Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available and that the constraint gradients are sparse.
We discuss an SQP algorithm that uses a smooth augmented Lagrangian merit function and makes explicit provision for infeasibility in the original problem and the QP subproblems. SNOPT is a particular implementation that makes use of a semidefinite QP solver. It is based on a limited-memory quasi-Newton approximation to the Hessian of the Lagrangian and uses a reduced-Hessian algorithm (SQOPT) for solving the QP subproblems. It is designed for problems with many thousands of constraints and variables but a moderate number of degrees of freedom (say, up to 2000). An important application is to trajectory optimization in the aerospace industry. Numerical results are given for most problems in the CUTE and COPS test collections (about 900 examples).

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SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization

Analytic hierarchy process : An overview of applications

In this paper, we will propose a Slacks-Based measure (SBM) of efficiency in DEA. This scalar measure deals directly with the input surplus and the output shortage of the decision making unit (DMU) concerned. It is unit invariant and monotone decreasing with respect to input surplus and output shortage. Furthermore, this measure is decided only by consulting with the reference set of the DMU and is not affected by statistics over the whole data set. The new measure has a close connection with other measures proposed so far, e.g., CCR and BCC. The dual side of this model can be interpreted as profit maximization, in contrast to the ratio maximization of the CCR model. Numerical experiments show its validity as an efficiency measurement tool and its compatibility with other measures of efficiency.

A Slacks Based Measure of Efficiency in Data Envelopment Analysis

A slacks-based measure of super-efficiency in data envelopment analysis

Economists have shown that large and persistent differences in productivity levels across businesses are ubiquitous. This finding has shaped research agendas in a number of fields, including (but not limited to) macroeconomics, industrial organization, labor, and trade. This paper surveys and evaluates recent empirical work addressing the question of why businesses differ in their measured productivity levels. The causes are manifold, and differ depending on the particular setting. They include elements sourced in production practices -- and therefore over which producers have some direct control, at least in theory -- as well as from producers' external operating environments. After evaluating the current state of knowledge, I lay out what I see are the major questions that research in the area should address going forward. (JEL D24, G31, L11, M10, O30, O47)

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What Determines Productivity

Evaluating performances for activities in Pacific Rim countries

This paper applies a slacks-based measure dynamic data envelopment analysis (SBM-DNDEA) model to simultaneously evaluate overall, deposit, lending, period, deposit-period and lending-period efficiencies for 22 Taiwanese banks over the period from 1999 to 2011. We treat deposit as the intermediate output, and use non-performing loan as undesirable output capturing the effect of carry-over activity. The results indicate that the improvement in individual process has positive effect on banks' performance, while efficiency in the deposit process may not guarantee efficiency in the lending process, and vice versa. The period efficiency for all banks has the stable variance. Besides, the efficiencies based on operational characteristics are further compared. Keyword: Dynamic network data envelopment analysis, slacks-based measure, efficiency, bank, non-performing loan

https://www.grips.ac.jp/cms/wp-content/uploads/2013/03/DEA_Chapter9.pdf

Operational efficiency in Taiwan banks with consideration of nonperforming loans: A dynamic network DEA

A Japanese manufacturer of electronic goods is planning to construct a new, state-of-the-art factory to manufacture large scale integrated circuits. A team of company managers must decide on the appropriate location for the factory taking many different criteria into account. This paper reports on the decision process that the project team employed to model the site selection problem.

Site Selection for a Large Scale Integrated Circuits Factory

PurposeThe purpose of this study is twofold. First, this research estimates banks' efficiencies from the perspectives of resource utilization and investment after incorporating risk measures as an exogenous input in the investment-efficiency stage. Second, the current study examines the relationship between intellectual capital (IC) and banks' efficiencies.Design/methodology/approachFirst, this study uses a dynamic network data envelopment analysis approach in investigating the efficiencies of 24 Taiwanese banks in 2007–2018 from two perspectives. Second, this research utilizes various regression techniques, namely, ordinary least squares (OLS), robust least squares and truncated regression, to gauge the impact of IC on banks' efficiencies. Typically, IC is determined based on a monetary value-based measure and value-added intellectual coefficient (VAICTM).FindingsResource-utilization (investment) efficiencies were observed as 0.941 (0.964), thereby contributing to the mean overall efficiency of the sample banks at 0.952. However, the related efficiency changes decline over the sample period, thereby suggesting that the average banks' efficiencies hardly increase. Regression analyses show a significantly positive relationship between IC and banks' overall resource-utilization and investment efficiencies.Research limitations/implicationsOverall, this study suggests that researchers should consider risks when estimating banks' efficiencies owing to their connection to banks' investment performance. From banks' dynamic two-stage efficiencies, this study demonstrated that investments in IC will bring improved future economic benefits.Originality/valueDifferent from prior studies, this study improves banks' efficiency evaluation models by incorporating risk measures and assuming weighted periods for the 2007–2008 global financial crisis. Moreover, the use of monetary value-based measure of IC provides consistent results as the commonly-used VAICTM does.

Risk-adjusted banks' resource-utilization and investment efficiencies: does intellectual capital matter?

In data envelopment analysis, we are often puzzled by the large difference between the constant-returns-scale and variable returns-to-scale scores, and by the convexity production set syndrome in spite of the S-shaped curve, often observed in many real data sets. In this paper, we propose a solution to these problems. Initially, we evaluate the constant-returns-scale and variable returns-to-scale scores for all decision-making units by means of conventional methods. We obtain the scale-efficiency for each decision-making unit. Using the scale-efficiency, we decompose the constant-returns-scale slacks for each decision-making unit into scale-independent and scale-dependent parts. Following this, we eliminate scale-dependent slacks from the data set, and thus obtain a scale-independent data set. Next, we classify decision-making units into several clusters, depending either on the degree of scale-efficiency or on some other predetermined characteristics. We evaluate slacks of scale-independent decision-making units within the same cluster using the constant-returns-scale model, and obtain the in-cluster slacks. By summing the scale-dependent and the in-cluster slacks, we define the total slacks for each decision-making unit. Following this, we evaluate the efficiency score of the decision-making unit and project it onto the efficient frontiers, which are no longer guaranteed to be convex and are usually non-convex. Finally, we define the scale-dependent data set by which we can find the scale elasticity of each decision-making unit. We apply this model to a data set of Japanese universities' research activities.

Kaoru Tone

Papers

Evaluating performances for activities in Pacific Rim countries

Operational efficiency in Taiwan banks with consideration of nonperforming loans: A dynamic network DEA

Site Selection for a Large Scale Integrated Circuits Factory

Risk-adjusted banks' resource-utilization and investment efficiencies: does intellectual capital matter?

How to Deal with Non-Convex Frontiers in Data Envelopment Analysis