Combining the assumptions of variable and constant returns to scale in the efficiency evaluation of secondary schools

Our paper reports on the use of data envelopment analysis (DEA) for the assessment of performance of secondary schools in Malaysia during the implementation of the policy of teaching and learning mathematics and science subjects in the English language (PPSMI). The novelty of our application is that it makes use of the hybrid returns-to-scale (HRS) DEA model. This combines the assumption of constant returns to scale with respect to quantity inputs and outputs (teaching provision and students) and variable returns to scale (VRS) with respect to quality factors (attainment levels on entry and exit) and socio-economic status of student families. We argue that the HRS model is a better-informed model than the conventional VRS model in the described application. Because the HRS technology is larger than the VRS technology, the new model provides a tangibly better discrimination on efficiency than could be obtained by the VRS model. To assess the productivity change of secondary schools over the years surrounding the introduction of the PPSMI policy, we adapt the Malmquist productivity index and its decomposition to the case of HRS model.     

Non-dominance and potential optimality for partial preference relations

In this paper we obtain new theoretical results relating the notions of potential optimality and non-dominance without an assumption that a value function exists. In particular, we investigate a decision problem involving the choice of single or multiple best objects. Our results show that the notions of potential optimality and non-dominance are equivalent in a special case of preferences of the decision maker expressed by partial quasi-orders.     

A simple derivation of scale elasticity in data envelopment analysis

In this paper, we suggest a simple derivation of the formulae for the scale elasticity in the variable returns-to-scale technology as used in data envelopment analysis. Our development is consistent with the existing literature but the proof is much shorter and applies to the general case without any simplifying conditions.     

Mixed partial elasticities in constant returns-to-scale production technologies

Recently, Podinovski and Førsund (2010) developed a linear programming approach to the analysis and calculation of a class of mixed partial elasticity measures in variable returns-to-scale (VRS) production technologies. In the current paper, we extend their approach to the constant returns-to-scale (CRS) technologies and formulate linear programs required for the computation of elasticity measures. Among other results obtained in this paper, we prove a new result, valid in both VRS and CRS technologies, that allows us to identify the reason why the corresponding elasticity measure is undefined at the unit. This removes the need for a preliminary sorting of the units into those units where the elasticity measure applies and those where it does not.     

Interval articulation of superiority and precise elicitation of priorities

This paper develops an approach to obtaining precise (point) estimates of priorities of objects, in particular, coefficients of importance of criteria. It is assumed that the judgements regarding the preference superiority of one object over another are given in the forms of intervals, that is by indicating the lower and upper bounds. The suggested approach is suitable both in the case of consistent and inconsistent preferences. In the former case, the available intervals are processed by contracting them to the maximum degree, in the latter, by extending them to the minimum degree. The degrees of contraction or extension are regarded as the indexes of indeterminacy or inconsistency of preferences, and treated as multiple objective functions. A method of transformation of such a multicriterial problem to a sequence of several linear programming problems is suggested.     

Production trade-offs and weight restrictions in data envelopment analysis

In this paper we suggest two equivalent ways in which the information about production trade-offs between the inputs and outputs can be incorporated into the models of data envelopment analysis (DEA). Firstly, this can be implemented by modifying envelopment DEA models. Secondly, the same information can be captured using weight restrictions in multiplier DEA models. Unlike other methods used for the assessment of weight restrictions, for example those based on value judgements or monetary considerations, the trade-off approach developed in this paper ensures that the radial target of any inefficient unit is technologically realistic and, therefore, the efficiency measure retains its traditional meaning of the extreme radial improvement factor. In other words, this paper suggests that ‘technology thinking’ could be used instead of ‘value thinking’ in the construction of weight restrictions, which offers real practical advantages. The method is equally applicable to the models under constant and variable returns-to-scale assumptions.     

Bilinear optimization in the analysis of multicriteria problems using criteria importance theory under inexact information about preferences

Exact efficient numerical methods are proposed for solving bilinear optimization problems that arise when various solution variants are compared based on their preferability using an additive value function in the case of interval estimates of the degrees of superiority of certain criteria over others and in the case of interval restrictions on the growth of preferences along the criteria range.     

Sensitivity analysis for choice problems with partial preference relations

In this paper we consider choice problems under the assumption that the preferences of the decision maker are expressed in the form of a parametric partial weak order without assuming the existence of any value function. We investigate both the sensitivity (stability) of each non-dominated solution with respect to the changes of parameters of this order, and the sensitivity of the set of non-dominated solutions as a whole to similar changes. We show that this type of sensitivity analysis can be performed by employing techniques of linear programming.