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.     

Optimal Least-Squares Unidimensional Scaling: Improved Branch-and-Bound Procedures and Comparison to Dynamic Programming

There are two well-known methods for obtaining a guaranteed globally optimal solution to the problem of least-squares unidimensional scaling of a symmetric dissimilarity matrix: (a) dynamic programming, and (b) branch-and-bound. Dynamic programming is generally more efficient than branch-and-bound, but the former is limited to matrices with approximately 26 or fewer objects because of computer memory limitations. We present some new branch-and-bound procedures that improve computational efficiency, and enable guaranteed globally optimal solutions to be obtained for matrices with up to 35 objects. Experimental tests were conducted to compare the relative performances of the new procedures, a previously published branch-and-bound algorithm, and a dynamic programming solution strategy. These experiments, which included both synthetic and empirical dissimilarity matrices, yielded the following findings: (a) the new branch-and-bound procedures were often drastically more efficient than the previously published branch-and-bound algorithm, (b) when computationally feasible, the dynamic programming approach was more efficient than each of the branch-and-bound procedures, and (c) the new branch-and-bound procedures require minimal computer memory and can provide optimal solutions for matrices that are too large for dynamic programming implementation.The authors gratefully acknowledge the helpful comments of three anonymous reviewers and the Editor. We especially thank Larry Hubert and one of the reviewers for providing us with the MATLAB files for optimal and heuristic least-squares unidimensional scaling methods.This revised article was published online in June 2005 with all corrections incorporated.     

Identifying a Reordering of Rows and Columns for Multiple Proximity Matrices Using Multiobjective Programming

This paper is concerned with a problem where K (n×n) proximity matrices are available for a set of n objects. The goal is to identify a single permutation of the n objects that provides an adequate structural fit, as measured by an appropriate index, for each of the K matrices. A multiobjective programming approach for this problem, which seeks to optimize a weighted function of the K indices, is proposed, and illustrative examples are provided using a set of proximity matrices from the psychological literature. These examples show that, by solving the multiobjective programming model under different weighting schemes, the quantitative analyst can uncover information about the relationships among the matrices and often identify one or more permutations that provide good to excellent index values for all matrices.     

Compact integer-programming models for extracting subsets of stimuli from confusion matrices

This paper presents an integer linear programming formulation for the problem of extracting a subset of stimuli from a confusion matrix. The objective is to select stimuli such that total confusion among the stimuli is minimized for a particular subset size. This formulation provides a drastic reduction in the number of variables and constraints relative to a previously proposed formulation for the same problem. An extension of the formulation is provided for a biobjective problem that considers both confusion and recognition in the objective function. Demonstrations using an empirical interletter confusion matrix from the psychological literature revealed that a commercial branch-and-bound integer programming code was always able to identify optimal solutions for both the single-objective and biobjective formulations within a matter of seconds. A further extension and demonstration of the model is provided for the extraction of multiple subsets of stimuli, wherein the objectives are to maximize similarity within subsets and minimize similarity between subsets.     

Heuristic Implementation of Dynamic Programming for Matrix Permutation Problems in Combinatorial Data Analysis

Dynamic programming methods for matrix permutation problems in combinatorial data analysis can produce globally-optimal solutions for matrices up to size 30×30, but are computationally infeasible for larger matrices because of enormous computer memory requirements. Branch-and-bound methods also guarantee globally-optimal solutions, but computation time considerations generally limit their applicability to matrix sizes no greater than 35×35. Accordingly, a variety of heuristic methods have been proposed for larger matrices, including iterative quadratic assignment, tabu search, simulated annealing, and variable neighborhood search. Although these heuristics can produce exceptional results, they are prone to converge to local optima where the permutation is difficult to dislodge via traditional neighborhood moves (e.g., pairwise interchanges, object-block relocations, object-block reversals, etc.). We show that a heuristic implementation of dynamic programming yields an efficient procedure for escaping local optima. Specifically, we propose applying dynamic programming to reasonably-sized subsequences of consecutive objects in the locally-optimal permutation, identified by simulated annealing, to further improve the value of the objective function. Experimental results are provided for three classic matrix permutation problems in the combinatorial data analysis literature: (a) maximizing a dominance index for an asymmetric proximity matrix; (b) least-squares unidimensional scaling of a symmetric dissimilarity matrix; and (c) approximating an anti-Robinson structure for a symmetric dissimilarity matrix. We are extremely grateful to the Associate Editor and two anonymous reviewers for helpful suggestions and corrections.     

