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Showing 11 results for Linear Programming
Hosseinzadeh Lotfi, Noora, Jahanshahloo,
Volume 2, Issue 1 (4-2010)
Abstract
We suggest a method for finding the non-dominated points of the production possibility set (PPS) with variable returns to scale (VRS) technology in data envelopment analysis (DEA). We present a multiobjective linear programming (MOLP) problem whose feasible region is the same as the PPS under variable returns to scale for generating non-dominated points. We demonstrate that Pareto solutions of the MOLP produce efficient units in DEA, and vice versa. We solve the MOLP problem by using a finite number of weights which are extreme rays of the cone generated by the efficient solutions. We obtain new efficient points by changing weights, and thus the efficient solutions set is produced.
Etebari, Aaghaie, Khoshalhan,
Volume 3, Issue 1 (4-2012)
Abstract
In recent years, enriching traditional revenue management models by considering the customer choice behavior has been a main challenge for researchers. The terminology for the airline application is used as representative of the problem. A popular and an efficient model considering these behaviors is choice-based deterministic linear programming (CDLP). This model assumes that each customer belongs to a segment, which is characterized by a consideration set, which is a subset of the products provided by the firm that a customer views as options. Initial models consider a market segmentation, in which each customer belongs to one specific segment. In this case, the segments are defined by disjoint consideration sets of products. Recent models consider the extension of the CDLP to the general case of overlapping segments. The main difficulty, from a computational standpoint, in this approach is solving the CDLP efficiently by column generation. Indeed, it turns out that the column generation subproblem is difficult on its own. It has been shown that for the case of nonoverlapping segments, this can be done in polynomial time. For the more general case of overlapping segments, the column generation sub-problem is NP-hard for which greedy heuristics are proposed for computing approximate solutions. Here, we present a new approach to solve this problem by using a genetic algorithm and compare it with the column generation method. We comparatively investigate the effect of using the new approach for firm’s revenue
Izadi, Ranjbarian, Ketabi, Nassiri-Mofakham,
Volume 4, Issue 1 (5-2013)
Abstract
Among various statistical and data mining discriminant analysis proposed so far for group classification, linear programming discriminant analysis has recently attracted the researchers’ interest. This study evaluates multi-group discriminant linear programming (MDLP) for classification problems against well-known methods such as neural networks and support vector machine. MDLP is less complicated as compared to other methods and does not suffer from having local optima. This study also proposes a fuzzy Delphi method to select and gather the required data, when databases suffer from deficient data. In addition, to absorb the uncertainty infused to collecting data, interval MDLP (IMDLP) is developed. The results show that the performance of MDLP and specially IMDLP is better than conventional classification methods with respect to correct classification, at least for small and medium-size datasets.
A.r. Nazemi, M.h. Farahi,
Volume 4, Issue 2 (10-2013)
Abstract
A high performance numerical technique in the study of aorto-coronaric bypass anastomoses configurations using steady Stokes equations is presented. The problem is first expressed as an optimal control problem. Then, by using an embedding method, the class of admissible shapes is replaced by a class of positive Borel measures. The optimization problem in measure space is then approximated by a linear programming problem. The optimal measure representing optimal shape is approximated by solving this finite-dimensional linear programming problem. An illustrative example demonstrates the effectiveness of the method.
M. Mortezaee, Dr. Ali Reza Nazemi,
Volume 6, Issue 2 (9-2015)
Abstract
We consider an approximation scheme using Haar wavelets for solving a class of infinite horizon optimal control problems (OCP's) of nonlinear interconnected large-scale dynamic systems. A computational method based on Haar wavelets in the time-domain is proposed for solving the optimal control problem. Haar wavelets integral operational matrix and direct collocation method are utilized to find the approximated optimal trajectory of the original problem. Numerical results are also given to demonstrate the applicability and the efficiency of the proposed method.
Dr. Hadi Nasseri, Mr. Ghorbanali Ramzanniakeshteli,
Volume 9, Issue 1 (7-2018)
Abstract
We are concerned with solving Fuzzy Flexible Linear Programming (FFLP) problems. Even though, this model is very practical and is useful for many applications, but there are only a few methods for its situation. In most approaches proposed in the literature, the solution process needs at least, two phases where each phase needs to solve a linear programming problem. Here, we propose a method to solve the given problem in just one phase using only one problem. Furthermore, using our approach, sensitivity analysis of Fuzzy Flexible Linear Programming (FFLP) problem is simpler. For an illustration of our method, some numerical examples given. In particular, a practical problem is formulated and is solved by our method and several other methods and the obtained results are compared.
