Efficiency measurement using independent component analysis and data envelopment analysis

Efficiency measurement is an important issue for any firm or organization. Efficiency measurement allows organizations to compare their performance with their competitors’ and then develop corresponding plans to improve performance. Various efficiency measurement tools, such as conventional statistical methods and non-parametric methods, have been successfully developed in the literature. Among these tools, the data envelopment analysis (DEA) approach is one of the most widely discussed. However, problems of discrimination between efficient and inefficient decision-making units also exist in the DEA context (Adler and Yazhemsky, 2010). In this paper, a two-stage approach of integrating independent component analysis (ICA) and data envelopment analysis (DEA) is proposed to overcome this issue. We suggest using ICA first to extract the input variables for generating independent components, then selecting the ICs representing the independent sources of input variables, and finally, inputting the selected ICs as new variables in the DEA model. A simulated dataset and a hospital dataset provided by the Office of Statistics in Taiwan’s Department of Health are used to demonstrate the validity of the proposed two-stage approach. The results show that the proposed method can not only separate performance differences between the DMUs but also improve the discriminatory capability of the DEA’s efficiency measurement.     

A bargaining game model for measuring performance of two-stage network structures

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs), where the internal structures of DMUs are treated as a black-box. Recently DEA has been extended to examine the efficiency of DMUs that have two-stage network structures or processes, where all the outputs from the first stage are intermediate measures that make up the inputs to the second stage. The resulting two-stage DEA model not only provides an overall efficiency score for the entire process, but also yields an efficiency score for each of the individual stages. The current paper develops a Nash bargaining game model to measure the performance of DMUs that have a two-stage structure. Under Nash bargaining theory, the two stages are viewed as players and the DEA efficiency model is a cooperative game model. It is shown that when only one intermediate measure exists between the two stages, our newly developed Nash bargaining game approach yields the same results as applying the standard DEA approach to each stage separately. Two real world data sets are used to demonstrate our bargaining game model.     

New third and fourth order nonlinear solvers for computing multiple roots

We present a new third order method for finding multiple roots of nonlinear equations based on the scheme for simple roots developed by Kou et al. [J. Kou, Y. Li, X. Wang, A family of fourth-order methods for solving non-linear equations, Appl. Math. Comput. 188 (2007) 1031-1036]. Further investigation gives rise to new third and fourth order families of methods which do not require second derivative. The fourth order family has optimal order, since it requires three evaluations per step, namely one evaluation of function and two evaluations of first derivative. The efficacy is tested on a number of relevant numerical problems. Computational results ascertain that the present methods are competitive with other similar robust methods.     

Allocating fixed costs and common revenue via data envelopment analysis

An issue of considerable importance involves the allocation of fixed costs or common revenue among a set of competing entities in an equitable way. Based on the data envelopment analysis (DEA) theory, this paper proposes new methods for (i) allocating fixed costs to decision making units (DMUs) and (ii) distributing common revenue among DMUs, in such a way that the relative efficiencies of all DMUs remain unchanged and the allocations should reflect the relative efficiencies and the input-output scales of individual DMUs. To illustrate our methods, numerical results for an example are described in this paper.     

A note on efficiency decomposition in two-stage data envelopment analysis

Data envelopment analysis (DEA) is a useful tool of efficiency measurement for firms and organizations. Kao and Hwang (2008) take into account the series relationship of the two sub-processes in a two-stage production process, and the overall efficiency of the whole process is the product of the efficiencies of the two sub-processes. To find the largest efficiency of one sub-process while maintaining the maximum overall efficiency of the whole process, Kao and Hwang (2008) propose a solution procedure to accomplish this purpose. Nevertheless, one needs to know the overall efficiency of the whole process before calculating the sub-process efficiency. In this note, we propose a method that is able to find the sub-process and overall efficiencies simultaneously.     

A stochastic approach to capture crystal plasticity

A stochastic crystal plasticity model is proposed and applied within the rate-independent regime. As opposed to conventional deterministic algorithms wherein multiple slip systems are activated and redundant constraints may exist, the new Monte Carlo plasticity (MCP) paradigm is based on a stochastic chain of singly activated slip systems and thus avoids the possible ill-condition associated with multi-slip algorithms. The choice of the activated slip system is made at each Monte Carlo (MC) step based on the Metropolis algorithm. The MCP model is implemented within a Material Point Method (MPM) as a constitutive model to capture the elasto-plastic behavior of polycrystalline materials. A comparison with a commonly used singular value decomposition (SVD) algorithm indicates that MCP offers superior computational efficiency while maintaining comparable accuracy.     

Density gradients in packed columns: II. Effects of density gradients on efficiency in supercritical fluid separations

To investigate how fluid compressibility affects efficiency in supercritical fluid separations, band dispersion along a packed capillary column was measured from on-column elution rate profiles obtained under solvating gas chromatography (SGC) conditions; this allowed efficiency to be determined with respect to position along the column. Theoretical efficiency was also modeled. The model indicates that the primary cause of band broadening in SGC is high mobile phase velocity near the column outlet. However, the experimental results show that significant band broadening also occurs near the column inlet in a region that corresponds to high elution rates of the analyte. On-column detection also revealed spatial focusing of the analyte as it moves down the column density gradient.     

