demand weights. Typical ordered median model allows weighting of several clients only by straightforward rescaling of the distance values. However, the OWA aggregation of distances enables us to introduce demand weights by rescaling accordingly clients measure within the distribution of distances. It is equivalent to the so-called weighted OWA (WOWA) aggregation of distances covering as special cases both the weighted median solution concept defined with the demand weights (in the case of equal all the preference weights), as well as the ordered median solution concept defined with the preference weights (in the case of equal all the demand weights). This paper studies basic models and properties of the weighted ordered median problem (WOMP) taking into account the demand weights following the WOWA aggregation rules. Linear programming formulations were introduced for optimization of the WOWA objective with monotonic preference weights thus representing the equitable preferences in the WOMP. We show MILP models for general WOWA optimization.     

Restricting weights in supplier selection decisions in the presence of dual-role factors

One of the uses of data envelopment analysis (DEA) is supplier selection. Weight restrictions allow for the integration of managerial preferences in terms of relative importance levels of various inputs and outputs. As well, in some situations there is a strong argument for permitting certain factors to simultaneously play the role of both inputs and outputs. The objective of this paper is to propose a method for selecting the best suppliers in the presence of weight restrictions and dual-role factors. This paper depicts the supplier selection process through a DEA model, while allowing for the incorporation of decision maker’s preferences and considers multiple factors which simultaneously play both input and output roles. The proposed model does not demand exact weights from the decision maker. This paper presents a robust model to solve the multiple-criteria problem. A numerical example demonstrates the application of the proposed method.     

Additive DEA based on MCDA with imprecise information

This work exploits links between Data Envelopment Analysis (DEA) and multicriteria decision analysis (MCDA), with decision making units (DMUs) playing the role of decision alternatives. A novel perspective is suggested on the use of the additive DEA model in order to overcome some of its shortcomings, using concepts from multiattribute utility models with imprecise information. The underlying idea is to convert input and output factors into utility functions that are aggregated using a weighted sum (additive model of multiattribute utility theory), and then let each DMU choose the weights associated with these functions that minimize the difference of utility to the best DMU. The resulting additive DEA model with oriented projections has a clear rationale for its efficiency measures, and allows meaningful introduction of constraints on factor weights.     

SMAA - Stochastic multiobjective acceptability analysis

Stochastic multiobjective acceptability analysis (SMAA) is a multicriteria decision support technique for multiple decision makers based on exploring the weight space. Inaccurate or uncertain input data can be represented as probability distributions. In SMAA the decision makers need not express their preferences explicitly or implicitly; instead the technique analyses what kind of valuations would make each alternative the preferred one. The method produces for each alternative an acceptability index measuring the variety of different valuations that support that alternative, a central weight vector representing the typical valuations resulting in that decision, and a confidence factor measuring whether the input data is accurate enough for making an informed decision.     

Locating a waste treatment facility by using stochastic multicriteria acceptability analysis with ordinal criteria

In this paper we describe a real-life application of an ordinal multicriteria method in the context of choosing a location for a waste treatment facility near Lappeenranta in South-Eastern Finland. The associated environmental impact assessment (EIA) procedure is briefly described. The application was characterized by two interesting properties: no preference information was available, and only ordinal measurements for the criteria were available. The large amount of data obtained was then analyzed using the SMAA-O method – Stochastic Multicriteria Acceptability Analysis with Ordinal criteria designed for this problem setting. SMAA-O converts ordinal information into cardinal data by simulating all possible mappings between ordinal and cardinal scales that preserve the given rankings. As with the basic SMAA-method, the decision makers' (DMs) unknown or partly known preferences are at the same time simulated by choosing weights randomly from appropriate distributions. The main results of the analysis are acceptability indices for alternatives describing the variety of preferences that could make each alternative the best choice. Based on these and additional considerations, the DMs made the final choice for the location of the plant.     

基于信息熵权TOPSIS法的双腔半环面型CVT传动性能优化

针对双腔半环面型CVT的结构特点和应用背景,建立以输入扭矩分矩比和输出输入扭矩比为目标函数的优化模型。采用带有精英策略的非支配排序遗传算法(non-dominated sorting genetic algorithm with the elite strategy, NSGA-II)求解该模型的Pareto最优解。为了确定最佳的Pareto最优解,首先将获得的Pareto最优解构成决策矩阵,其次利用客观赋权的信息熵(information entropy weight, IEW)法计算各属性的权值,最后运用逼近理想解的排序法(technique for order preference by similarity to ideal solution, TOPSIS)对Pareto最优解排序。将最佳Pareto最优解对应的设计变量值代入输入扭矩分矩比、输出输入扭矩比以及传动效率的表达式,使用MATLAB软件绘制相应的特性曲线。结果表明,通过TOPSIS确定的最佳Pareto最优解能够实现双腔半环面型CVT高效率传动、大扭矩输出和无级变速单元承受较小输入扭矩的功能。     

Constructing a monotonic quadratic objective function in n variables from a few two-dimensional indifferences

We develop a model for constructing quadratic objective functions in n target variables. At the input, a decision maker is asked a few simple questions about his ordinal preferences (comparing two-dimensional alternatives in terms `better', `worse', `indifferent'). At the output, the model mathematically derives a quadratic objective function used to evaluate n-dimensional alternatives.Thus the model deals with some imaginary decisions (criteria aggregates) at the input, and disaggregates the decision maker's preference into partial criteria and their cross-correlations (=a quadratic objective function). Therefore, the model provides an approximation step which is next to the disaggregation of a preference into additively separable linear criteria with weight coefficients.The model is based on least squares fitting a quadratic indifference hypersurface (if n=2, indifference curve) to several alternatives which are supposed to be equivalent in preference. The resulting ordinal preference is independent of the cardinal utility scale used in intermediate computations which implies that the model is ordinal. The monotonicity of the quadratic objective function is implemented by means of a finite number of linear constraints, so that the computational model is reduced to restricted least squares.In illustration, we construct a quadratic objective function of German economic policy in four target variables: inflation, unemployment, GNP growth, and increase in public debt. This objective function is used to evaluate the German economic development in 1980–1994.In another application, we construct a quadratic objective function of ski station customers. Then it is used to adjust prices of 10 ski stations to the South of Stuttgart.In Appendix A we provide an original fast algorithm for restricted least squares and quadratic programming used in the main model.     

