Kim Fung Lam

Minimizing deviations from the group mean: A new linear programming approach for the two-group classification problem

Abstract This paper proposes a new linear programming approach to solve the two-group classification problem in discriminant analysis. This new approach is based on an idea from cluster analysis that objects within the same group should be more similar than objects between groups. Consequently, it is desirable for the classification score of an object to be nearer to its mean classification score, but further from the mean classification score of the other group. This objective is accomplished by minimizing the total deviation of the classification scores of the objects from their group mean scores in a linear programming approach. When applied to an actual managerial problem and simulated data, the proposed linear programming approach performs well both in groups separation and group-membership predictions of new objects. Moreover, this new approach has an advantage of obtaining more stable classification function across different samples than most of the existing linear programming approaches.

Selection criteria and the impact of personality on getting hired

Based on an earlier policy‐capturing study of the Big Five personality traits and general mental ability, this paper explores and analyzes the hiring preference of Hong Kong employers across five important personal attributes, including not only personality but also practical skill dimensions. The preferences and trade‐offs of 300 experienced recruiters were obtained via conjoint analysis, a theoretically grounded statistical tool that is used to discompose and analyze decisions, for assessing the hiring decisions for entry‐level professional positions. Among knowledge, skills, abilities, and personality, the personality of a candidate has a relatively greater impact on the hiring decision. Three of the Big Five personality traits were elected from among five major hiring attributes for effective performance, with conscientiousness being the most dominant attribute across all eight major industries. The other attributes, in order of importance, include English communication skills, openness to new experiences, academic performance, and agreeableness. Discrepancies between intended and actual decisions were also addressed by comparing the results with self‐reported ratings.

Combining discriminant methods in solving classification problems in two-group discriminant analysis

Abstract As no single-discriminant method outperforms other discriminant methods under all circumstances, decision-makers may solve a classification problem using several discriminant methods and examine their performance for classification purposes in the training sample. Based on this performance, better classification methods might be adopted and poor methods might be avoided. However, which single-discriminant method is best to predict the classification of new observations is still not clear, especially when some methods offer a similar classification performance in the training sample. In this paper, we present a method that combines several discriminant methods to predict the classification of new observations. Simulation experiments are run to test this combining technique.

An experimental comparison of some recently developed linear programming approaches to the discriminant problem

This article studies and evaluates several recently proposed linear programming formulations to solve classification problems in discriminant analysis. Some of the new linear programming formulations have merits and perform well in a simulation experiment. A weighted deviation approach is introduced to correct the imbalance of misclassifications across the two groups.

In the determination of weight sets to compute cross-efficiency ratios in DEA

Data envelopment analysis (DEA) measures the production performance of decision-making units (DMUs) which consume multiple inputs and produce multiple outputs. Although DEA has become a very popular method of performance measure, it still suffers from some shortcomings. For instance, one of its drawbacks is that multiple solutions exist in the linear programming solutions of efficient DMUs. The obtained weight set is just one of the many optimal weight sets that are available. Then why use this weight set instead of the others especially when this weight set is used for cross-evaluation? Another weakness of DEA is that extremely diverse or unusual values of some input or output weights might be obtained for DMUs under assessment. Zero input and output weights are not uncommon in DEA. The main objective of this paper is to develop a new methodology which applies discriminant analysis, super-efficiency DEA model and mixed-integer linear programming to choose suitable weight sets to be used in computing cross-evaluation. An advantage of this new method is that each obtained weight set can reflect the relative strengths of the efficient DMU under consideration. Moreover, the method also attempts to preserve the original classificatory result of DEA, and in addition this method produces much less zero weights than DEA in our computational results.

A note on minimizing absolute percentage error in combined forecasts

In this note, two new approaches of combined forecasts are proposed. One approach minimizes mean absolute percentage error while the other approach minimizes the maximum absolute percentage error. A goal programming model is used to obtain the weights to combine different forecasts to minimize the mean absolute percentage error. This formulation can be solved readily by any linear programming computer code. The other approach, minimizing the maximum absolute percentage error, can also be formulated as a goal programming model. Scope and purposeMean absolute percentage error has been widely used as a performance measure in forecasting. One of the major reasons for its popularity is that it is easy to interpret and understand and it becomes a good alternative to mean squared error. Our proposed linear programming models can provide solutions of the minimum mean absolute percentage error and the minimum of the maximum absolute percentage error in combined forecasts. The models we proposed could be solved readily by any linear programming computer code.

Minimizing deviations of input and output weights from their means in data envelopment analysis

In this paper, we propose a model that minimizes deviations of input and output weights from their means for efficient decision-making units in data envelopment analysis. The mean of an input or output weight is defined as the average of the maximum and the minimum attainable values of the weight when the efficient decision making unit under evaluation remains efficient. Alternate optimal weights usually exist in the linear programming solutions of efficient decision-making units and the optimal weights obtained from most of the linear programming software are somewhat arbitrary. Our proposed model can yield more rational weights without a priori information about the weights. Input and output weights can be used to compute cross-efficiencies of decision-making units in peer evaluations or group decision-making units, which have similar production processes via cluster analysis. If decision makers want to avoid using weights with extreme or zero values to access performance of decision-making units, then choosing weights that are close to their means, may be a rational choice.

Linear goal programming in estimation of classification probability

Classification of objects into groups is a common practice in everyday life. Normally, the scores of some pertinent criteria about the objects are available and form the most important factor in the classification decision. Discriminant analysis [4], logistic regression [1,3], and linear goal programming [2,5] are alternative techniques used to determine the criterion weights. Classification with these techniques is based upon the weighted sum of the criterion scores of each object. The classification itself ignores more discriminating information about objects within groups. For example, dividing companies into bankrupt and non-bankrupt groups ignores the fact that the non-bankrupt group contains companies of varying qualities. Thus, it is more appropriate to determine the group membership probabilities for each object instead of just the pure classification into one of the groups. These probabilities can readily be used to discriminate objects within the same group.

Deriving the partial values in MCDM by goal programming

Preference for a set of alternatives evaluated under multiple criteria is frequently expressed in the form of pairwise comparisons. We propose a linear goal programming model for deriving the partial and overall preference values of the alternatives directly from pairwise comparisons. This model can be a useful alternative to AHP. The partial values represent the contribution of the criteria to the overall preference. Simulation experiments, which are conducted to compare the performance of the model with that of two other existing models, show that the model has good performance.

A linear goal programming model for classification with non-monotone attributes

Abstract Classification function analysis concerns separating two or more groups of objects in a data set and allocating new objects to previously defined groups. Usually, a set of attribute weights are estimated and the classification decision of an object is based on the weighted sum of its attribute scores. Statistical linear discriminant analysis, logistic regression, and linear programming approaches to classification problems have been proposed to address this problem. However, monotonicity of the attribute scores with respect to the likelihood of belonging to one specific group is presumed by these approaches. This may not be realistic in many applications. In this paper, a linear goal programming approach with the ability to capture the non-monotonicity of some attribute scores in classification problems is proposed. Classification performances of this approach and other classification approaches are evaluated by a simulation experiment. The results are very encouraging for the proposed approach.