Relating reference points and weights in MOLP

A frequent problem for decision makers (DMs) analysing decisions involving multiple objectives is the identification and selection of the most preferred option from the set of non‐dominated solutions. Two techniques, weighted sum optimization and reference point optimization, have been developed to address this problem for multiobjective linear programming problems (MOLP). In this paper, we examine the relationship between these two techniques. We demonstrate that the values of the dual variables associate with auxiliary constraints of the reference point technique are equal to the weight values used to compute the same non‐dominated solution via the weighted sum technique. This insight will enable the development of new interactive solution procedures for MOLPs which allow the DM to readily switch from one method to the other during the search for the most preferred non‐dominated solution. The advantages of the approach are discussed in the paper. Copyright © 1999 John Wiley & Sons, Ltd.     

A maximin model for IRT-based test design with practical constraints

A maximin model for IRT-based test design is proposed. In the model only the relative shape of the target test information function is specified. It serves as a constraint subject to which a linear programming algorithm maximizes the information in the test. In the practice of test construction, several demands as linear constraints in the model. A worked example of a text construction problem with practical constraints is presented. The paper concludes with a discussion of some alternative models of test construction.The authors are indebted to Jos J. Adea for suggesting Equation 17 as a Simplification of an earlier version of this constraint. This research was suuorted in part by a grant from the Dutch Organization for Research (NWO) through the Foundation for Psychological and Psychonomic Research in the Netherlands (Psychon).     

Indifference sets of reference points in multi‐objective integer linear programming

Reference point approaches for multi‐objective problems rely on the definition of an achievement scalarizing function that projects reference points onto the non‐dominated solution set. In this paper, we investigate the behaviour of reference points using a Tchebycheff metric‐based scalarizing function in multi‐objective pure integer linear programming (MOILP). Since the non‐dominated solutions are discrete in MOILP, there are multiple reference points that lead to the same solution, i.e. there are indifference sets on the reference point space. We investigate some properties of the reference points in MOILP and also the graphical representation of indifference sets for tri‐objective problems. We further investigate properties of the reference points when additional limitations on the objective function values are introduced. Copyright © 2001 John Wiley & Sons, Ltd.     

Binary programming and test design

An algorithmic approach to test design, using information functions, is presented. The approach uses a special branch of linear programming, i.e. binary programming. In addition, results of some benchmark problems are presented. Within the same framework, it is also possible to formulate the problem of individualized testing.I would like to thank my colleagues N. Veldhuijzen, H. Verstralen and M. Zwarts for their suggestions and comments. Furthermore, I would like to thank Professor W. van der Linden, Department of Educational Measurement and Data Analysis, Technological University Twente, for offering facilities at his department; Ellen Timminga of the same department and S. Baas, department of Operational Research at the same University for their efforts in linear programming.     

The Stochastic Goal Programming Model: Theory and Applications

Supported by a network of researchers and practitioners, the goal programming (GP) model is alive today more than ever and is continually fed with theoretical developments and new applications with resounding success. The standard formulation of the GP model was introduced in the earliest of 1960s, and since then, important extensions and numerous applications have been proposed. One of these variants is the stochastic GP model that deals with the uncertainty of some decision‐making situations by using stochastic calculus. In such a situation, the decision maker is not able to assess with certainty the different parameters. However, he or she can provide some information regarding the likelihood of occurrence of the decision‐making parameter values. The aim of this paper is to highlight the main methodological developments of the stochastic GP model and to present an overview of its applications in several domains. Copyright © 2012 John Wiley & Sons, Ltd.     

An interactive fuzzy satisficing method for multiobjective stochastic linear programming problems using chance constrained conditions

Two major approaches to deal with randomness or ambiguity involved in mathematical programming problems have been developed. They are stochastic programming approaches and fuzzy programming approaches. In this paper, we focus on multiobjective linear programming problems with random variable coefficients in objective functions and/or constraints. Using chance constrained programming techniques, the stochastic programming problems are transformed into deterministic ones. As a fusion of stochastic approaches and fuzzy ones, after determining the fuzzy goals of the decision maker, interactive fuzzy satisficing methods to derive a satisficing solution for the decision maker by updating the reference membership levels is presented. Copyright © 2003 John Wiley & Sons, Ltd.     

Material handling device selection in cellular manufacturing

This paper presents a new multi‐criteria decision model for the material handling device (MHD) selection problem in cellular manufacturing systems. Given a set of manufacturing cells based on several automatic work‐centres, the technique makes it possible to select a particular MHD for each cell in an integrated way, with different constraints being taken into consideration. The approach is based on two different multi‐attribute analyses executed with analytic hierarchy process (AHP) methodology, and a final integer linear programming including important limitations faced by the designer when making MHD investment decisions. An example using real data is provided to illustrate this methodology. Copyright © 2002 John Wiley & Sons, Ltd.     

