Majid Zohrehbandian - Academia.edu (original) (raw)

Papers by Majid Zohrehbandian

Research paper thumbnail of Extension of Portfolio Selection Problem with Fuzzy Goal Programming: A Fuzzy Allocated Portfolio Approach

Journal of Optimization in Industrial Engineering, 2011

Recently, the economic crisis has resulted in instability in stock exchange market and this has c... more Recently, the economic crisis has resulted in instability in stock exchange market and this has caused high volatilities in stock value of exchanged firms. Under these conditions, considering uncertainty for a favorite investment is more serious than before. Multi-objective Portfolio selection (Return, Liquidity, Risk and Initial cost of Investment objectives) using MINMAX fuzzy goal programming for a Fuzzy Allocated Portfolio is considered in this research and all the main sectors of investment are assumed under uncertainty. A numerical example on stock exchange is presented to demonstrate the validity and strengths of the proposed approach.

Research paper thumbnail of Determination of Defining Hyperplanes of Dea Production Possibility Set

The ability of determining all defining hyperplanes of DEA production possibility set (efficient ... more The ability of determining all defining hyperplanes of DEA production possibility set (efficient frontier) prior to the DEA computations is of extreme importance. Specially, access to efficient frontier permits a complete analysis (e.g. calculation of efficiency scores, returns to scale, sensitivity analysis and so on) in second phase for the corresponding model. This paper presents a linear system of constraints which its extreme points correspond to defining hyperplanes (both weak and strong ones). Numerical examples are provided to explore the advantage of using the proposed method.

Research paper thumbnail of Myths and Counterexamples in Special Forms of Mathematical Programming

This section presents some myths and counterexamples for mathematical programs that do not t easi... more This section presents some myths and counterexamples for mathematical programs that do not t easily into one of the other sections, notably some particular applications. Consult the Mathematical Programming Glossary [19] for terms and concepts not dened here. SF Myth 1. A good cluster results from maximizing inter-cluster distances and minimizing cluster diameters. Counterexample. The following is taken from Climer and Zhang [8]. Using Euclidean distance as the similarity measure for (a), the intuitive cluster is (b). The myth fails because many points are closer to a dierent cluster than their own (so the diameters are not minimized), and the distance between clusters is less than maximal. SF Myth 2. A chance-constraint stochastic program has a solution if its certainty equivalent has a solution. The model is given by: max E[f (x; θ)] : x ∈ X, Pr[g(x; θ) ≤ 0] ≥ α, where θ is a vector of uncertain parameters and α ∈ (0, 1). In words, this seeks a policy to maximize the expected value of the objective, subject to it being feasible with probability at least α. The probability and expected value operators are generally taken with respect to θ, and x is a pure strategy solution. Greenberg [15] pointed out that one could allow mixed-strategy solutions, in which case the chance constraint could be violated a certain percentage of time. The model becomes: max H x∈X θ f (x; θ)dF (θ)dH(x) : Pr[g(x; θ) ≤ 0] ≥ α,

Research paper thumbnail of Approximation of value efficiency in DEA with negative data

Advances in Environmental Biology, 2013

This paper considers the problem of negative data in Data Envelopment Analysis (DEA) models. Our ... more This paper considers the problem of negative data in Data Envelopment Analysis (DEA) models. Our focus is on how to calculate value efficiency in DEA models with negative data. In this paper, we will introduce an Multi Objectives Linear Programming (MOLP) model which its objective functions are input/output variables subject to the defining constraints of Production Possibility Set (PPS) of DEA models. So, we propose an effective method to find the best solution, such that by that we obtain the Most Preferred solution (MPS). Finally, value efficiency scores are calculated related to the inefficient units having the same value related to the MPS.

Research paper thumbnail of Selecting dispatching rule in manufacturing systems via DEA cross efficiency

International Journal of Information and Decision Sciences, 2017

Planning and scheduling techniques are the main concern of management of production systems, and ... more Planning and scheduling techniques are the main concern of management of production systems, and the dispatching rules play an important role in scheduling industrial and production segments. In this regard, the correct selection of the facility dispatching rules in a production system is of great importance and selection of the best technique can improve the efficiency of the industrial segments. In this condition, a so called efficiency score can be identified for each dispatching rule according which the best can be chosen. Data envelopment analysis, as a scientific method, is used in evaluation of unit work but the classical models of that cannot present an overall work of the decision making units and in most cases it gives a specific score to more than one unit. As a result, the efficacy computed by this method cannot be suitable for ranking. Evaluation of cross efficiency is one of the suitable methods for ranking which has DEA ranking and, therefore the selection of the best units in different models would be a secondary goal. In this article, the cross efficiency method along with Liang et al. (2008) is used to select the best dispatching rule under secondary goal and a comparison is provided for the new and already used method.