Integer programs for one- and two-mode blockmodeling based on prespecified image matrices for structural and regular equivalence

Establishing blockmodels for one- and two-mode binary network matrices has typically been accomplished using multiple restarts of heuristic algorithms that minimize functions of inconsistency with an ideal block structure. Although these algorithms likely yield exceptional performance, they are not assured to provide blockmodels that optimize the functional indices. In this paper, we present integer programming models that, for a prespecified image matrix, can produce guaranteed optimal solutions for matrices of nontrivial size. Accordingly, analysts performing a confirmatory analysis of a prespecified blockmodel structure can apply our models directly to obtain an optimal solution. In exploratory cases where a blockmodel structure is not prespecified, we recommend a two-stage procedure, where a heuristic method is first used to identify an image matrix and the integer program is subsequently formulated and solved to identify the optimal solution for that image matrix. Although best suited for ideal block structures associated with structural equivalence, the integer programming models have the flexibility to accommodate functional indices pertaining to regular equivalence. Computational results are reported for a variety of one- and two-mode matrices from the blockmodeling literature.     

Simulating correlated multivariate nonnormal distributions: Extending the fleishman power method

A procedure for generating multivariate nonnormal distributions is proposed. Our procedure generates average values of intercorrelations much closer to population parameters than competing procedures for skewed and/or heavy tailed distributions and for small sample sizes. Also, it eliminates the necessity of conducting a factorization procedure on the population correlation matrix that underlies the random deviates, and it is simpler to code in a programming language (e.g., FORTRAN). Numerical examples demonstrating the procedures are given. Monte Carlo results indicate our procedure yields excellent agreement between population parameters and average values of intercorrelation, skew, and kurtosis.     

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.     

The Role of Notation and Knowledge Representation in the Determination of Programming Strategy: A Framework for Integrating Models of Programming Behavior

A number of accounts of expert programming behavior have been advanced. These models of the programming activity have served to highlight the range of factors that are thought to underpin programming strategy. However, such accounts have tended to emphasize either the effects of the organization of the programmer's knowledge representation or the role played by features of the notation of the task language on the emergence, development, and support of particular forms of strategy. Such work has neglected to (a) provide an account of the way in which these factors might interact to determine programming strategy, and (b) shed light upon the nature of the development of particular strategies as programming skill increases. This article presents the results of an empirical analysis of the strategies employed by programmers of varying skill levels using different programming languages. The development of particular forms of strategy is hypothesized to be related both to the development of systematic asymmetries in programmers' generic plan-based representations of programming knowledge and to the way in which features of the notation of particular programming languages might differentially support particular strategies. However, the results of the study reported here suggest that these effects must be interpreted within a broad developmental context. Hence, as programming skill develops, it appears that the notation of the task language tends to take precedence as a determinant of strategy, but has less relevance at beginning stages of skill development and within the context of expert performance. This finding would not be predicted by current models of the programming activity because such models suggest that any notational effects will tend to be consistent regardless of the skill level attained by the programmer. This article endeavors to extend current models of programming by emphasizing the need to consider in detail not only the development of programming strategy, but also the way in which knowledge representation and features of the task langauge interact to give rise to particular forms of programming behavior.     

Motor Programming Within a Sequence of Responses

Choice reaction time prior to a motor response has been shown to depend on the nature of the response to be made. This effect is assumed to represent variations in programming time. However, as the length of a response sequence increases this effect becomes smaller, suggesting that some response programming is postponed until after the response sequence is initiated. The present experiment studied this assumed programming within a sequence of responses. For sequences comprised of two Morse Code responses (e.g. dit-dah) the initial reaction time was independent of the terminal response. However, programming of this terminal response was apparent as a lengthening of the duration of intervals within the response when the terminal response was dah rather than dit. When programming of parts of the sequence is postponed beyond the reaction time interval, the programming occurs later and influences the timing of the sequence of responses.     

A verification framework for agent programming with declarative goals

A long and lasting problem in agent research has been to close the gap between agent logics and agent programming frameworks. The main reason for this problem of establishing a link between agent logics and agent programming frameworks is identified and explained by the fact that agent programming frameworks have hardly incorporated the concept of a declarative goal. Instead, such frameworks have focused mainly on plans or goals-to-do instead of the end goals to be realised which are also called goals-to-be. In this paper, the programming language GOAL is introduced which incorporates such declarative goals. The notion of a commitment strategy—one of the main theoretical insights due to agent logics, which explains the relation between beliefs and goals—is used to construct a computational semantics for GOAL. Finally, a proof theory for proving properties of GOAL agents is introduced. Thus, the main contribution of this paper, rather than the language GOAL itself, is that we offer a complete theory of agent programming in the sense that our theory provides both for a programming framework and a programming logic for such agents. An example program is proven correct by using this programming logic.     

