Optimizing search engines results using linear programming

When a query is passed to multiple search engines, each search engine returns a ranked list of documents. Researchers have demonstrated that combining results, in the form of a "metasearch engine", produces a significant improvement in coverage and search effectiveness. This paper proposes a linear programming mathematical model for optimizing the ranked list result of a given group of Web search engines for an issued query. An application with a numerical illustration shows the advantages of the proposed method. © 2011 Elsevier Ltd. All rights reserved.

Finding relevant search engine results:a minimax linear programming approach

For a submitted query to multiple search engines finding relevant results is an important task. This paper formulates the problem of aggregation and ranking of multiple search engines results in the form of a minimax linear programming model. Besides the novel application, this study detects the most relevant information among a return set of ranked lists of documents retrieved by distinct search engines. Furthermore, two numerical examples aree used to illustrate the usefulness of the proposed approach.

Measuring information society with linear programming

The measurement of different aspects of information society has been problematic over along time, and the International Telecommunication Union (ITU) is spearheading in developing a single ICT index. In Geneva during the first World Summit on Information Society (WSIS) in December 2003, the heads of states declared their commitment to the importance of benchmarking and measuring progress toward the information society. Consequently, they re-affirmed their Geneva commitments in their second summit held in Tunis in 2005. In this paper, we propose a multiplicative linear programming model to measure Opportunity Index. We also compared our results with the common measure of ICT opportunity index and we found that the two indices are consistent in their measurement of digital opportunity though differences still exist among regions.

A stepwise fuzzy linear programming model with possibility and necessity relations

Linear programming (LP) is the most widely used optimization technique for solving real-life problems because of its simplicity and efficiency. Although conventional LP models require precise data, managers and decision makers dealing with real-world optimization problems often do not have access to exact values. Fuzzy sets have been used in the fuzzy LP (FLP) problems to deal with the imprecise data in the decision variables, objective function and/or the constraints. The imprecisions in the FLP problems could be related to (1) the decision variables; (2) the coefficients of the decision variables in the objective function; (3) the coefficients of the decision variables in the constraints; (4) the right-hand-side of the constraints; or (5) all of these parameters. In this paper, we develop a new stepwise FLP model where fuzzy numbers are considered for the coefficients of the decision variables in the objective function, the coefficients of the decision variables in the constraints and the right-hand-side of the constraints. In the first step, we use the possibility and necessity relations for fuzzy constraints without considering the fuzzy objective function. In the subsequent step, we extend our method to the fuzzy objective function. We use two numerical examples from the FLP literature for comparison purposes and to demonstrate the applicability of the proposed method and the computational efficiency of the procedures and algorithms. © 2013-IOS Press and the authors. All rights reserved.

An application of linear programming in the pottery industry

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A fuzzy AHP based integer linear programming model for the multi-criteria transshipment problem

Purpose – The purpose of this research is to develop a holistic approach to maximize the customer service level while minimizing the logistics cost by using an integrated multiple criteria decision making (MCDM) method for the contemporary transshipment problem. Unlike the prevalent optimization techniques, this paper proposes an integrated approach which considers both quantitative and qualitative factors in order to maximize the benefits of service deliverers and customers under uncertain environments. Design/methodology/approach – This paper proposes a fuzzy-based integer linear programming model, based on the existing literature and validated with an example case. The model integrates the developed fuzzy modification of the analytic hierarchy process (FAHP), and solves the multi-criteria transshipment problem. Findings – This paper provides several novel insights about how to transform a company from a cost-based model to a service-dominated model by using an integrated MCDM method. It suggests that the contemporary customer-driven supply chain remains and increases its competitiveness from two aspects: optimizing the cost and providing the best service simultaneously. Research limitations/implications – This research used one illustrative industry case to exemplify the developed method. Considering the generalization of the research findings and the complexity of the transshipment service network, more cases across multiple industries are necessary to further enhance the validity of the research output. Practical implications – The paper includes implications for the evaluation and selection of transshipment service suppliers, the construction of optimal transshipment network as well as managing the network. Originality/value – The major advantages of this generic approach are that both quantitative and qualitative factors under fuzzy environment are considered simultaneously and also the viewpoints of service deliverers and customers are focused. Therefore, it is believed that it is useful and applicable for the transshipment service network design.

Selecting the most preferable alternatives in a group decision making problem using DEA

Group decision making is the study of identifying and selecting alternatives based on the values and preferences of the decision maker. Making a decision implies that there are several alternative choices to be considered. This paper uses the concept of Data Envelopment Analysis to introduce a new mathematical method for selecting the best alternative in a group decision making environment. The introduced model is a multi-objective function which is converted into a multi-objective linear programming model from which the optimal solution is obtained. A numerical example shows how the new model can be applied to rank the alternatives or to choose a subset of the most promising alternatives.