Research paper thumbnail of DEA efficiency analysis with identifying efficient and full-inefficient frontier

International Mathematical Forum, 2007

Data envelopment analysis (DEA) is a mathematical programming technique for identifying relative ... more Data envelopment analysis (DEA) is a mathematical programming technique for identifying relative efficiency scores of decision making units (DMUs). Recently, Amirteimoori (2007) Introduced an alternative efficiency measure based on efficient and anti-efficient frontiers. In this paper we introduce a new computational framework for identifying full-efficient and inefficient frontier of production possibility set (PPS) in DEA models with variable return to scale. This facets apply in finding full-efficient and inefficient DMUs, sensitivity and stability analysis, ranking, and etc.

Research paper thumbnail of Returns to Scale and Scale Elasticity in Two-Stage Dea

Mathematical and Computational Applications, 2012

Data Envelopment Analysis (DEA) provides a method to evaluate the relative efficiency of peer Dec... more Data Envelopment Analysis (DEA) provides a method to evaluate the relative efficiency of peer Decision Making Units (DMUs) that have multiple inputs and outputs. Production process in two-stage DEA is performed in the two consecutive phases and DMUs have intermediate measures, in addition to their inputs and outputs. A unique feature of the intermediate measures is that the outputs in the first stage are being treated as inputs in the second stage. The aim of this paper is to determine the returns to scale (RTS) classification and scale elasticity (SE) in two-stage DEA. Therefore an approach is introduced for estimating the RTS situation of DMUs with two-stage structure based on the consideration of SE quantity in each of the individual stages. The utilization of the proposed approach is demonstrated with a real data set.

Research paper thumbnail of Estimation of Efficiency and Infinitesimals in Data Envelopment Analysis

Mathematical and Computational Applications, 2004

Research paper thumbnail of A Cutting Plane Approach for Solving Linear Bilevel Programming Problems

Advances in Intelligent Systems and Computing, 2015

Bilevel programming (BLP) problems are hierarchical optimization problems having a parametric opt... more Bilevel programming (BLP) problems are hierarchical optimization problems having a parametric optimization problem as part of their constraints. From the mathematical point of view, the BLP problem is NP-hard even if the objectives and constraints are linear. This paper proposes a cutting plane approach to solve linear BLP problem which is the simplest case of BLP problems. Our approach is based on the idea that is commonly used in computational mathematics: solving a relaxation problem that is easier to solve and giving a tight approximation by introduction of cutting planes. Therefore, by exploring the theoretical properties of linear BLP, we extend the cutting plane approach for solving linear BLP problems. Numerical examples are provided to illustrate the approach.

Research paper thumbnail of Ant colony optimization techniques for the Hamiltonian p-median problem

Location-Routing problems involve locating a number of facilities among candidate sites and estab... more Location-Routing problems involve locating a number of facilities among candidate sites and establishing delivery routes to a set of users in such a way that the total system cost is minimized. A special case of these problems is Hamiltonian p-Median problem (HpMP). This research applies the metaheuristic method of ant colony optimization (ACO) to solve the HpMP. Modifications are made to the ACO algorithm used to solve the traditional vehicle routing problem (VRP) in order to allow the search of the optimal solution of the HpMP. Regarding this metaheuristic algorithm a computational experiment is reported as well.

Research paper thumbnail of A Preference Directional Distance Model for DEA with Negative Inputs/Outputs

The traditional DEA models have this assumption that all inputs and outputs are non-negative. But... more The traditional DEA models have this assumption that all inputs and outputs are non-negative. But the recent decade articles have proposed variation examples of situations in which both negative inputs and negative outputs occur and have suggested models for dealing with these situations. Portela et al. (2004)[1] proposed the Range Directional Model (RDM) which was inspired by the directional distance model of Chambers et al. (1996, 1998)[2,3]. In this paper by using an M CDM methodology for finding an appropriate direction of improvement we propose a new directional model which is based on the importance of inputs and outputs for each DMU. Then, we compare our model with the other models by an example.

