goal programming

Data envelopment analysis (DEA) is a method to estimate a relative efficiency of decision making units (DMUs) performing similar tasks in a production system that consumes multiple inputs to produce multiple outputs. The original DEA model does not include a decision maker’s (DM’s) preference structure while measuring relative efficiency. Regarding to relationship between DEA and multiple objective linear programming (MOLP) this paper propose a method based on fuzzy goal programming to incorporate DM’s wishes in evaluation of DMUs then it analyzes the situations that the input-output levels of the estimated benchmark will not or may worsen. A compromised method is suggested that not only considers DM’s wishes in target setting but also improve the efficiency of DMUs while none of input-output levels deteriorate.

Portfolio construction and achieving the set of securities with the most desirability is one of the most critical problems in financial markets. Generally, there are two types of financial problems in literature, choosing the right stock portfolio from a set of possible options which is called portfolio selection, and calculating the portion of the purchase for each option which is called Portfolio optimization. In this paper, a new two-phase robust portfolio selection and optimization approach is proposed to deal with the uncertainty of the data. In the first phase of this approach, all candidate stocks’ efficiency is measured using a data envelopment analysis (DEA) method. Financial criteria for evaluation chosen from fundamental perspectives. Then in the second phase, by applying the Fuzzy Weighted Goal programming (FWGP) model with criteria related to modern portfolio theory (return and risk) as well as the mentioned criteria, the portion of investment in each qualified stock is determined and the optimal investment portfolio is formed. Finally, the proposed approach is implemented in a real case study of the Dow Jones Industrial Market (DJIA). The resulting portfolios for the proposed models are compared against each other as well as against the Dow Jones Industrial Average index. The results show that for the data used and factors investigated some of the constructed portfolios, with a much smaller number of constituents, could potentially outperform DJIA in terms of their performance.

Increasing the discrimination power the of data envelopment analysis method and choosing appropriate weights is one of the important issues in data envelopment analysis. One of the ways to overcome this problem is to use multi-objective data coverage analysis. In multi-objective problems, the goal of the objective functions is usually contradictory to each other, so it is not possible to find an optimal solution for all the objective functions simultaneously. In this article, we use the ideal programming approach to solve the problem of multi-criteria data envelopment analysis, and then we compare the presented method with previous methods in the framework of preferential voting.

Portfolio construction and achieving the set of securities with the most desirability is one of the most critical problems in financial markets. Generally, there are two types of financial problems in literature, choosing the right stock portfolio from a set of possible options which is called portfolio selection, and calculating the portion of the purchase for each option which is called Portfolio optimization. In this paper, a new two-phase robust portfolio selection and optimization approach is proposed to deal with the uncertainty of the data. In the first phase of this approach, all candidate stocks’ efficiency is measured using a data envelopment analysis (DEA) method. Financial criteria for evaluation chosen from fundamental perspectives. Then in the second phase, by applying the Fuzzy Weighted Goal programming (FWGP) model with criteria related to modern portfolio theory (return and risk) as well as the mentioned criteria, the portion of investment in each qualified stock is determined and the optimal investment portfolio is formed. Finally, the proposed approach is implemented in a real case study of the Dow Jones Industrial Market (DJIA). The resulting portfolios for the proposed models are compared against each other as well as against the Dow Jones Industrial Average index. The results show that for the data used and factors investigated some of the constructed portfolios, with a much smaller number of constituents, could potentially outperform DJIA in terms of their performance.

The purpose of the present study was to provide a dynamic model of data envelopment analysis by utilizing from goal programming based on variables of population and education in order to evaluate the relative efficiency of industrial development in provinces of Iran during the years 2007 to 2016. For this purpose, the demographic, education and industry development variables were firstly determined with the help of 42 university and industry experts, then the research model was developed which included: objective function in the form of minimizing adverse deviations of goal constraints based on variations of units at different time periods, and model constraints in the forms of goal constraints and system constraints. In the next step, the model was solved through GAMS Software after designing and implementing dynamic and goal models of data envelopment analysis for provinces of the country in the mentioned period. The relative efficiency of industries development of the provinces was separately calculated for each of the understudy years, then the obtained values were used to calculate the relative efficiency of industry development for each province. According to results, Khuzestan province was ranked first and Sistan and Baluchistan province ranked last in term of average relative efficiency.

Traditional Data Envelopment Analysis (DEA) models evaluate the efficiency of decision making units (DMUs) with common crisp input and output data. However, the data in real applications are often imprecise or ambiguous. This paper transforms fuzzy fractional DEA model constructed using fuzzy arithmetic, into the conventional crisp model. This transformation is performed considering the goal programming that is one of the Multi Objective Programming (MOP) methods. Therefore, in this research the one linear programming model measures the fuzzy efficiencies of DMUs with fuzzy input and fuzzy output data.

Today the most organizations (e.g. banks and insurance institutes) consist of the various units which under the control of the main organization (unified management) act independently. Sometimes the manager presents some services which incur costs such as advertisement and introducing a new technology. Most organizations consist of several individual units. Resource allocation issue appears when requiring to determine an equitable share of costs for these independent units. Data Envelopment Analysis has been proved as a useful technique to solve allocation problems. This paper presents a linear programming model based on DEA methodology to find an equitable allocation. To compare obtained results, we use the proposed model to a data set of prior studies.

