Agha Iqbal Ali

Translation invariance in data envelopment analysis

Conditions are established under which DEA models are translation invariant. Specifically, an affine displacement does not alter the efficient frontier for models incorporating the convexity constraint. This affords a ready solution to the problems of scaling and the presence of zero values which arise in Data Envelopment Analysis.

DEA Malmquist productivity measure: New insights with an application to computer industry

Abstract Data envelopment analysis (DEA) measures the relative efficiency of decision making units (DMUs) with multiple inputs and multiple outputs. DEA-based Malmquist productivity index measures the productivity change over time. The DEA-based Malmquist productivity index can be decomposed into two components: one measuring the technical change and the other measuring the frontier shift. In the current study, we provide an extension to the DEA-based Malmquist approach by further analyzing these two Malmquist components. Our proposed new approach not only reveals patterns of productivity change and presents a new interpretation along with the managerial implication of each Malmquist component, but also identifies the strategy shifts of individual DMUs based upon isoquant changes. We can make judgments on whether or not such strategy shifts are favorable and promising. The approach is illustrated with a set of Fortune Global 500 Computer and Office Equipment companies from 1991 to 1997.

Computational Accuracy and Infinitesimals In Data Envelopment Analysis

The role of the non-Archimedean construct ∈ in the CCR and BCC models is clarified. It is established that the associated dual linear programs can be infeasible (for the multiplier side) and unboun...

Components of efficiency evaluation in data envelopment analysis

This paper examines three essential components which comprise efficiency evaluation in data envelopment analysis. The three components are present in each DEA model and determine the implicit evaluation scheme associated with the model. These components provide a framework for classifying the various DEA models with respect to (i) the form of envelopment surface, (ii) the orientation, and (iii) the pricing mechanism implicit in the multiplier lower bounds. The discussion focuses on the standard DEA models, includes additional issues relating to efficiency evaluation, and is illustrated by a computational example.

Streamlined computation for data envelopment analysis

Abstract This paper discusses issues related to an efficient computational methodology for performing data envelopment analysis focussing on three data envelopment analysis models: CCR, BCC, and ADDITIVE. It introduces constructs that facilitate efficiency of computation in solving a sequence of as many linear programs as there are decision making units. Computational testing with real-world data sets with up to 533 decision making units indicates that employing these constructs reduces computation time significantly.

Output-input ratio analysis and DEA frontier

Abstract Data envelopment analysis (DEA) is a mathematical programming technique for identifying efficient frontiers for peer decision making units (DMUs). The ability of identifying frontier DMUs prior to the DEA calculation is of extreme importance to an effective and efficient DEA computation. In this paper, we present mathematical properties which characterize the inherent relationships between DEA frontier DMUs and output–input ratios. It is shown that top-ranked performance by ratio analysis is a DEA frontier point. This in turn allows identification of membership of frontier DMUs without solving a DEA program. Such finding is useful in streamlining the solution of DEA.

Dual algorithms for pure network problems

This paper reports the development of a new algorithmic implementation of the dual algorithm for the capacitated minimum cost network flow problem. Furthermore, it introduces dual reoptimization procedures and compares primal and dual algorithms for the optimization and reoptimization of network problems. The implementation makes use of cut-sets for the efficient execution of the entering variable selection and the selection of the leaving variable is tied to the basis structure at an iteration. Empirical testing of the dual algorithm for optimization shows that it dominates the primal procedure for assignment problems with 400 nodes, transportation problems with more than 600 nodes, and transshipment problems with more than 1500 nodes. Computational testing with typical changes found in decomposition and relaxation procedures indicates the superiority of dual reoptimization over primal reoptimization. For a sequence of parametric changes, as would be typical in large-scale programming techniques, on the average, dual reoptimization is found to require between 75 and 93% fewer pivots and between 20 and 50% less time than primal reoptimization depending on the type of change.

The asymmetric m-traveling salesman problem: A duality based branch-and-bound algorithm

Abstract This paper presents a new model and branch-and-bound algorithm for the asymmetric m-travelling salesmen problem. The algorithm uses a Lagrangean relaxation, a subgradient algorithm to solve the Lagrangean dual, a greedy algorthim for obtaining minimal m-trees, penalties to strengthen the lower bounds on candidate problems, and a new concept known as staged optimization. Computational experience for problems having up to 100 cities is presented.

The equal flow problem

Abstract This paper presents a new algorithm for the solution of a network problem with equal flow side constraints. The solution technique is motivated by the desire to exploit the special structure of the side constraints and to maintain as much of the characteristics of pure network problems as possible. The proposed algorithm makes use of Lagrangean relaxation to obtain a lower bound and decomposition by right-hand-side allocation to obtain upper bounds. The lagrangean dual serves not only to provide a lower bound used to assist in termination criteria for the upper bound, but also allows an initial allocation of equal flows for the upper bound. The algorithm has been tested on problems with up to 1500 nodes and 6000 arcs. Computational experience indicates that solutions whose objective function value is well within 1% of the optimum can be obtained in 1%–65% of the MPSX time depending on the amount of imbalance inherent in the problem. Incumbent integer solutions which are within 99.99% feasible and well within 1% of the proven lower bound are obtained in a straightforward manner requiring, on the average, 30% of the MPSX time required to obtain a linear optimum.

The Impact of Deregulation during 1990–1997 on Banking in Austria

The operating environment for banking in Austriachanged substantially during 1990–1997. The changes during the periodcan be seen as a gradualadjustment towards adherence to European banking standards, which becamea legal requirement on Austrias entry, in 1995, into the European Union. Inthis paper, we investigate the relative performance of Austrian banksduring this period and thereby test the hypothesis of increasedcompetition. The study reveals that Aktiengesellschaften hadconsistent productivity improvement over the period, Sparkassen,and Volksbanken exhibited a turnaround in productivity in 1997,and Raiffeisenbanken experienced consistent productivity decline.Overall, Austrian banks experienced a decline in average efficiencyand productivity until 1996 with slight improvements in 1997. Thestudy reveals evidence of product diversification rather thanincreased price competition; a decrease in the spread of prices paidfor inputs indicates increased competitiveness over the period, whichcan be attributed to deregulation brought about by EU-membership.