Sungmook Lim

Use of DEA cross-efficiency evaluation in portfolio selection: An application to Korean stock market

We propose a way of using DEA cross-efficiency evaluation in portfolio selection. While cross efficiency is an approach developed for peer evaluation, we improve its use in portfolio selection. In addition to (average) cross-efficiency scores, we suggest to examine the variations of cross-efficiencies, and to incorporate two statistics of cross-efficiencies into the mean-variance formulation of portfolio selection. Two benefits are attained by our proposed approach. One is selection of portfolios well-diversified in terms of their performance on multiple evaluation criteria, and the other is alleviation of the so-called “ganging together” phenomenon of DEA cross-efficiency evaluation in portfolio selection. We apply the proposed approach to stock portfolio selection in the Korean stock market, and demonstrate that the proposed approach can be a promising tool for stock portfolio selection by showing that the selected portfolio yields higher risk-adjusted returns than other benchmark portfolios for a 9-year sample period from 2002 to 2011.

Minimax and maximin formulations of cross-efficiency in DEA

In the conventional cross-efficiency formulation, the efficiency score of a DMU under evaluation is maximized as the primary goal while the average cross-efficiency of peer DMUs is minimized (or maximized) as the secondary goal. The proposed models replace the secondary goal with the minimization (or maximization) of the best (or worst) cross-efficiency of peer DMUs. We demonstrate the appropriateness of the proposed formulations of cross-efficiency for certain efficiency evaluation contexts, and show how they help enhance the usefulness of cross-efficiency evaluation in DEA using a randomly generated sample data set. For a solution method for the proposed models of cross-efficiency, we develop a bisection algorithm whose computational complexity is polynomial.

Integrated data envelopment analysis: Global vs. local optimum

Chiou et al. (2010) (A joint measurement of efficiency and effectiveness for non-storable commodities: integrated data envelopment analysis approaches. European Journal of Operational Research 201, 477–489) propose an integrated data envelopment analysis model in measuring decision making units (DMUs) that have a two-stage internal network structure with multiple inputs, outputs, and consumptions. They claim that any optimal solutions determined by their DEA model are a global optimum, not a local optimum. We show that such a conclusion is a false statement due to their misuse of Hessian matrix in examining the concavity of the objective function, and their DEA model is actually a non-convex optimization problem. As a result, their DEA model is unusable in practice due to a lack of efficient algorithm for this particular non-convex DEA model. We further show that Chiou et al.’s (2010) model is a special case of a well-known two-stage network DEA model, and it can be transformed into a parametric linear program for which an approximate global optimal solution can be obtained by solving a sequence of linear programs in combination with a simple search algorithm.

Incorporating performance measures with target levels in data envelopment analysis

Data envelopment analysis (DEA) is a technique for evaluating relative efficiencies of peer decision making units (DMUs) which have multiple performance measures. These performance measures have to be classified as either inputs or outputs in DEA. DEA assumes that higher output levels and/or lower input levels indicate better performance. This study is motivated by the fact that there are performance measures (or factors) that cannot be classified as an input or output, because they have target levels with which all DMUs strive to achieve in order to attain the best practice, and any deviations from the target levels are not desirable and may indicate inefficiency. We show how such performance measures with target levels can be incorporated in DEA. We formulate a new production possibility set by extending the standard DEA production possibility set under variable returns-to-scale assumption based on a set of axiomatic properties postulated to suit the case of targeted factors. We develop three efficiency measures by extending the standard radial, slacks-based, and Nerlove–Luenberger measures. We illustrate the proposed model and efficiency measures by applying them to the efficiency evaluation of 36 US universities.

A Robust Joint Optimal Pricing and Lot-Sizing Model

The problem of jointly determining a robust optimal bundle of price and order quantity for a retailer in a singleretailer, single supplier, single-product supply chain is considered. Demand is modeled as a decreasing power function of product price, and unit purchasing cost is modeled as a decreasing power function of order quantity and demand. Parameters defining the two power functions are uncertain but their possible values are characterized by ellipsoids. We extend a previous study in two ways; the purchasing cost function is generalized to take into account the economies of scale realized by higher product demand in addition to larger order quantity, and an exact transformation into an equivalent convex optimization program is developed instead of a geometric programming approximation scheme proposed in the previous study.