题库智能化组卷的心理计量理论与方法

现代教育成就测验的广泛应用,促使题库技术迅速发展。现代教育测量理论与计算机技术的结合,更使智能化组卷成为可能。本文报告了以项目反应理论为指导,并改进一般线性规划法为分步离差加权模型法,编制程序在高等教育自学考试“逻辑学”题库上,成功实现智能化组卷的研究成果,从而为计算机技术在题库建设中的应用作了新的探讨。     

Evaluating Fund Performance by Compromise Programming with Linear‐Quadratic Composite Metric: An Actual Case on The CaixaBank in Spain

This paper proposes an additive measure on the basis of compromise programming to evaluate fund performance from multiple criteria, of which the most usual are profitability and risk. This proposal is motivated by the fact that compromise programming is a sound decision support model to obtain scores of alternatives by minimizing weighted distances to an ideal point, the weights reflecting the investor's preferences for the criteria. To define the distance objective function, the linear‐quadratic composite metric is used, which combines advantages of linear and non‐linear objective functions. A critical advantage of compromise programming for fund performance evaluation is that the model can be extended to more than two financial criteria while other measures currently used (either ratio‐based or leverage‐based measures) only consider two criteria, say, profitability and risk. In the application, three investor's profiles are defined, which involve different weighting systems and lead to different fund rankings. These rankings are compared with domination relationships, the latter formulating if a fund is dominated or non‐dominated by convex combinations of other funds. Numerical tables are provided with data, computational process and results, which are analysed. Copyright © 2012 John Wiley & Sons, Ltd.     

Origins,uses of,and relations between goal programming and data envelopment analysis

Origins and uses of ‘goal programming’ and ‘data envelopment analysis’ (DEA) are identified and discussed. The purpose of this paper is not only to review some of the history of these developments, but also to show some of their uses (e.g. in statistical regression formulations) in order to suggest paths for possible further developments. Turning to how the two types of models relate to each other, the ‘additive model’ of DEA is shown to have the same structure as a goal programming model in which only ‘one‐sided deviations’ are permitted. A way for formally relating the two to each other is then provided. However, the objectives are differently oriented because goal programming is directed to future performances as part of the planning function whereas DEA is directed to evaluating past performances as part of the control function of management. Other possible ways of comparing and combining the two approaches are also noted including statistical regressions that utilize goal programming to ensure that the resulting estimates satisfy the multi‐criteria conditions that are often encountered in managerial applications. Both goal programming and DEA originated in actual applications that were successfully addressed. The research was then generalized and published. This leads to what is referred to as an ‘applications‐driven theory’ strategy for research that is also described in this paper. Copyright © 2006 John Wiley & Sons, Ltd.     

Price-directive decision making in hierarchical systems with conflicting preferences

In this paper we consider a classical model of price-directive decision making in hierarchical organizations, namely Dantzig-Wolfe decomposition, well known from single-objective programming. Here, however, we allow for preference differences that are usually observed between a central unit and a subunit in an organizational structure. The procedure models, therefore, how decision making may evolve in a context with decentralized information as well as intra- and interpersonal conflicts. Several numerical experiments with the procedure have been performed. The results of those experiments demonstrate that the procedure in many instances converges towards an efficient solution, despite the differences in the criteria weights used in the master problem and the subproblem respectively. This suggests that some amount of goal discordance need not prohibit efficient decision making in a hierarchical organization.     

A Recourse Stochastic Goal Programming Approach for the Multi‐objective Stochastic Vehicle Routing Problem

This paper addresses a multi‐objective stochastic vehicle routing problem where several conflicting objectives such as the travel time, the number of vehicles in use and the probability of an accident are simultaneously minimized. We suppose that demands and travel durations are of a stochastic nature. In order to build a certainty equivalent program to the multi‐objective stochastic vehicle routing problem, we propose a solution strategy based on a recourse approach, a chance‐constrained approach and a goal‐programming approach. The resulting certainty equivalent program is solved to optimality using CPLEX. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal trade-offs of multiple factors in transfer pricing problems

Transfer pricing problems have been extensively researched by a number of scholars. It is well recognized that transfer pricing problems have a multiple-criteria (objectives) feature and can be formulated as a model of multiple-criteria linear programming. However, few methods have the capability of dealing with all possible optimal trade-offs of multiple criteria in optimal solutions of the models. In this paper a linear multiple-factor model is developed to provide managers with a more systematic and comprehensive scenario of all possible optimal transfer prices depending on both multiple criteria and multiple constraint levels. The trade-offs of all possible optimal transfer prices can be used as a basis for managers of a corporation to make a high-quality decision in selecting their transfer pricing systems for business competition. © 1998 John Wiley & Sons, Ltd.     

Using Lexicographic Parametric Programming for Searching a Non-dominated Set in Multiple-Objective Linear Programming

In this paper we propose an approach which makes it possible to search non-dominated and only non-dominated solutions in multiple-objective linear programming. The approach is based on the use of a reference direction and lexicographic parametric programming. The requisite theory is developed in the paper. The use of the approach is illustrated with a numerical example.     

