A Revised Optimal Spanning Table Method for Expanding Competence Sets1/UNE METHODE DE TABLEAU CONSTRUIT OPTIMALE REVISEE POUR DEVELOPPER LES ENSEMBLES DE COMPETENCE

Abstract: The optimal expansion problem of competence sets can be solves by either mathematical programming method or table based method developed by Feng (2001). Compared to the mathematical programming method, table based method for competence set expansion is a more efficient algorithm in using relevant tableaus to solve the optimal expansion problems. This paper proposes a revised table based method to facilitate developing a computer code. A computer program, called TBM, based on the revised algorithm, was developed to solve the large scale problems of expanding competence sets. A numerical example is given, and some possible future research topics on the related theme are discussed. Keywords: competence set expansion; habitual domains; spanning table method Resume: Le probleme de l'expansion optimale des ensembles de competence peut etre resolu soit par la methode de programmation mathematique, soit par une methode basee sur les tableaux developpee par Feng (2001). Comparee a la methode de programmation mathematique, la methode basee sur les tableaux pour l'expansion des ensembles de competence est un algorithme plus efficace dans l'utilisation des tableaux appropries pour resoudre les problemes d'expansion optimale. Cet article propose une methode basee sur les tableaux revise pour faciliter l'elaboration d'un code informatique. Un programme d'ordinateur, appele TBM, base sur l'algorithme revise, a ete developpe pour resoudre les problemes de l'expansion des ensembles de competences a grande echelle. Un exemple numerique est donne, et quelques sujets possibles de futures recherches sur le theme sont debattues. Mots-cles: expansion des ensembles de competences; domaines habituels; methode de tableau construit (ProQuest: ... denotes formula omitted.) 1. INTRODUCTION Helping decision makers most efficiently and effectively acquire the needed competence sets so that they can confidently and competently solve their decision making problems is one of the important issues in decision aiding and competence set analysis and more competence management. The problem to analyze the competence set can be viewed as the problem how to acquire the needed competence set with optimal total benefit. As stated by Feng (1998), the competence set expansion problem is an optimal spanning tree problem, so traditional methods for competence set analysis including competence set expansion algorithms are discussed based on either graph theory or mathematical programming. Feng and Yu (1998) and Feng (2001) presented a new way based on table to discuss the competence set expansion problems. Given the cost function c (i, j) from skill i to skill j among the given skills of the needed competence set (briefly called CS), the problem on how to expand from a subset of CS to the whole CS has been studied analytically and mathematically by Yu and Zhang (1990) when c is symmetric, and by Shi and Yu (1996) when c is asymmetric. When the competence set involves the compound skills, using the deduction graph without cycles, Li and Yu (1994) proposed a method to solve the expansion problems. These works all used the mathematical programming approaches to study the expansion problems. But the mathematical programming method usually results in a large number of constraints and decision variables in formulation even though the problem size is not very large. For example, assume that Sk=x0}, TnSk=(Xi5X2,. . .,xn}, where Sk is the decision maker's acquired competence set of skills and Tr is the true competence set of the skills for a particular problem. According to the mathematical programming formulation given by Shi and Yu(1 996), which is widely used in the field of competence set expansion analysis, both the number of decision variables and the number of constraints are n2+2n when skills are fully connected. For instance, if there are 20 skills to be acquired in an expanding competence set problem, when the skills are fully connected, there are 380=20(20-1) connections among the skills, then the corresponding mathematical programming needs use 440 decision variables and 440 constraints in formulation. …

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