Context-Dependent Data Envelopment Analysis with Cross-Efficiency Evaluation

To address some problems with the original context-dependent data envelopment analysis (DEA), this paper proposes a new version of context-dependent DEA; this version is based on cross-efficiency evaluations. One of the problems with the original context-dependent DEA is that the attractiveness and progress measures only represent the radial distance between the decision-making unit (DMU) under evaluation and the evaluation context. This representation only shows how distinct the DMU is from a single specific DMU on the evaluation context, not from the entire evaluation context overall. Another problem is that the magnitude of attractiveness and progress scores in the original context-dependent DEA may not have significant meanings. It may not be proper to say that a DMU is more attractive simply because it has a higher attractiveness score for the same reason that the performance of inefficient DMUs cannot be compared with one another simply based on their efficiency scores. We incorporate cross-efficiency evaluations into the context-dependent DEA to overcome the preceding shortcomings of the original context-dependent DEA. We also demonstrate the proposed models appropriateness and usefulness with an illustrative example.

Modified matrix splitting method for the support vector machine and its application to the credit classification of companies in Korea

Highlights? We propose a solving approach for the ?-support vector machine (SVM) for classification problems. We use the modified matrix splitting method and incomplete Cholesky decomposition. The matrix splitting method combined with the projection gradient method. The incomplete Cholesky decomposition is used for the large scale Hessian. The proposed method applies for the credit prediction for small-sized Korean companies. This research proposes a solving approach for the ?-support vector machine (SVM) for classification problems using the modified matrix splitting method and incomplete Cholesky decomposition. With a minor modification, the dual formulation of the ?-SVM classification becomes a singly linearly constrained convex quadratic program with box constraints. The Kernel Hessian matrix of the SVM problem is dense and large. The matrix splitting method combined with the projection gradient method solves the subproblem with a diagonal Hessian matrix iteratively until the solution reaches the optimum. The method can use one of several line search and updating alpha methods in the projection gradient method. The incomplete Cholesky decomposition is used for the calculation of the large scale Hessian and vectors. The newly proposed method applies for a real world classification problem of the credit prediction for small-sized Korean companies.

An Optimization Approach to the Construction of a Sequence of Benchmark Targets in DEA-Based Benchmarking

Stepwise efficiency improvement in data envelopment analysis (DEA)-based benchmarking is a realistic and effective method by which inefficient decision making units (DMUs) can choose benchmarks in a stepwise manner and, thereby, effect gradual performance improvement. Most of the previous research relevant to stepwise efficiency improvement has focused primarily on how to stratify DMUs into multiple layers and how to select immediate benchmark targets in leading levels for lagging-level DMUs. It can be said that the sequence of benchmark targets was constructed in a myopic way, which can limit its effectiveness. To address this issue, this paper proposes an optimization approach to the construction of a sequence of benchmarks in DEA-based benchmarking, wherein two optimization criteria are employed : similarity of input-output use patterns, and proximity of input-output use levels between DMUs. To illustrate the proposed method, we applied it to the benchmarking of 23 national universities in South Korea.

Multi-Criteria ABC Inventory Classification Using the Cross-Efficiency Method in DEA

Multi-criteria ABC inventory classification, which aims to classify inventory items by considering more than one criterion, is one of the most widely employed techniques for inventory control. The weighted linear optimization (WLO) model proposed by Ramanathan (2006) solves the problem of multi-criteria ABC inventory classification by generating a set of criterion weights for each inventory item and assigning a normalized score to the item for ABC analysis. However, the WLO model has some limitations. First, many inventory items can share the same optimal score, which can hinder a precise classification of inventory items. Second, the model allows too much flexibility in weighting multiple criteria; each item is allowed to choose its own weights so that it can maximize its score. As a result, if an item dominates the others in terms of a certain criterion, it may be classified into a higher class regardless of other criteria by assigning an overwhelming weight to the criterion. Consequently, an item with a high value in an unimportant criterion and low values in others may be inappropriately classified as class A, leading to an inaccurate classification of inventory items. To overcome these shortcomings, we extend the WLO model by using the cross-efficiency method in data envelopment analysis. We claim that the proposed model can provide a more reasonable and accurate classification of inventory items by mitigating the adverse effect of flexibility in the choice of weights and yielding a unique ordering of inventory items.

Method of Benchmarking Route Choice Based on the Input Similarity Using DEA

Benchmarking requires an effective methodology for finding the best performer, which entails an evaluation of the relative efficiencies of competitors in terms of multiple input and output factors. To identify the best performer, Data Envelopment Analysis (DEA) has been popularly used. However, the conventional DEA has some deficiencies with respect to its use for benchmarking. First, the reference set of an inefficient DMU often has multiple efficient DMUs. Second, it might be quite impossible for an inefficient DMU to achieve its target’s efficiency in a single step, especially when the target is far removed from the DMU. To overcome these deficiencies of conventional DEA, we propose a new stepwise benchmarking method using DEA, which enables inefficient DMUs to select the more appropriate benchmarking DMU based on the similarity.