Research paper thumbnail of Practical common weights scalarizing function approach for efficiency analysis

A characteristic of Data Envelopment Analysis (DEA) is to allow individual decision making units ... more A characteristic of Data Envelopment Analysis (DEA) is to allow individual decision making units (DMUs) to select the factor weights which are the most advantageous for them in calculating their efficiency scores. This flexibility in selecting the weights, on the other hand, deters the comparison among DMUs on a common base. For dealing with this difficulty and assessing all the DMUs on the same scale, this paper proposes using a multiple objective linear programming (MOLP) approach based on scalarizing function for generating common set of weights under the DEA framework. This is an advantageous of the proposed approach against general approaches in the literature which are based on multiple objective nonlinear programming.

Research paper thumbnail of Practical common weights for technology selection: Maximin and Scalarizing function approach

To select the best technologies two practical common weight Maximin and scalarizing function appr... more To select the best technologies two practical common weight Maximin and scalarizing function approaches are introduced. Both proposed approaches enable the evaluation of the relative eciency of decision making units (DMUs) with

Research paper thumbnail of Using DEA for Evaluating the Attribute Weights and solving one MADM Problem

Multiple Attribute Decision Making (MADM) addresses the problem of choosing an optimum choice con... more Multiple Attribute Decision Making (MADM) addresses the problem of choosing an optimum choice containing the highest degree of satisfaction from a set of alternatives which are characterized in terms of their attributes. In order to make a decision or choose a best alternative, a decision maker (DM) is often asked to provide his/her preferences either on alternatives or on the relative weights of attributes or on both of them. In this paper some basic principles from data envelopment analysis (DEA) is used in order to extract the necessary information for solving an MADM problem. We will introduce a comprehensive yet efficient approach for accountable and understandable MADM. For obtaining the attribute weights and choosing the best alternative, we use the Common Set of Weights (CSW) in DEA. The DMUs correspond to the alternatives which have to be evaluated. We will obtain the common set of weights of these DMUs and then we consider these weights as weight of attributes. We compute the efficiency score of each DMU and we will consider the efficient DMU as the best alternative.

Research paper thumbnail of Finding common weights based on the DM's preference information

Journal of the Operational Research Society, 2010

Data Envelopment Analysis (DEA) is basically a linear programming based technique used for measur... more Data Envelopment Analysis (DEA) is basically a linear programming based technique used for measuring the relative performance of organizational units, referred to as Decision Making Units (DMUs). The flexibility in selecting the weights in standard DEA models deters the comparison among DMUs on a common base. Moreover, these weights are not suitable to measure the preferences of a decision maker (DM). For dealing with the first difficulty, the concept of common weights was proposed in the DEA literature. But, none of the common weights approaches address the second difficulty. This paper proposes an alternative approach we term 'preference common weights' which is both practical and intellectually consistent with the DEA philosophy. To do this, we introduce an MOLP model in which objective functions are input/output variables subject to the constraints similar to the equations which define production possibility set (PPS) of standard DEA models. Then by using the Zionts-Wallenius method, we can generate common weights as the DM's underlying value structure about objective functions.

Research paper thumbnail of A compromise solution approach for finding common weights in DEA: an improvement to Kao and Hung's approach

Journal of the Operational Research Society, 2009

Data envelopment analysis (DEA) is the leading technique for measuring the relative efficiency of... more Data envelopment analysis (DEA) is the leading technique for measuring the relative efficiency of decision making units (DMUs) on the basis of multiple inputs and multiple outputs. In this technique, the weights for inputs and outputs are estimated in the best advantage for each unit so as to maximize its relative efficiency. But, this flexibility in selecting the weights deters the comparison among DMUs on a common base. For dealing with this difficulty, Kao and Hung (2005) proposed a compromise solution approach for generating common weights under the DEA framework. The proposed MCDM model was derived from the original non-linear DEA model. This paper presents an improvement to Kao and Hung's approach by means of introducing an MCDM model which is derived from a new linear DEA model.