Inverse forecasting:a new approach for predictive modelling

In the last two decades there have been substantial developments in the mathematical theory of inverse optimization problems, and their applications have expanded greatly. In parallel, time series analysis and forecasting have become increasingly important in various fields of research such as data mining, economics, business, engineering, medicine, politics, and many others. Despite the large uses of linear programming in forecasting models there is no a single application of inverse optimization reported in the forecasting literature when the time series data is available. Thus the goal of this paper is to introduce inverse optimization into forecasting field, and to provide a streamlined approach to time series analysis and forecasting using inverse linear programming. An application has been used to demonstrate the use of inverse forecasting developed in this study. © 2007 Elsevier Ltd. All rights reserved.

Measurement efficiency and productivity in SAS/OR

This paper explores the use of the optimisation procedures in SAS/OR software with application to the measurement of efficiency and productivity of decision-making units (DMUs) using data envelopment analysis (DEA) techniques. DEA was originally introduced by Charnes et al. [J. Oper. Res. 2 (1978) 429] is a linear programming method for assessing the efficiency and productivity of DMUs. Over the last two decades, DEA has gained considerable attention as a managerial tool for measuring performance of organisations and it has widely been used for assessing the efficiency of public and private sectors such as banks, airlines, hospitals, universities and manufactures. As a result, new applications with more variables and more complicated models are being introduced. Further to successive development of DEA a non-parametric productivity measure, Malmquist index, has been introduced by Fare et al. [J. Prod. Anal. 3 (1992) 85]. Employing Malmquist index, productivity growth can be decomposed into technical change and efficiency change. On the other hand, the SAS is a powerful software and it is capable of running various optimisation problems such as linear programming with all types of constraints. To facilitate the use of DEA and Malmquist index by SAS users, a SAS/MALM code was implemented in the SAS programming language. The SAS macro developed in this paper selects the chosen variables from a SAS data file and constructs sets of linear-programming models based on the selected DEA. An example is given to illustrate how one could use the code to measure the efficiency and productivity of organisations.

A genetic algorithm for the generalised transportation problem

The generalised transportation problem (GTP) is an extension of the linear Hitchcock transportation problem. However, it does not have the unimodularity property, which means the linear programming solution (like the simplex method) cannot guarantee to be integer. This is a major difference between the GTP and the Hitchcock transportation problem. Although some special algorithms, such as the generalised stepping-stone method, have been developed, but they are based on the linear programming model and the integer solution requirement of the GTP is relaxed. This paper proposes a genetic algorithm (GA) to solve the GTP and a numerical example is presented to show the algorithm and its efficiency.

Using interior point algorithms for the solution of linear programs with special structural features

Linear Programming (LP) is a powerful decision making tool extensively used in various economic and engineering activities. In the early stages the success of LP was mainly due to the efficiency of the simplex method. After the appearance of Karmarkar's paper, the focus of most research was shifted to the field of interior point methods. The present work is concerned with investigating and efficiently implementing the latest techniques in this field taking sparsity into account. The performance of these implementations on different classes of LP problems is reported here. The preconditional conjugate gradient method is one of the most powerful tools for the solution of the least square problem, present in every iteration of all interior point methods. The effect of using different preconditioners on a range of problems with various condition numbers is presented. Decomposition algorithms has been one of the main fields of research in linear programming over the last few years. After reviewing the latest decomposition techniques, three promising methods were chosen the implemented. Sparsity is again a consideration and suggestions have been included to allow improvements when solving problems with these methods. Finally, experimental results on randomly generated data are reported and compared with an interior point method. The efficient implementation of the decomposition methods considered in this study requires the solution of quadratic subproblems. A review of recent work on algorithms for convex quadratic was performed. The most promising algorithms are discussed and implemented taking sparsity into account. The related performance of these algorithms on randomly generated separable and non-separable problems is also reported.

SAS/OWA:ordered weighted averaging in SAS optimization

This paper explores the use of the optimization procedures in SAS/OR software with application to the ordered weight averaging (OWA) operators of decision-making units (DMUs). OWA was originally introduced by Yager (IEEE Trans Syst Man Cybern 18(1):183-190, 1988) has gained much interest among researchers, hence many applications such as in the areas of decision making, expert systems, data mining, approximate reasoning, fuzzy system and control have been proposed. On the other hand, the SAS is powerful software and it is capable of running various optimization tools such as linear and non-linear programming with all type of constraints. To facilitate the use of OWA operator by SAS users, a code was implemented. The SAS macro developed in this paper selects the criteria and alternatives from a SAS dataset and calculates a set of OWA weights. An example is given to illustrate the features of SAS/OWA software. © Springer-Verlag 2009.