Analysis and visualization of complex psychophysiological data: Coordinated use of multiple applications on a microcomputer

Personal computers have become ubiquitous for data analysis and visualization. Complex analyses and visualizations of large data sets prove challenging for microcomputer environments and highlight a tradeoff between customized programming to enhance specificity and processing speed and the use of commercially available software packages. We frame this choice in terms of a continuum that exists from low-level programming languages to higher-level languages, and beyond this to object-oriented programming environments and other advanced software products; we argue that there is no sharp conceptual distinction between programming and not programming. In this light, we discuss the pros and cons of using several commercial software packages in concert on a single platform to facilitate complex research tasks and discuss the implications of this choice for innovative research.     

Distribution of Programming in a Rapid Aimed Sequential Movement

Studies indicate that rapid sequential movements are preprogrammed and that preprogramming increases with complexity, but more complex sequences that require on-line programming have seldom been studied. The purpose of this investigation was to determine whether on-line programming occurs in a 7-target sequence in which there is a unique target constraint and if so, to determine how different task constraints affect the distribution of additional programming. Subjects contacted seven targets with a hand-held stylus as quickly as possible while maintaining a 90% hit rate. Initiation- and execution-timing patterns and movement kinematics were measured to determine when the additional programming took place. Results indicated that additional programming occurred before initiation and during movement to the first target when the constraint required more spatial accuracy (small target). A different type of unique target (a triple hit of one target) caused the additional programming to occur on-line one or two segments before its execution. Different positions of the unique target also affected timing patterns. Results were discussed in terms of: (1) capacity of processing; (2) control of movement variance; and (3) mean velocity as a programmed parameter in sequential aiming movements.     

Oculomotor programming disturbances in the dementia syndrome

Three types of oculomotor programming disturbances are described in patients with the dementia syndrome. This report describes two of these abnormalities, poorly regulated gaze patterns and a programming type of gaze perseveration. All patients showed poorly regulated gaze patterns in contrast to the normal controls, whereas on the whole only the moderately affected patients showed the programming type of gaze perseveration. The third type of oculomotor programming disturbance is efferent perseveration of gaze (a hypokinetic, "staring" type of gaze pattern) and can be seen with severe dementia. The possible significance of these findings is discussed.     

Cross validation issues in multiobjective clustering

The implementation of multiobjective programming methods in combinatorial data analysis is an emergent area of study with a variety of pragmatic applications in the behavioural sciences. Most notably, multiobjective programming provides a tool for analysts to model trade offs among competing criteria in clustering, seriation, and unidimensional scaling tasks. Although multiobjective programming has considerable promise, the technique can produce numerically appealing results that lack empirical validity. With this issue in mind, the purpose of this paper is to briefly review viable areas of application for multiobjective programming and, more importantly, to outline the importance of cross‐validation when using this method in cluster analysis.     

Several programming models with unascertained parameters and their applications

Several programming models are introduced with the consideration of available unascertained information. In this case, the so‐called unascertained information is some numerical values whose ranges are known but their exact values are not. These models resolve several vital weaknesses of the traditional programming methods to a certain degree. Our study includes considerations of linear and non‐linear programming models with grey parameters, grey 0–1 programming, and satisfactory and quasi‐optimal solutions of grey linear programmings. Finally, some practical applications are given in order to test the applicability of our theory. Copyright © 1999 John Wiley & Sons, Ltd.     

Specification of direction and duration during programming of discrete sliding movements

Summary Two experiments on duration programming of a discrete sliding movement in choice reactions are reported. In the first experiment it was examined whether duration of movement might be preprogrammed when varied across sessions. The result suggested that programming of movement duration is dependent on direction uncertainty. Experiment 2 used the movement precue technique in an attempt to further examine programming of movement duration and direction. Movement duration, movement direction, movement form and foreperiod duration were manipulated. When duration was not precued, a duration effect was found, while precueing resulted in disappearance of the duration effect, demonstrating that duration of sliding movements can be preprogrammed. Moreover, (pre)programming duration was independent of direction uncertainty, supporting an independent order notion of programming of these response variables. Evidence that motor preparation comprises different processing stages was derived from the additive effects of foreperiod duration and of the movement variables duration and direction.