Research paper thumbnail of Notes on Sensitivity and Stability of the Classifications of Returns to Scale in Data Envelopment Analysis: A Comment

Journal of Productivity Analysis, 2005

Research paper thumbnail of A New Formulation of the Hamiltonian p Median Problem

Location-Routing problems involve locating a number of facilities among candidate sites and estab... more Location-Routing problems involve locating a number of facilities among candidate sites and establishing delivery routes to a set of users in such a way that the total system cost is minimized. A special case of these problems is Hamiltonian p Median Problem (HpMP). In at- tempting to solve this problem, numerous mathematical formulations have been proposed. Most of them have in common that their descrip- tions as integer optimization problems are not polyhedral ones (ILP formulation). In this paper, an ILP formulation, based on the formula- tion of vehicle routing problem, is presented. The proposed formulation is simpler and more practicable than those have been proposed up to now.

Research paper thumbnail of A data envelopment analysis approach to supplier selection in volume discount environments

International Journal of Procurement Management, 2008

Many practitioners and researchers have presented the advantages of supply chain management. In o... more Many practitioners and researchers have presented the advantages of supply chain management. In order to increase their competitive advantage, many companies consider that a well-designed and well-implemented supply chain system is an important tool. Under this condition, building on the closeness and long-term relationships between buyers and suppliers is a critical success factor to establish the supply chain system. Therefore, the supplier selection problem becomes the most important issue in implementing a successful supply chain system. Traditionally, many optimisation models of supplier selection assume that the average unit price of procured items is a constant. This assumption is not realistic because suppliers usually offer quantity discounts to encourage the buyers to order more. For dealing with this difficulty and for selecting the best suppliers with regard to multiple criteria, this paper introduces an innovative algorithm, which is based on Data Envelopment Analysis (DEA). A numerical example demonstrates the application of the proposed method.

Research paper thumbnail of Technology selection with both quantitative and qualitative outputs

International Journal of Procurement Management, 2009

Technology selection is an important part of the management of technology. To select the best tec... more Technology selection is an important part of the management of technology. To select the best technologies, a practical common-weight Multi-Objective Linear Programming (MOLP) approach with an improved discriminating power is introduced. The proposed MOLP approach enables the evaluation of the relative efficiency of Decision-Making Units (DMUs) with respect to multiple exact and ordinal outputs and a single exact input. Its robustness and discriminating power are illustrated via a previously reported robot evaluation problem by comparing the ranking that is obtained by the proposed MOLP framework with that obtained by the classical Data Envelopment Analysis (DEA) model.

Research paper thumbnail of Extension of Portfolio Selection Problem with Fuzzy Goal Programming: A Fuzzy Allocated Portfolio Approach

Journal of Optimization in Industrial Engineering, 2011

Recently, the economic crisis has resulted in instability in stock exchange market and this has c... more Recently, the economic crisis has resulted in instability in stock exchange market and this has caused high volatilities in stock value of exchanged firms. Under these conditions, considering uncertainty for a favorite investment is more serious than before. Multi-objective Portfolio selection (Return, Liquidity, Risk and Initial cost of Investment objectives) using MINMAX fuzzy goal programming for a Fuzzy Allocated Portfolio is considered in this research and all the main sectors of investment are assumed under uncertainty. A numerical example on stock exchange is presented to demonstrate the validity and strengths of the proposed approach.

Research paper thumbnail of Determination of Defining Hyperplanes of Dea Production Possibility Set

The ability of determining all defining hyperplanes of DEA production possibility set (efficient ... more The ability of determining all defining hyperplanes of DEA production possibility set (efficient frontier) prior to the DEA computations is of extreme importance. Specially, access to efficient frontier permits a complete analysis (e.g. calculation of efficiency scores, returns to scale, sensitivity analysis and so on) in second phase for the corresponding model. This paper presents a linear system of constraints which its extreme points correspond to defining hyperplanes (both weak and strong ones). Numerical examples are provided to explore the advantage of using the proposed method.

Research paper thumbnail of Myths and Counterexamples in Special Forms of Mathematical Programming