Evaluating productive efficiency:comparative study of commercial banks in Gulf countries

Financial institutes are an integral part of any modern economy. In the 1970s and 1980s, Gulf Cooperation Council (GCC) countries made significant progress in financial deepening and in building a modern financial infrastructure. This study aims to evaluate the performance (efficiency) of financial institutes (banking sector) in GCC countries. Since, the selected variables include negative data for some banks and positive for others, and the available evaluation methods are not helpful in this case, so we developed a Semi Oriented Radial Model to perform this evaluation. Furthermore, since the SORM evaluation result provides a limited information for any decision maker (bankers, investors, etc...), we proposed a second stage analysis using classification and regression (C&R) method to get further results combining SORM results with other environmental data (Financial, economical and political) to set rules for the efficient banks, hence, the results will be useful for bankers in order to improve their bank performance and to the investors, maximize their returns. Mainly there are two approaches to evaluate the performance of Decision Making Units (DMUs), under each of them there are different methods with different assumptions. Parametric approach is based on the econometric regression theory and nonparametric approach is based on a mathematical linear programming theory. Under the nonparametric approaches, there are two methods: Data Envelopment Analysis (DEA) and Free Disposal Hull (FDH). While there are three methods under the parametric approach: Stochastic Frontier Analysis (SFA); Thick Frontier Analysis (TFA) and Distribution-Free Analysis (DFA). The result shows that DEA and SFA are the most applicable methods in banking sector, but DEA is seem to be most popular between researchers. However DEA as SFA still facing many challenges, one of these challenges is how to deal with negative data, since it requires the assumption that all the input and output values are non-negative, while in many applications negative outputs could appear e.g. losses in contrast with profit. Although there are few developed Models under DEA to deal with negative data but we believe that each of them has it is own limitations, therefore we developed a Semi-Oriented-Radial-Model (SORM) that could handle the negativity issue in DEA. The application result using SORM shows that the overall performance of GCC banking is relatively high (85.6%). Although, the efficiency score is fluctuated over the study period (1998-2007) due to the second Gulf War and to the international financial crisis, but still higher than the efficiency score of their counterpart in other countries. Banks operating in Saudi Arabia seem to be the highest efficient banks followed by UAE, Omani and Bahraini banks, while banks operating in Qatar and Kuwait seem to be the lowest efficient banks; this is because these two countries are the most affected country in the second Gulf War. Also, the result shows that there is no statistical relationship between the operating style (Islamic or Conventional) and bank efficiency. Even though there is no statistical differences due to the operational style, but Islamic bank seem to be more efficient than the Conventional bank, since on average their efficiency score is 86.33% compare to 85.38% for Conventional banks. Furthermore, the Islamic banks seem to be more affected by the political crisis (second Gulf War), whereas Conventional banks seem to be more affected by the financial crisis.

Multi-criteria logistics distribution network design using SAS/OR

This paper explores the use of the optimization procedures in SAS/OR software with application to the contemporary logistics distribution network design using an integrated multiple criteria decision making approach. Unlike the traditional optimization techniques, the proposed approach, combining analytic hierarchy process (AHP) and goal programming (GP), considers both quantitative and qualitative factors. In the integrated approach, AHP is used to determine the relative importance weightings or priorities of alternative warehouses with respect to both deliverer oriented and customer oriented criteria. Then, a GP model incorporating the constraints of system, resource, and AHP priority is formulated to select the best set of warehouses without exceeding the limited available resources. To facilitate the use of integrated multiple criteria decision making approach by SAS users, an ORMCDM code was implemented in the SAS programming language. The SAS macro developed in this paper selects the chosen variables from a SAS data file and constructs sets of linear programming models based on the selected GP model. An example is given to illustrate how one could use the code to design the logistics distribution network.

Fuzzy data envelopment analysis:a discrete approach

Data envelopment analysis (DEA) as introduced by Charnes, Cooper, and Rhodes (1978) is a linear programming technique that has widely been used to evaluate the relative efficiency of a set of homogenous decision making units (DMUs). In many real applications, the input-output variables cannot be precisely measured. This is particularly important in assessing efficiency of DMUs using DEA, since the efficiency score of inefficient DMUs are very sensitive to possible data errors. Hence, several approaches have been proposed to deal with imprecise data. Perhaps the most popular fuzzy DEA model is based on a-cut. One drawback of the a-cut approach is that it cannot include all information about uncertainty. This paper aims to introduce an alternative linear programming model that can include some uncertainty information from the intervals within the a-cut approach. We introduce the concept of "local a-level" to develop a multi-objective linear programming to measure the efficiency of DMUs under uncertainty. An example is given to illustrate the use of this method.