DEA with common set of weights based on a multi objective fractional programming problem

Data envelopment analysis operates as a tool to appraise the relative efficiency of a set of homogenous decision making units. DEA allows each DMU to take its optimal weight in comparison to other DMUs while a similar condition is considered for other units. This feature threats the comparability of different units because different weighting schemes are used for different DMUs. In this paper, a model is presented to determine a common set of weights to calculate DMUs efficiency. This model is developed based on a multi objective fractional linear programming model that considers the original DEA's results as ideal solution and seeks a set of common weights to evaluate DMUs and increases the model's discrimination power. A numerical example is solved and the proposed method's results are compared to some previous methods. This Comparison has shown the proposed method's advantages in ranking DMUs

Game theoretic approach for coordinating unlimited multi echelon supply chains

In order to achieve the overall objectives of the supply chain (SC), there have been seen many contradictions between the components and different levels, and these disorders may result in decreased strength and competitiveness The main contradictions that are considered in this paper comprise inventory, pricing and marketing costs in an unlimited three echelon supply chain. The basics of the game theory make it a suitable and reliable tool for solving contradiction situations by considering all the levels and players’ goals. Initially, an unlimited three echelon supply chain, including S suppliers, M manufacturers, and K retailers, is considered in order to solve the aforementioned problem. Further on, a nonlinear mathematical cooperative model based on specific assumptions, game theory approach, Nash equilibrium definition, Pareto efficiency, and revenue sharing contract is proposed. Subsequently, the proposed model is employed in a numerical example, and the results are illustrated according to the genetic algorithm. Furthermore, the sensitivity of the proposed model is analysed using the design of experiment. Ultimately, the validation of the proposed cooperative model is assessed by the simulatio

A grey mathematical programming model to time-cost trade-offs in project management under uncertainty

Time and cost are two salient elements indicative of success in project management. This importance obliges the project managers to seek for the best feasible amalgamation of time and cost regarding project's activities. This condition engenders a trade-off problem in terms of creating a required balance between time and cost considerations to execute all activities in a project efficiently. Such problem relates to time and cost trade-offs issue. Time and cost trade-offs model is based on estimated values of time and cost required for a given activity to be complete in a normal or crashed form. Current models of time and cost trade-offs have made use of crisp values for these estimations. In this paper, we extend a model for time and cost trade-offs based on grey numbers to deal with the uncertain nature of time and cost estimation. The proposed method has also been applied in an example and interpretations pertaining to offered solutions have been examined

Multi‐objective linear programming with interval coefficients

Purpose The purpose of this paper is to extend a methodology for solving multi‐objective linear programming (MOLP) problems, when the objective functions and constraints coefficients are stated as interval numbers. Design/methodology/approach The approach proposed in this paper for the considered problem is based on the maximization of the sum of membership degrees which are defined for each objective of multi objective problem. These membership degrees are constructed based on the deviation from optimal solutions of individual objectives. Then, the final model based on membership degrees is itself an interval linear programming which can be solved by current methods. Findings The efficiency of the solutions obtained by the proposed method is proved. It is shown that the obtained solution by the proposed method for an interval multi objective problem is Pareto optimal. Research limitations/implications The proposed method can be used in modeling and analyzing of uncertain systems which are modeled in the context of multi objective problems and in which required information is ill defined. Originality/value The paper proposed a novel and well‐defined algorithm to solve the considered problem

An Integer Grey Goal Programming For Project Time, Cost and Quality Trade-Off

Project management (PM) is one of the prominent fields in business and industry. Every task of an organization can be imagined as a project, being a coordinated set of activities toward a common goal. One important aspect of PM is analysing the information related to the optimum balance among the project’s objectives. Each project is a combination of different activities, being connected to each other and having several success criteria, among which the time, cost and quality of the project completion are more significant, due to their significant effect on obtained results. Accordingly, the time might lead to delay and penalty which means more cost; and cost may be underestimated than real required funds. They both will lead to failure in project management. On the other hand, quality is the final key which confirms the success. The aim of a time-cost-quality trade-off problem (TCQTP) is to select a set of activities and an appropriate execution mode for each activity; the cost and time of the project is minimized while the project quality is maximized. The purpose of this paper is to present a model for TCQTP in which these parameters are approximated by grey numbers. Since there are various modes to accomplish each activity, the trade-off problem is formulated based upon a multi-objective integer grey programming model. Afterwards, a goal programming- based approach is designed to solve this model. The model's results provide a framework for the project manager to manage his/ her project successfully, in acceptable time, with the lowest cost and the highest quality. The main originality of the proposed model is the approximation of time, cost and quality parameters of activities mode with grey numbers and the development of a two phase goal programming- based approach to solve this problem. Ultimately, the proposed model is applied in two different cases and results are illustrated to clarify the outstanding capabilities of the mode