This section presents some myths and counterexamples for mathematical programs that do not t easi... more This section presents some myths and counterexamples for mathematical programs that do not t easily into one of the other sections, notably some particular applications. Consult the Mathematical Programming Glossary [19] for terms and concepts not dened here. SF Myth 1. A good cluster results from maximizing inter-cluster distances and minimizing cluster diameters. Counterexample. The following is taken from Climer and Zhang [8]. Using Euclidean distance as the similarity measure for (a), the intuitive cluster is (b). The myth fails because many points are closer to a dierent cluster than their own (so the diameters are not minimized), and the distance between clusters is less than maximal. SF Myth 2. A chance-constraint stochastic program has a solution if its certainty equivalent has a solution. The model is given by: max E[f (x; θ)] : x ∈ X, Pr[g(x; θ) ≤ 0] ≥ α, where θ is a vector of uncertain parameters and α ∈ (0, 1). In words, this seeks a policy to maximize the expected value of the objective, subject to it being feasible with probability at least α. The probability and expected value operators are generally taken with respect to θ, and x is a pure strategy solution. Greenberg [15] pointed out that one could allow mixed-strategy solutions, in which case the chance constraint could be violated a certain percentage of time. The model becomes: max H x∈X θ f (x; θ)dF (θ)dH(x) : Pr[g(x; θ) ≤ 0] ≥ α,

Research paper thumbnail of Approximation of value efficiency in DEA with negative data

Advances in Environmental Biology, 2013

This paper considers the problem of negative data in Data Envelopment Analysis (DEA) models. Our ... more This paper considers the problem of negative data in Data Envelopment Analysis (DEA) models. Our focus is on how to calculate value efficiency in DEA models with negative data. In this paper, we will introduce an Multi Objectives Linear Programming (MOLP) model which its objective functions are input/output variables subject to the defining constraints of Production Possibility Set (PPS) of DEA models. So, we propose an effective method to find the best solution, such that by that we obtain the Most Preferred solution (MPS). Finally, value efficiency scores are calculated related to the inefficient units having the same value related to the MPS.

Research paper thumbnail of Selecting dispatching rule in manufacturing systems via DEA cross efficiency

International Journal of Information and Decision Sciences, 2017

Planning and scheduling techniques are the main concern of management of production systems, and ... more Planning and scheduling techniques are the main concern of management of production systems, and the dispatching rules play an important role in scheduling industrial and production segments. In this regard, the correct selection of the facility dispatching rules in a production system is of great importance and selection of the best technique can improve the efficiency of the industrial segments. In this condition, a so called efficiency score can be identified for each dispatching rule according which the best can be chosen. Data envelopment analysis, as a scientific method, is used in evaluation of unit work but the classical models of that cannot present an overall work of the decision making units and in most cases it gives a specific score to more than one unit. As a result, the efficacy computed by this method cannot be suitable for ranking. Evaluation of cross efficiency is one of the suitable methods for ranking which has DEA ranking and, therefore the selection of the best units in different models would be a secondary goal. In this article, the cross efficiency method along with Liang et al. (2008) is used to select the best dispatching rule under secondary goal and a comparison is provided for the new and already used method.

Research paper thumbnail of DEA efficiency analysis with identifying efficient and full-inefficient frontier

International Mathematical Forum, 2007

Data envelopment analysis (DEA) is a mathematical programming technique for identifying relative ... more Data envelopment analysis (DEA) is a mathematical programming technique for identifying relative efficiency scores of decision making units (DMUs). Recently, Amirteimoori (2007) Introduced an alternative efficiency measure based on efficient and anti-efficient frontiers. In this paper we introduce a new computational framework for identifying full-efficient and inefficient frontier of production possibility set (PPS) in DEA models with variable return to scale. This facets apply in finding full-efficient and inefficient DMUs, sensitivity and stability analysis, ranking, and etc.

Research paper thumbnail of Returns to Scale and Scale Elasticity in Two-Stage Dea

Mathematical and Computational Applications, 2012

Data Envelopment Analysis (DEA) provides a method to evaluate the relative efficiency of peer Dec... more Data Envelopment Analysis (DEA) provides a method to evaluate the relative efficiency of peer Decision Making Units (DMUs) that have multiple inputs and outputs. Production process in two-stage DEA is performed in the two consecutive phases and DMUs have intermediate measures, in addition to their inputs and outputs. A unique feature of the intermediate measures is that the outputs in the first stage are being treated as inputs in the second stage. The aim of this paper is to determine the returns to scale (RTS) classification and scale elasticity (SE) in two-stage DEA. Therefore an approach is introduced for estimating the RTS situation of DMUs with two-stage structure based on the consideration of SE quantity in each of the individual stages. The utilization of the proposed approach is demonstrated with a real data set.