In the Iranian economy, banks play a key role in financing and developing the capital market.Therefore, it is important to evaluate the performance of stock banks. Data Envelopment Analysis (DEA) is a wide range of mathematical models used to measure the relative efficiency for a set of homogeneous decision-making units with similar inputs and outputs. In this paper, a novel efficiency ranking approach is proposed with two flexible mixed models derived from Goal Programming Data Envelopment Analysis (GPDEA) models.To solve this mismatch, we use Gantt chart to show DMUs’ floating ranking and use another model to appoint the ranks exactly. In this paper, we analyze 18 stocks efficiency from bank industry of Tehran Exchange in 2016 using the GPDEA approach. Results demonstrate that the novel efficiency ranking approach has higher ability than the basic models in efficiency ranking

Data envelopment analysis (DEA) is a nonparametric approach to estimate relative efficiency of Decision Making Units (DMUs). DEA and is one of the best quantitative approach and balanced scorecard (BSC) is one of the best qualitative method to measure efficiency of an organization. Since simultaneous evaluation of network performance of the quad areas of BSC model is considered as a necessity and separate use of DEA and BSC is not effective and leads to miscalculation of performance, integrated DEA-BSC model is applied. Regarding to multi-objective nature of the proposed model, two techniques including goal programming and weighted average method are used to solve such problems. At the end of the study, based on data relating to indexes of quad areas of BSC model, the results of the mentioned methods is compared. Besides assessing validation of the proposed model, the overall efficiency and each of the different stages of BSC is obtained. So that, finding a model for decision making units in various stages of BSC is the innovation of this research study.

Data envelopment analysis (DEA) is a technique based on linear programming (LP) to measure the relative efficiency of homogeneous units by considering inputs and outputs. The lack of discrimination among efficient decision making units (DMUs) and unrealistic input-outputs weights have been known as the drawback of DEA. In this paper the new scheme based on a goal programming data envelopment analysis (GPDEA) are developed to moderate the homogeneity and reasonability of weights distribution by using of facet analysis On GPDEA (GPDEA-CCR and GPDEA-BCC) models. These modifications are done by considering the lower bounds for each individual inputs and outputs weights in standard CCR model and an upper bound just for free variable of standard BCC model. In the both of the cases the mentioned modification preserved the inputs and outputs weights from zero value. The modified GPDEA models also improve the discrimination power of DEA. The advantages of each modified GPDEA-CCR and GPDEA-BCC models are shown by some examples.

In this paper, we integrate goal programming (GP), Taylor Series, Kuhn-Tucker conditions and Penalty Function approaches to solve linear fractional bi-level programming (LFBLP)problems. As we know, the Taylor Series is having the property of transforming fractional functions to a polynomial. In the present article by Taylor Series we obtain polynomial objective functions which are equivalent to fractional objective functions. Then on using the Kuhn-Tucker optimality condition of the lower level problem, we transform the linear bilevel programming problem into a corresponding single level programming. The complementary and slackness condition of the lower level problem is appended to the upper level objective with a penalty, that can be reduce to a single objective function. In the other words, suitable transformations can be applied to formulate FBLP problems. Finally a numerical example is given to illustrate the complexity of the procedure to the solution.

There are several methods to ranking DMUs in Data Envelopment Analysis (DEA) and candidates in voting system. This paper proposes a new two phases method based on DEA’s concepts. The first phase presents an aspiration rank for each candidate and second phase propose final ranking.

One of the main challenges in Irans auto industry is goal setting in various functional domains. Managing costs of supply chains requires recognition of cost drivers and mathematical modeling for target setting. Realization of the main elements of supply chains and setting logical relations among variables and parameters in the form of a mathematical model are of the main purposes of this research paper. The main question is how it is possible to bring con ict goals of a supply chain together in a mathematical model with the help of goal programming. The relations among 10 au (1)1to part suppliers, 1 warehouse, 3 auto manufacturing plants and 3 agencies are investigated in this study. After collecting data of model parameters, model is solved through application of LINGO software and the following results are revealed. The positive goal deviation of the rst objective is equal to 2500 million Rials. The negative goal deviation of the second objective is equal to 1750 million Rials. The positive goal deviation of the third objective is 1250 million Rials.

The linear multiobjective transportation problem is a special type of vector minimum problem in which constraints are all equality type and the objectives are conicting in nature. This paper presents an application of fuzzy goal programming to the linear multiobjective transportation problem. In this paper, we use a special type of nonlinear (hyperbolic and exponential) membership functions to solve multiobjective transportation problem. It gives an optimal compromise solution. The obtained result has been compared with the solution obtained by using a linear membership function. To illustrate the methodology some numerical examples are presented.

This research proposes a methodology for ranking decision making units by using a goal programming model.We suggest a two phases procedure. In phase 1, by using some DEA problems for each pair of units, we construct a pairwise comparison matrix. Then this matrix is utilized to rank the units via the goal programming model.