Robust strategies for facility location under uncertainty

This paper considers a stochastic facility location problem in which multiple capacitated facilities serve customers with a single product, and a stockout probabilistic requirement is stated as a chance constraint. Customer demand is assumed to be uncertain and to follow either a normal or an ambiguous distribution. We study robust approximations to the problem in order to incorporate information about the random demand distribution in the best possible, computationally tractable way. We also discuss how a decision maker’s risk preferences can be incorporated in the problem through robust optimization. Finally, we present numerical experiments that illustrate the performance of the different robust formulations. Robust optimization strategies for facility location appear to have better worst-case performance than nonrobust strategies. They also outperform nonrobust strategies in terms of realized average total cost when the actual demand distributions have higher expected values than the expected values used as input to the optimization models.     

On the use of fuzzy inference techniques in assessment models: part I—theoretical properties

An assessment model is a mathematical model that produces a measuring index, either in the form of a numerical score or a category to a situation/object, with respect to the subject of measure. From the numerical score, decision can be made and action can be taken. To allow valid and useful comparisons among various situations/objects according to their associated numerical scores to be made, the monotone output property and the output resolution property are essential in fuzzy inference-based assessment problems. We investigate the conditions for a fuzzy assessment model to fulfill the monotone output property using a derivative approach. A guideline on how the input membership functions should be tuned is also provided. Besides, the output resolution property is defined as the derivative of the output of the assessment model with respect to its input. This derivative should be greater than the minimum resolution required. From the derivative, we suggest improvements to the output resolution property by refining the fuzzy production rules.     

Scenario-based portfolio selection of investment projects with incomplete probability and utility information

In the selection of investment projects, it is important to account for exogenous uncertainties (such as macroeconomic developments) which may impact the performance of projects. These uncertainties can be addressed by examining how the projects perform across several scenarios; but it may be difficult to assign well-founded probabilities to such scenarios, or to characterize the decision makers’ risk preferences through a uniquely defined utility function. Motivated by these considerations, we develop a portfolio selection framework which (i) uses set inclusion to capture incomplete information about scenario probabilities and utility functions, (ii) identifies all the non-dominated project portfolios in view of this information, and (iii) offers decision support for rejection and selection of projects. The proposed framework enables interactive decision support processes where the implications of additional probability and utility information or further risk constraints are shown in terms of corresponding decision recommendations.     

A generalized multiplicative directional distance function for efficiency measurement in DEA

For measuring technical efficiency relative to a log-linear technology, a generalized multiplicative directional distance function (GMDDF) is developed using the framework of multiplicative directional distance function (MDDF). Furthermore, a computational procedure is suggested for its estimation. The GMDDF serves as a comprehensive measure of efficiency in revealing Pareto-efficient targets as it accounts for all possible input and output slacks. This measure satisfies several desirable properties of an ideal efficiency measure such as strong monotonicity, unit invariance, translation invariance, and positive affine transformation invariance. This measure can be easily implemented in any standard DEA software and provides the decision makers with the option of specifying preferable direction vectors for incorporating their decision-making preferences. Finally, to demonstrate the ready applicability of our proposed measure, an illustrative empirical analysis is conducted based on real-life data set of 20 hardware computer companies in India.     

产出不确定性的三级供应链风险分担组合契约设计

研究了供应商和制造商产出随机且零售商面临随机需求的三级供应链协调模型,决策变量为供应商的原材料投入量、制造商的订购量和零售商的订购量。分析了集中决策下供应链协调基准的唯一性,论证了回购契约及其与产出风险分担组合契约的协调性。研究结果表明,对于产出和需求不确定的三级供应链,仅考虑在制造商和零售商之间采用回购契约可改善供应链绩效,但并不能实现供应链的全局最优化,而从风险分担的角度设计的回购和产出风险分担组合契约不仅能有效的协调供应链,且在一定条件下,各供应链成员的利润还能获得帕累托改进。通过算例验证了以上结论的正确性,并分析了回购价格对订购量、原材料投入量和利润的影响,以及各供应链成员对契约的偏好。     

Performance evaluation: An integrated method using data envelopment analysis and fuzzy preference relations

In a multi-attribute decision-making (MADM) context, the decision maker needs to provide his preferences over a set of decision alternatives and constructs a preference relation and then use the derived priority vector of the preference to rank various alternatives. This paper proposes an integrated approach to rate decision alternatives using data envelopment analysis and preference relations. This proposed approach includes three stages. First, pairwise efficiency scores are computed using two DEA models: the CCR model and the proposed cross-evaluation DEA model. Second, the pairwise efficiency scores are then utilized to construct the fuzzy preference relation and the consistent fuzzy preference relation. Third, by use of the row wise summation technique, we yield a priority vector, which is used for ranking decision-making units (DMUs). For the case of a single output and a single input, the preference relation can be directly obtained from the original sample data. The proposed approach is validated by two numerical examples.