Research paper thumbnail of Estimation of Efficiency and Infinitesimals in Data Envelopment Analysis

Mathematical and Computational Applications, 2004

Research paper thumbnail of A Cutting Plane Approach for Solving Linear Bilevel Programming Problems

Advances in Intelligent Systems and Computing, 2015

Bilevel programming (BLP) problems are hierarchical optimization problems having a parametric opt... more Bilevel programming (BLP) problems are hierarchical optimization problems having a parametric optimization problem as part of their constraints. From the mathematical point of view, the BLP problem is NP-hard even if the objectives and constraints are linear. This paper proposes a cutting plane approach to solve linear BLP problem which is the simplest case of BLP problems. Our approach is based on the idea that is commonly used in computational mathematics: solving a relaxation problem that is easier to solve and giving a tight approximation by introduction of cutting planes. Therefore, by exploring the theoretical properties of linear BLP, we extend the cutting plane approach for solving linear BLP problems. Numerical examples are provided to illustrate the approach.

Research paper thumbnail of Ant colony optimization techniques for the Hamiltonian p-median problem

Location-Routing problems involve locating a number of facilities among candidate sites and estab... more Location-Routing problems involve locating a number of facilities among candidate sites and establishing delivery routes to a set of users in such a way that the total system cost is minimized. A special case of these problems is Hamiltonian p-Median problem (HpMP). This research applies the metaheuristic method of ant colony optimization (ACO) to solve the HpMP. Modifications are made to the ACO algorithm used to solve the traditional vehicle routing problem (VRP) in order to allow the search of the optimal solution of the HpMP. Regarding this metaheuristic algorithm a computational experiment is reported as well.

Research paper thumbnail of A Preference Directional Distance Model for DEA with Negative Inputs/Outputs

The traditional DEA models have this assumption that all inputs and outputs are non-negative. But... more The traditional DEA models have this assumption that all inputs and outputs are non-negative. But the recent decade articles have proposed variation examples of situations in which both negative inputs and negative outputs occur and have suggested models for dealing with these situations. Portela et al. (2004)[1] proposed the Range Directional Model (RDM) which was inspired by the directional distance model of Chambers et al. (1996, 1998)[2,3]. In this paper by using an M CDM methodology for finding an appropriate direction of improvement we propose a new directional model which is based on the importance of inputs and outputs for each DMU. Then, we compare our model with the other models by an example.

Research paper thumbnail of Practical common weights scalarizing function approach for efficiency analysis

A characteristic of Data Envelopment Analysis (DEA) is to allow individual decision making units ... more A characteristic of Data Envelopment Analysis (DEA) is to allow individual decision making units (DMUs) to select the factor weights which are the most advantageous for them in calculating their efficiency scores. This flexibility in selecting the weights, on the other hand, deters the comparison among DMUs on a common base. For dealing with this difficulty and assessing all the DMUs on the same scale, this paper proposes using a multiple objective linear programming (MOLP) approach based on scalarizing function for generating common set of weights under the DEA framework. This is an advantageous of the proposed approach against general approaches in the literature which are based on multiple objective nonlinear programming.

Research paper thumbnail of Practical common weights for technology selection: Maximin and Scalarizing function approach

To select the best technologies two practical common weight Maximin and scalarizing function appr... more To select the best technologies two practical common weight Maximin and scalarizing function approaches are introduced. Both proposed approaches enable the evaluation of the relative eciency of decision making units (DMUs) with

Research paper thumbnail of Using DEA for Evaluating the Attribute Weights and solving one MADM Problem

Multiple Attribute Decision Making (MADM) addresses the problem of choosing an optimum choice con... more Multiple Attribute Decision Making (MADM) addresses the problem of choosing an optimum choice containing the highest degree of satisfaction from a set of alternatives which are characterized in terms of their attributes. In order to make a decision or choose a best alternative, a decision maker (DM) is often asked to provide his/her preferences either on alternatives or on the relative weights of attributes or on both of them. In this paper some basic principles from data envelopment analysis (DEA) is used in order to extract the necessary information for solving an MADM problem. We will introduce a comprehensive yet efficient approach for accountable and understandable MADM. For obtaining the attribute weights and choosing the best alternative, we use the Common Set of Weights (CSW) in DEA. The DMUs correspond to the alternatives which have to be evaluated. We will obtain the common set of weights of these DMUs and then we consider these weights as weight of attributes. We compute the efficiency score of each DMU and we will consider the efficient DMU as the best alternative.