Advantages of a small-volume counter-current chromatography column

Counter-current chromatography (CCC) works with a support-free liquid stationary phase. This allows for preparative separations and purifications. However, there are serious technical constraints because of the need to keep a liquid stationary phase in a column. Centrifugal fields are used. A new commercial hydrodynamic 18 mL column made with a narrow-bore 0.8 mm Teflon tubing was evaluated by comparing it with older hydrodynamic CCC columns and a similar 19 mL column but made with 1.6 mm Teflon tubing. A small-volume CCC column allows for reliable and fast solute partition coefficient determination. When resolution is required, both high efficiency and liquid stationary phase retention are needed. Unfortunately, these two requirements bear technical contradictions. A column coiled with a narrow tubing bore will provide a high chromatographic efficiency while a column containing wider tubing bore will achieve higher stationary phase retention. In all cases, increasing the magnitude of the centrifugal field also increases the stationary phase retention. The solution is to build centrifuges able to produce high fields that will provide acceptable liquid phase retention with narrow-bore tubes. The new 18 mL 0.8 mm tubing bore column is able to rotate as fast as 2100 rpm generating a 240 × g field. The two older CCC columns cannot compete with the new one. However, the small 19 mL column with 1.6 mm bore tubing can be useful when fast results are desired without top resolution.     

Effect of mobile phase anionic additives on selectivity,efficiency, and sample loading capacity of cationic drugs in reversed-phase liquid chromatography

In the present work, we study the effect of mobile phase anionic additive type and concentration on the selectivity, efficiency, and sample loading capacity of cationic drugs in reversed-phase liquid chromatography (RPLC). The type and concentration of an anionic additive are known to have a strong effect on the absolute retention of cations in RPLC; in contrast they have only a small effect on the selectivity of one cation relative to a second as seen here. This is mainly due to the similarity of the ion pair formation constants between the selected cations. The limiting retention factors of cations (i.e. the retention factor of the fully ion-paired analyte at very high additive concentration) are roughly proportional to their inherent hydrophobicities (i.e. the retention factor of the analyte in the absence of the anionic additive). With a given anion, differences in ion pairing strength between the solutes are required for effective selectivity adjustment. Based on the Wade–Lucy–Carr (W–L–C) kinetic model of overload peaks, the approach we developed in our previous work was used to study the effect of mobile phase anionic additives type and concentration on the limiting plate count (N₀) and sample loading capacity (ω_0.5) of various cationic drugs. Under linear chromatographic conditions, where the analyte exhibits its smallest peak width and thus maximum apparent plate count, the type and concentration of anionic additives have almost no effect on peak width. In comparison to neutral analytes the sorption isotherms of cationic species are very easily overloaded even when many fewer moles of cations as compared to neutrals are injected. We showed that different anionic additives profoundly affect the cations’ “overload profiles” (i.e. plots of plate count versus amount injected) by changing the sample loading capacities. The increase in sample loading capacities with different anions show the same order as the extent of ion pairing between the anions and the basic analytes. The detrimental effect of sample overloading on peak width can be greatly diminished by using either a stronger ion pairing agent or a higher concentration of a given ion pairing agent. Both effects operate by increasing the sample loading capacity, thereby allowing more solute to be injected. We believe that the increase in sample loading capacity described above is due in part to the increase in the number of ion-exchange sites as more anions sorb to the stationary phase. At the same time, the formation of a neutral ion-paired analyte also increases the amount of cation which can be loaded onto the stationary phase by allowing a greater fraction of the analyte to be present in the stationary phase as an electrically neutral (i.e. ion-paired) species.     

Determining maximal efficient faces in multiobjective linear programming problem

Finding an efficient or weakly efficient solution in a multiobjective linear programming (MOLP) problem is not a difficult task. The difficulty lies in finding all these solutions and representing their structures. Since there are many convenient approaches that obtain all of the (weakly) efficient extreme points and (weakly) efficient extreme rays in an MOLP, this paper develops an algorithm which effectively finds all of the (weakly) efficient maximal faces in an MOLP using all of the (weakly) efficient extreme points and extreme rays. The proposed algorithm avoids the degeneration problem, which is the major problem of the most of previous algorithms and gives an explicit structure for maximal efficient (weak efficient) faces. Consequently, it gives a convenient representation of efficient (weak efficient) set using maximal efficient (weak efficient) faces. The proposed algorithm is based on two facts. Firstly, the efficiency and weak efficiency property of a face is determined using a relative interior point of it. Secondly, the relative interior point is achieved using some affine independent points. Indeed, the affine independent property enable us to obtain an efficient relative interior point rapidly.