Portfolio Selection from Multiple Benchmarks: A Goal Programming Approach to an Actual Case

This paper deals with benchmark‐based portfolio choice for buy‐and‐hold strategies of investing. Multiple benchmarks for returns are considered, which is more realistic than taking a unique benchmark – a unique aspiration difficult to select in practice among the various aspirations for returns that the investor has in mind. Portfolio selection with multiple benchmarks leads to a multi‐objective problem, which is addressed by mean value – stochastic goal programming. In particular, two benchmarks are considered, which involves two goals. Weights for goals depend on investor's preferences and Arrow's absolute risk aversion coefficients. An efficient frontier of portfolios is obtained. Advantages of this stochastic method in our context are as follows: (i) Mean value‐stochastic goal programming relies on classical utility theory under uncertainty and Arrow's absolute risk aversion, which ensures soundness and strictness, and (ii) the numerical model is easily solved by using available software such as mean–variance software. Numerical results are tabulated and discussed. Copyright © 2011 John Wiley & Sons, Ltd.     

运用基因表达式编程的自陈量表数据建模

探讨基因表达式编程对自陈量表测量数据的建模方法。运用威廉斯创造力测验和认知需求量表获得400位中学生的测量分数,通过数据清洗,保留383个被试的分数作为建模的数据集。运用哈曼单因素检验方法没有发现共同方法偏差。采用均匀设计方法对基因表达式编程中的5个参数进行优化配置,在测试拟合度最大的试验条件下,找到了测试误差最小的模型。比较基因表达式编程和BP神经网络、支持向量回归机、多元线性回归、二次多项式回归所建模型的预测精度。研究表明,基因表达式编程能用于自陈量表测量数据的建模,该模型比传统方法所建的模型具有更高的预测精度,而且模型是稳健的。     

On portfolio management with value at risk and uncertain returns via an artificial neural network scheme

This paper focuses on the computation issue of portfolio optimization with scenario-based Value-at-Risk. The main idea is to replace the portfolio selection models with linear programming problems. According to the convex optimization theory and some concepts of ordinary differential equations, a neural network model for solving linear programming problems is presented. The equilibrium point of the proposed model is proved to be equivalent to the optimal solution of the original problem. It is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the portfolio selection problem with uncertain returns. Several illustrative examples are provided to show the feasibility and the efficiency of the proposed method in this paper.     

Generating interior search directions for multiobjective linear programming

A new multiobjective linear programming (MOLP) algorithm is presented. The algorithm uses a variant of Karmarkar's interior-point algorithm known as the affine-scaling primal algorithm. Using this single-objective algorithm, interior search directions are generated and used to provide an approximation to the gradient of the (implicitly known) utility function. The approximation is guided by assessing locally relevant preference information for the various interior directions through interaction with a decision maker (DM). The resulting algorithm is an interactive approach that makes its progress towards the solution through the interior of the constraints polytope.     

Reliability measures in item response theory: Manifest versus latent correlation functions

For item response theory (IRT) models, which belong to the class of generalized linear or non‐linear mixed models, reliability at the scale of observed scores (i.e., manifest correlation) is more difficult to calculate than latent correlation based reliability, but usually of greater scientific interest. This is not least because it cannot be calculated explicitly when the logit link is used in conjunction with normal random effects. As such, approximations such as Fisher's information coefficient, Cronbach's α, or the latent correlation are calculated, allegedly because it is easy to do so. Cronbach's α has well‐known and serious drawbacks, Fisher's information is not meaningful under certain circumstances, and there is an important but often overlooked difference between latent and manifest correlations. Here, manifest correlation refers to correlation between observed scores, while latent correlation refers to correlation between scores at the latent (e.g., logit or probit) scale. Thus, using one in place of the other can lead to erroneous conclusions. Taylor series based reliability measures, which are based on manifest correlation functions, are derived and a careful comparison of reliability measures based on latent correlations, Fisher's information, and exact reliability is carried out. The latent correlations are virtually always considerably higher than their manifest counterparts, Fisher's information measure shows no coherent behaviour (it is even negative in some cases), while the newly introduced Taylor series based approximations reflect the exact reliability very closely. Comparisons among the various types of correlations, for various IRT models, are made using algebraic expressions, Monte Carlo simulations, and data analysis. Given the light computational burden and the performance of Taylor series based reliability measures, their use is recommended.     

Regressive Imagery in Creative Problem‐Solving: Comparing Verbal Protocols of Expert and Novice Visual Artists and Computer Programmers

We applied computer‐based text analyses of regressive imagery to verbal protocols of individuals engaged in creative problem‐solving in two domains: visual art (23 experts, 23 novices) and computer programming (14 experts, 14 novices). Percentages of words involving primary process and secondary process thought, plus emotion‐related words, were tabulated. Visual art protocols were higher in primary process thought and emotion‐related words; those from programming were higher in secondary process thought. Almost no main effects of expertise or interactions were found. Correlations between the measures (particularly those involving emotion‐related words) also varied as a function of task. This pattern suggests cognitive processes vary considerably across different creative problem‐solving tasks or domains, and that a more domain‐specific approach to creative cognition may be advisable. Further implications for integrating and consolidating some extant lines of creativity research are discussed.