Research paper thumbnail of Finding common weights based on the DM's preference information

Journal of the Operational Research Society, 2010

Data Envelopment Analysis (DEA) is basically a linear programming based technique used for measur... more Data Envelopment Analysis (DEA) is basically a linear programming based technique used for measuring the relative performance of organizational units, referred to as Decision Making Units (DMUs). The flexibility in selecting the weights in standard DEA models deters the comparison among DMUs on a common base. Moreover, these weights are not suitable to measure the preferences of a decision maker (DM). For dealing with the first difficulty, the concept of common weights was proposed in the DEA literature. But, none of the common weights approaches address the second difficulty. This paper proposes an alternative approach we term 'preference common weights' which is both practical and intellectually consistent with the DEA philosophy. To do this, we introduce an MOLP model in which objective functions are input/output variables subject to the constraints similar to the equations which define production possibility set (PPS) of standard DEA models. Then by using the Zionts-Wallenius method, we can generate common weights as the DM's underlying value structure about objective functions.

Research paper thumbnail of A compromise solution approach for finding common weights in DEA: an improvement to Kao and Hung's approach

Journal of the Operational Research Society, 2009

Data envelopment analysis (DEA) is the leading technique for measuring the relative efficiency of... more Data envelopment analysis (DEA) is the leading technique for measuring the relative efficiency of decision making units (DMUs) on the basis of multiple inputs and multiple outputs. In this technique, the weights for inputs and outputs are estimated in the best advantage for each unit so as to maximize its relative efficiency. But, this flexibility in selecting the weights deters the comparison among DMUs on a common base. For dealing with this difficulty, Kao and Hung (2005) proposed a compromise solution approach for generating common weights under the DEA framework. The proposed MCDM model was derived from the original non-linear DEA model. This paper presents an improvement to Kao and Hung's approach by means of introducing an MCDM model which is derived from a new linear DEA model.

Research paper thumbnail of Notes on Sensitivity and Stability of the Classifications of Returns to Scale in Data Envelopment Analysis: A Comment

Journal of Productivity Analysis, 2005

Research paper thumbnail of A New Formulation of the Hamiltonian p Median Problem

Location-Routing problems involve locating a number of facilities among candidate sites and estab... more Location-Routing problems involve locating a number of facilities among candidate sites and establishing delivery routes to a set of users in such a way that the total system cost is minimized. A special case of these problems is Hamiltonian p Median Problem (HpMP). In at- tempting to solve this problem, numerous mathematical formulations have been proposed. Most of them have in common that their descrip- tions as integer optimization problems are not polyhedral ones (ILP formulation). In this paper, an ILP formulation, based on the formula- tion of vehicle routing problem, is presented. The proposed formulation is simpler and more practicable than those have been proposed up to now.

Research paper thumbnail of A data envelopment analysis approach to supplier selection in volume discount environments

International Journal of Procurement Management, 2008

Many practitioners and researchers have presented the advantages of supply chain management. In o... more Many practitioners and researchers have presented the advantages of supply chain management. In order to increase their competitive advantage, many companies consider that a well-designed and well-implemented supply chain system is an important tool. Under this condition, building on the closeness and long-term relationships between buyers and suppliers is a critical success factor to establish the supply chain system. Therefore, the supplier selection problem becomes the most important issue in implementing a successful supply chain system. Traditionally, many optimisation models of supplier selection assume that the average unit price of procured items is a constant. This assumption is not realistic because suppliers usually offer quantity discounts to encourage the buyers to order more. For dealing with this difficulty and for selecting the best suppliers with regard to multiple criteria, this paper introduces an innovative algorithm, which is based on Data Envelopment Analysis (DEA). A numerical example demonstrates the application of the proposed method.

Research paper thumbnail of Technology selection with both quantitative and qualitative outputs

International Journal of Procurement Management, 2009

Technology selection is an important part of the management of technology. To select the best tec... more Technology selection is an important part of the management of technology. To select the best technologies, a practical common-weight Multi-Objective Linear Programming (MOLP) approach with an improved discriminating power is introduced. The proposed MOLP approach enables the evaluation of the relative efficiency of Decision-Making Units (DMUs) with respect to multiple exact and ordinal outputs and a single exact input. Its robustness and discriminating power are illustrated via a previously reported robot evaluation problem by comparing the ranking that is obtained by the proposed MOLP framework with that obtained by the classical Data Envelopment Analysis (DEA) model.