مجله پژوهش های نوین در ریاضی
پیاپی 3 (Autumn 2015)

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.

Recently, fuzzy linear programming problems have been considered by many. In the literature of fuzzy linear programming several models are offered and therefore some various methods have been suggested to solve these problems. One of the most important of these problems that recently has been considered; are Fully Fuzzy Linear Programming (FFLP), which all coefficients and variables of the problem are the same kind of fuzzy numbers. One of most common of them is the model in which all fuzzy parameters are discussed by triangle numbers. In this paper, we first define a fully fuzzy linear programming with trapezoidal numbers and then suggest a new method based on reducing the original problem to the problem with triangle number. Specially, a conversion function for converting two trapezoidal and triangular numbers to each other is offered. Finally, the mentioned method is illustrated by a numerical example.

In this paper we present a recurrent neural network model to recognize efficient Decision Making Units(DMUs) in Data Envelopment Analysis(DEA). The proposed neural network model is derived from an unconstrained minimization problem. In theoretical aspect, it is shown that the proposed neural network is stable in the sense of lyapunov and globally convergent. The proposed model has a single-layer structure. Simulation shows that the proposed model is effective to identify efficient DMUs in DEA.

Transportation problem is a linear programming which considers minimum cost for shipping a product from some origins to other destinations such as from factories to warehouse, or from a warehouse to supermarkets. To solve this problem simplex algorithmis utilized. In real projects costs and the value of supply and demands are fuzzy numbers and it is expected that optimal solutions for determining the value of commodities transported from a source to a destination be obtained as a fuzzy. So the first idea is to present the in the full fuzzy condition and then an algorithmwhich is of importance for solving such a problem. In this article, a new algorithm is suggested for solving fully fuzzy transportation problem. This algorithm transforms the fully fuzzy transportation problem into a triple-objective problem and then it utilizes a weighted method for solving multi-objective problems and solves the new problem using simplex transportation method. At the end, the suggested method is utilized for the real data.

Congestion is a wasteful stage of the production process where outputs are reduced due to excessive amount of inputs. There are several approaches in data envelopment analysis (DEA) literatures to treat congestion. The concept of strong and weak congestion first developed by Tone and Sahoo [Tone, K., Sahoo, B.K., 2004. Degree of scale economies and congestion: A unified DEA approach. European Journal of Operational Research 158, 755–772]. Evidence of strong congestion occurs whenever reducing proportionally all inputs can increase all outputs. Tone and Sahoo extended the relationship between congestion and other economic concept such as marginal productivity. They proved that existence of strong congestion is hinged to negative marginal productivity. Nonetheless the definition of strong congestion is too restrictive, since it has severe condition of “proportionate’’ reduction in all inputs causes an augmentation in all outputs. So the number of strongly congested DMUs appeared to be limited. In this paper we define a new less restrictive definition of congestion namely “ strict congestion’’ which is identified if and only if a reduction in all inputs causes an increase in all outputs. Therewith this study first proposes a new approach for the congestion recognition. Then another scheme is presented to determine the status of congestion (weak or strict). The validity of the proposed approach is demonstrated using numerical examples.

Heart chaotic system and the ability of particle swarm optimization (PSO) method motivated us to benefit the method of chaotic particle swarm optimization (CPSO) to synchronize the heart three-oscillator model. It can be a suitable algorithm for strengthening the controller in presence of unknown parameters. In this paper we apply adaptive control (AC) on heart delay model, also examine the system stability by the Lyapunov stability theorem. Then we improve results with using CPSO algorithm and define an appropriate cost function. At the end of we implement the proposed approach on an example.

Reliability optimization problem has a wide application in engineering area. One of the most important problems in reliability is redundancy allocation problem (RAP). In this research, we worked on a RAP with repairable components and k-out-of-n sub-systems structure. The objective function was to maximize system reliability under cost and weight constraints. The aim was determining optimal components number of each subsystem, including the optimal number of repairmen allocated to each subsystem. Because this model belongs to Np. Hard problem, we used genetic algorithm (GA) for solving the presented model and response surface methodology (RSM) was used for tuning of algorithm parameters. Also for calculating the reliability of each subsystem (and system reliability) we used a simulation method. Finally, a numerical example was solved to test the algorithm performance.