A bi-objective score-variance based linear assignment method for group decision making with hesitant fuzzy linguistic term sets

open access articleDecision makers usually prefer to express their preferences by linguistic variables. Classic fuzzy sets allowed expressing these preferences using a single linguistic value. Considering inevitable hesitancy of decision makers, hesitant fuzzy linguistic term sets allowed them to express individual evaluation using several linguistic values. Therefore, these sets improve the ability of humans to determine believes using their own language. Considering this feature, in this paper a method upon linear assignment method is proposed to solve group decision making problems using this kind of information, when criteria weights are known or unknown. The performance of the proposed method is illustrated in a numerical example and the results are compared with other methods to delineate the models efficiency. Following a logical and well-known mathematical logic along with simplicity of execution are the main advantages of the proposed method

A fuzzy data envelopment analysis approach based on parametric programming

In this paper, a fuzzy version of original data envelopment models, CCR and BCC, is extended and its solution approach is developed. The basic idea of the proposed method is to transform the original DEA model to an equivalent linear parametric programming model, applying the notion of α-cuts. Then, a bi-objective model is constructed which its solution has determined the optimal range of decision making units efficiency. The proposed method can be used both for symmetric and asymmetric fuzzy numbers, while the feasibility of its solution for the original problem is guaranteed. The application of the proposed method is examined in two numerical examples and its results are compared with two current models of fuzzy DEA

Fuzzy C-Means based Data Envelopment Analysis for Mitigating the Impact of Units' Heterogeneity

Purpose Data envelopment analysis (DEA) is a non-parametric model that is developed for evaluating the relative efficiency of a set of homogeneous decision-making units that each unit transforms multiple inputs into multiple outputs. However, usually the decision-making units are not completely similar. The purpose of this paper is to propose an algorithm for DEA applications when considered DMUs are non-homogeneous. Design/methodology/approach To reach this aim, an algorithm is designed to mitigate the impact of heterogeneity on efficiency evaluation. Using fuzzy C-means algorithm, a fuzzy clustering is obtained for DMUs based on their inputs and outputs. Then, the fuzzy C-means based DEA approach is used for finding the efficiency of DMUs in different clusters. Finally, the different efficiencies of each DMU are aggregated based on the membership values of DMUs in clusters. Findings Heterogeneity causes some positive impact on some DMUs while it has negative impact on other ones. The proposed method mitigates this undesirable impact and a different distribution of efficiency score is obtained that neglects this unintended impacts. Research limitations/implications The proposed method can be applied in DEA applications with a large number of DMUs in different situations, where some of them enjoyed the good environmental conditions, while others suffered from bad conditions. Therefore, a better assessment of real performance can be obtained. Originality/value The paper proposed a hybrid algorithm combination of fuzzy C-means clustering method with classic DEA models for the first time

A hybrid model of fuzzy goal programming and grey numbers in continuous project time, cost, and quality tradeoff

The purpose of this paper is to develop current mathematical models of cost, time, and quality tradeoffs in conditions that parameters of project activities are estimated uncertainly by grey numbers. In some projects like construction projects, activities can be done within a much shorter time by increasing in the resources, while project's cost may rise at the same time. In such situations, managers are usually required to determine the best combination of cost, time, and quality parameters of the activities, although their information regarding these parameters is limited and rather incomplete. The greyness of these parameters in the proposed method can aid managers to deal with these conditions. The most important aspect of the proposed model is that it considers uncertainty of the project planning data in the form of grey numbers. A combination of fuzzy goal programming and grey linear programming is also developed to solve the proposed model. Finally, this model will provide the managers with a stronger ability to face with uncertainty in project management and planning. The application of this model is examined in a numerical example. As its major finding, the model determines an optimal range in which the project managers can respond to intrinsic changes that may occur in the parameters during a project

A new bi-level data envelopment analysis model for efficiency measurement and target setting

Data envelopment analysis (DEA) is a well-known and widely used method for performance evaluation in a set of homogeneous units. We propose a new bi-level DEA model for efficiency measurement and target setting. The fundamental novelty of the proposed model is threefold. We: (1) set both efficiency and profit concurrently as targets; (2) limit the amount of changes in the inputs and outputs to prevent unachievable targets; and (3) predict some targets for efficient units beyond the inefficient ones. We present a case study in the banking industry to demonstrate the efficacy of efficiency measurement and target setting in the proposed models