Gholam R. Amin

Finding the most efficient DMUs in DEA: An improved integrated model

In many applications of DEA finding the most efficient DMUs is desirable. This paper presents an improved integrated DEA model in order to detect the most efficient DMUs. The proposed integrated DEA model does not use the trial and error method in the objective function. Also, it is able to find the most efficient DMUs without solving the model n times (one linear programming (LP) for each DMU) and therefore allows the user to get faster results. It is shown that the improved integrated DEA model is always feasible and capable to rank the most efficient one. To illustrate the model capability the proposed methodology is applied to a real data set consisting of the 19 facility layout alternatives.

Improving minimax disparity model to determine the OWA operator weights

Determining the Ordered Weighted Averaging (OWA) operator weights is important in decision making applications. Several approaches have been proposed in the literature to obtain the associated weights. This paper provides an alternative disparity model to identify the OWA operator weights. The proposed mathematical model extends the existing disparity approaches by minimizing the sum of the deviation between two distinct OWA weights. The proposed disparity model can be used for a preference ranking aggregation. A numerical example in preference ranking and an application in search engines prove the usefulness of the generated OWA weights.

An extended minimax disparity to determine the OWA operator weights

This paper contributes to extend the minimax disparity to determine the ordered weighted averaging (OWA) model based on linear programming. It introduces the minimax disparity approach between any distinct pairs of the weights and uses the duality of linear programming to prove the feasibility of the extended OWA operator weights model. The paper finishes with an open problem.

Railway station site selection using analytical hierarchy process and data envelopment analysis

This paper deals with the problem of finding the optimum site for a railway station for the city of Mashhad, northeast Iran, using the methods of analytical hierarchy process (AHP) and data envelopment analysis (DEA). The paper identifies a four-level hierarchy model for the railway station site-selection problem. The model uses four main criteria: (1) rail-related, (2) passenger services, (3) architecture and urbanism, and (4) economics. In addition, there are 26 subcriteria as well as five (potential) candidates or alternatives. Comparison matrices are used to obtain the local weights and priorities of the railway-station candidates. A DEA model is proposed to determine the optimum site for a railway station. It is shown that the local priorities (or weights) obtained from the AHP can be defined as the multiple outputs of a DEA model for finding the best site for a railway station.

An Assurance Interval for the Non-Archimedean Epsilon in DEA Models

This paper clarifies the role of non-Archimedean infinitesimal e in DEA models so that the associated linear programs may be infeasible (for the multiplier side) and unbounded (for the envelopment side) for certain values of e. It is shown that the bound of e proposed by Ali and Seiford (1993) is invalid for feasibility and boundedness of the linear programs. A procedure is presented for determining an assurance interval of e. It is also shown that an assurance value for e can be found using a single linear program.

An improved MCDM DEA model for technology selection

This paper presents an Improved MCDM Data Envelopment Analysis (DEA) model in order to evaluate the best efficient DMUs in Advanced Manufacturing Technology (AMT). This model is capable of ranking the next most efficient DMUs after removing the previous best one.

Short Communication: Comments on finding the most efficient DMUs in DEA: An improved integrated model

This paper improves the integrated DEA model proposed for finding the most efficient DMUs introduced by Amin and Toloo, [Amin, Gholam R., Toloo, M. (2007). Finding the most efficient DMUs in DEA: An improved integrated model. Computers & Industrial Engineering, 52(2), 71-77]. The paper shows the problem of using the integrated DEA model and presents an improved integrated DEA model for determining a single efficient unit. Also the paper indicates the property of the improvements mathematically and a numerical example shows the usefulness and intelligibility of the study.

A cell formation problem considering machine utilization and alternative process routes by scatter search

Cell formation (CF) is the first step in the design of cellular manufacturing systems (CMSs), which has been recognized as an effective way to enhance the productivity in a factory. There is a set of criteria on which to judge route of product, machine grouping and part family simultaneously in terms of the effective utilization of these cells. In this study, we consider four objectives simultaneously: (1) Minimizing the total fixed and variable cost including costs of purchasing, operation, and maintenance; (2) minimizing cost of intercellular movements; (3) maximizing the utilization of machines in the system; and (4) minimizing deviations among the levels of the cell utilization (i.e., balancing the workload between cells). In this paper, these objectives are first weighted by their relative importance and then a new mathematical model is presented. To solve this model, a scatter search (SS) algorithm is proposed to select a process plan for each part with the minimum cost along with forming the part family and machine grouping simultaneously. The performance of the proposed SS is compared with the Lingo 8.0 software. A number of test problems are carried out to verify the good ability of the proposed SS in terms of the solution quality and computational time. The computational results reveal that the SS finds promising results, especially in the case of large-sized problems.

Maximum appreciative cross-efficiency in DEA

Suggests a cross-efficiency based ranking method in DEA.Uses individual appreciativeness to generate maximum appreciative cross-efficiency.Combines maximum cross-efficiency, preference voting, and OWA operator, to provide a full ranking.Illustrates an application of the proposed method in ranking 15 baseball players. Ranking decision making units (DMUs) is one of the most important applications of data envelopment analysis (DEA). In this paper, we exploit the power of individual appreciativeness in developing a methodology that combines cross-evaluation, preference voting and ordered weighted averaging (OWA). We show that each stage of the proposed methodology enhances discrimination among DMUs while offering more flexibility to the decision process. Our approach is illustrated through an example involving 15 baseball players.

On the boundedness of the SORM DEA models with negative data

Emrouznejad et al. (2010) proposed a Semi-Oriented Radial Measure (SORM) model for assessing the efficiency of Decision Making Units (DMUs) by Data Envelopment Analysis (DEA) with negative data. This paper provides a necessary and sufficient condition for boundedness of the input and output oriented SORM models.