Matrix Differential Calculus with Applications in Statistics and Econometrics

Robust optimization is a young and active research field that has been mainly developed in the last 15 years. Robust optimization is very useful for practice, since it is tailored to the information at hand, and it leads to computationally tractable formulations. It is therefore remarkable that real-life applications of robust optimization are still lagging behind; there is much more potential for real-life applications than has been exploited hitherto. The aim of this paper is to help practitioners to understand robust optimization and to successfully apply it in practice. We provide a brief introduction to robust optimization, and also describe important do׳s and don׳ts for using it in practice. We use many small examples to illustrate our discussions.

A practical guide to robust optimization

Network data envelopment analysis: A review

A survey of adjustable robust optimization

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

Minimax and maximin formulations of cross-efficiency in DEA

Research highlights? We propose a method of selecting benchmarking paths for inefficient DMUs in DEA. ? The proposed method directs an inefficient DMU to its target in an implementable way. ? It establishes a benchmarking path across a sequence of layers of DMUs. ? Benchmarks are chosen based on criteria: attractiveness, progress, and infeasibility. ? We provide an empirical study with the operational data of 26 container terminal in Asia. One of the existing DEA methods' limitations noted in the literature lies in the process of benchmarking of reference targets for inefficient DMUs. Difficulties arising in this process can be summarized to three aspects. First, the reference target might be a hypothetical DMU that does not actually exist (it is difficult and indeed unrealistic to learn from such a DMU). Second, the reference set of an inefficient DMU often has multiple efficient DMUs making it difficult to benchmark multiple best-practice DMUs simultaneously. Third, it is quite impossible for an inefficient DMU to achieve its target's efficiency in a single step, especially when the inefficient DMU is far from the efficient frontier. In order to overcome these difficulties, we propose, in place of the selection of benchmarked DMUs on the efficient frontier, a method of selecting effective benchmarking paths that direct an inefficient DMU to its target on the efficient frontier in an implementable and realistic way. The proposed method was designed based on the idea of the context-dependent DEA proposed by Seiford and Zhu (2003). It starts by clustering DMUs into several layers according to their efficiency scores, and then establishes a benchmarking path across the sequence of layers. Among the DMUs in the next layer, the most preferable one is selected as the next benchmark target, based on three criteria: attractiveness, progress, and infeasibility. We tested the proposed method by applying it to the evaluation of the relative efficiency of operations of 26 container terminals located in Asia.

A study on the selection of benchmarking paths in DEA

Integrated data envelopment analysis: Global vs. local optimum

We consider a robust optimization model of determining a joint optimal bundle of price and order quantity for a retailer in a two-stage supply chain under uncertainty of parameters in demand and purchase cost functions. Demand is modeled as a decreasing power function of product price, and unit purchase cost is modeled as a decreasing power function of order quantity and demand. While the general form of the power functions are given, it is assumed that parameters defining the two power functions involve a certain degree of uncertainty and their possible values can be characterized by ellipsoids. We show that the robust optimization problem can be transformed into an equivalent convex optimization which can be solved efficiently and effectively using interior-point methods. In addition, we propose a practical implementation of the model, where the stochastic characteristics of parameters are obtained from regression analysis on past sales and production data, and ellipsoidal representations of the parameter uncertainties are obtained based on a combined use of genetic algorithm and Monte Carlo simulation. An illustrative example is provided to demonstrate the model and its implementation.

Sungmook Lim

Papers

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

Minimax and maximin formulations of cross-efficiency in DEA

A study on the selection of benchmarking paths in DEA

Integrated data envelopment analysis: Global vs. local optimum

A joint optimal pricing and order quantity model under parameter uncertainty and its practical implementation