Dr. Davood Darvishi,
Volume 9, Issue 1 (7-2018)
Abstract
Linear programming problems with interval grey numbers have recently attracted some interest. In this paper, we study linear programs in which right hand sides are interval grey numbers. This model is relevant when uncertain and inaccurate factors make difficult the assignment of a single value to each right hand side. Some methods have been developed for solving these problems. In this paper, we propose a new approach for solving interval grey number linear programming problems is introduced without converting them to classical linear programming problems. A numerical example is provided to illustrate the proposed approach.
Mr. Masoud Alinezahd,
Volume 10, Issue 1 (7-2019)
Abstract
Nowadays, manufacturers need to satisfy consumer demands in order to compete in the real world. This requires the efficient operation of supply chain planning. On the other hand, increasing worldwide environmental, lack of food resources and social concerns are motivating manufacturers and consumers to implement recycling strategies such as product recovery, waste management, or usage of recycled materials. In this study, the closed-loop supply chain network has been proposed which consists of four echelons (suppliers, plants, distribution centers, and customers) in the forward chain and three echelons (collection centers, inspection centers, and disposal centers) in the backward chain. We present a multi-product and multi-period mixed-integer linear programming problem in this paper. The objective of this study is to maximize the profit in the closed-loop supply chain network. The proposed model is applied to an illustrative example based on inspiration from the dairy industry in Iran. The solution of the proposed model is achieved by using Gams software. The results give important insight for fostering the decision making process.
Dr. S. Hadi Nasseri, Mrs Roghaye Chameh, Dr. Mohammad Mahdi Paydar,
Volume 11, Issue 2 (2-2020)
Abstract
New concepts of  -feasibility and -efficiency of solutions for fuzzy mathematical programming problems are used, where is a vector of distinct satisfaction degrees. Recently, a special kind of fuzzy mathematical programming entitled Fuzzy Flexible Linear programming (FFLP) is attracted many interests. Using the mentioned concepts, we propose a two-phase approach to solve FFLP. In the first phase, the original FFLP problem converts it to a Multi-Parametric Linear Programing (MPLP) problem, and then in phase II using the convenient optimal solution with the higher feasibility degree is concluded. Using this concept, we have solved the problem of the animal diet. In the process of milk production, the highest cost relates to animal feed. Based on reports provided by the experts, around seventy percent of dairy livestock costs included feed costs. In order to minimize the total price of livestock feed, according to the limits of feed sources in each region or season, and also the transportation and maintenance costs and ultimately milk price reduction, optimization of the livestock nutrition program is an essential issue. Because of the uncertainty and lack of precision in the optimal food ration done with existing methods based on linear programming, there is a need to use appropriate methods to meet this purpose. Therefore, in this study formulation of completely mixed nutrient diets of dairy cows is done by using a fuzzy linear programming in early lactation. Application of fuzzy optimization method and floating price make it possible to formulate and change the completely mixed diets with adequate safety margins. Therefore, applications of fuzzy methods in feed rations of dairy cattle are recommended to optimize the diets. Obviously, it would be useful to design suitable software, which provides the possibility of using floating prices to set feed rations by the use of fuzzy optimization method.
Mr. Behnam Salehi , Dr. Kazem Nouri , Dr. Leila Torkzadeh ,
Volume 12, Issue 1 (6-2021)
Abstract
In this paper, an efficient method is proposed for solving nonlinear quadratic optimal control problems with inequality constraints. The method is based upon Chebyshev cardinal wavelets. The operational matrix of integration is given for related procedures. This matrix is used to reduce the solution of the nonlinear constrained optimal control to a nonlinear programming one to which existing well-developed algorithms may be applied. Finally, the applicability and validity of method are shown by numerical results of some examples. Moreover, the comparison with the existing results show the preference of this method.
Prof. Alireza Malekijavan , Prof. Hamidreza Zafarani , Prof. Mehdi Aslinejad ,
Volume 13, Issue 1 (6-2022)
Abstract
The paper presents a scheme to supply energy consumers by using a multicarrier energy system (MES). Each MES unit consists of electrical vehicles (EVs), and combined heat and power (CHP) units, which are called energy hubs (EHs) hereinafter. The objective function minimizes the cost of energy of the whole system while considering power flow equations in electricity, heat, and gas grids, where constraints include technical index limits of MESs, EVs, and CHPs. The model has been formed as a non-linear problem (NLP), in the following, the present study proposes a linear programming (LP) model as a substitute for equations of the NLP method so that the global optimal solution is found with a low computation error. Furthermore, the demand parameters, electricity price, and characteristics of EVs are uncertain. To model these uncertainties, we adopt the point estimate approach. The case study of this research considers electricity, gas, and heating grids simultaneously. The energy hubs relate all three grids to each other. The method is tested on a system through simulation using GAMS software. According to obtained numerical results, the suggested LP approach reaches an optimal point with reduced computation time and low error compared to the original formulations. As a result, the indices of different networks are improved using power management of the energy hubs.
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