مجله پژوهش های نوین در ریاضی
پیاپی 6 (تابستان 1395)

A Roman dominating function (RDF) on a graph G = 􀵫V¡E􀵯 is a function f: V(G) → {0¡1¡2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of an RDF f is w(f) = Σ􀭴∈􀭚 f(v). The Roman domination number of G is the minimum weight of an RDF in G. In this paper, we characterize all trees T of order n whose Roman domination number is n − 3.

Geometric programming is efficient tool for solving a variety of nonlinear optimization problems. Geometric programming is generalized for solving engineering design. However, Now Geometric programming is powerful tool for optimization problems where decision variables have exponential form. The geometric programming method has been applied with known parameters. However, the observed values of the parameters in real-life GP problems are often imprecise or vague. This data may be different faces such as bounded, interval, fuzzy and random. In this paper, geometric programming with random parameters to be considered. Then stochastic programming has converted to geometric programming with deterministic parameters. By using dual of geometric programming, optimal solutions of stochastic geometric programming can be obtained. Two illustrative examples are presented to demonstrate the efficacy of our method.

Markowitz model is the first modern formulation of portfolio optimization problem. Relying on historical return of stocks as basic information and using variance as a risk measure are tow drawbacks of this model. Since Markowitz model has been presented, many efforts have been done to remove theses drawbacks. On one hand several better risk measures have been introduced and proper models have been developed to detect optimized portfolio based on them. On the other hand the idea of using generated data by data envelopment analysis instead of historical return of stocks has been presented. In this paper, both improvements are collected by applying a conditional value at risk minimization linear model on cross efficiencies, generated by a proper model of data envelopment analysis model, called range adjusted model. Performance of proposed method, market portfolio as a benchmark and method of applying Markowitz model on cross efficiencies calculated according to sharp ratio using next year real return of each portfolio during years of study. Results support proper performance of proposed method.

Due to the power industry importance in the process of country economic development, studying the efficiency of power plant s is very important. By measuring the efficiency can be perceived the strength and awareness of different sectors and can improve their performance by provide the appropriate solutions. In this paper, power plants was assumed as a decision-making unit that consume gas and gasoline fuel as input to generate electricity production and pollutant gases as desirable and undesirable outputs respectively. In this research, we discussed to measure the technical efficiency of power plants in power generation Management Company of Jonoob-e-Fars since 2010 to 2014, by using the DEA with interval data and undesirable outputs. We got results and finally, we determined the efficient and inefficient units by implementation of all the proposed models of DEA in different technologies. In the following, we determine rank of units by using of topsis and Shannon’s entropy methods and discussed to determine the most economic rates of industry plants and provide the scientific proposal to improve the efficiency of the unit ineffective decision-making units.

Data envelopment analysis (DEA) is a nonparametric approach to evaluate the efficiency of decision making units (DMU) using mathematical programming techniques. Almost, all of the previous researches in stochastic DEA have been used the stochastic data when the inputs and outputs are normally distributed. But, this assumption may not be true in practice. Therefore, using a normal distribution will be lead to wrong results. The skew-normal (SN) distribution is one of the important distribution in statistics. The SN distribution is an asymmetric distribution which has similar properties to a normal distribution and it can be extended to the normal distributions. In the present study, a stochastic BCC model was proposed for measuring the stochastic efficiency of DMUs with inputs and outputs having Skew- Normal (SN) distribution. Moreover, it is shown that this model encompasses the BCC model assuming the normality of data as well. The proposed model in measuring the efficiency of a bank's 25 branches is used.

This paper proposes a compromise model, based on a new method, to solve the multiobjective large scale linear programming (MOLSLP) problems with block angular structure involving fuzzy parameters. The problem involves fuzzy parameters in the objective functions and constraints. In this compromise programming method, two concepts are considered simultaneously. First of them is that the optimal alternative is closer to fuzzy positive ideal solution (FPIS) and farther from fuzzy negative ideal solution (FNIS). Second of them is that the proposed method provides a maximum ‘‘group utility’’ for the ‘‘majority’’ and a minimum of an individual regret for the ‘‘opponent’’. In proposed method, the decomposition algorithm is utilized to reduce the large-dimensional objective space. A multi objective identical crisp linear programming derived from the fuzzy linear model for solving the problem. Then, a compromise solution method is applied to solve each sub problem based on TOPSIS and VIKOR simultaneously. Finally, to illustrate the proposed method, an illustrative example is provided.

Inverse maximum flow (IMDF), is among the most important problems in the field of dynamic network flow, which has been considered the Euclidean norms measure in previous researches. However, recent studies have mainly focused on the inverse problems under the Hamming distance measure due to their practical and important applications. In this paper, we studies a general approach for handling the inverse maximum dynamic flow problem under the weighted sum-type Hamming distance. We assume that a dynamic network flow, and a desired feasible dynamic flow on the network is given. We try to adjust the current arc capacity vector to maximize the dynamic flow and minimize the changes. The motivation for this study stems from the Hamming distance that is made practically important in the situation where we only care about the change, disregarding its magnitude. In this paper, first we prove some preliminary results, then we show that this problem (IMDF) can be transformed to a minimum dynamic cut problem. So, we proposed a combinatorial algorithm for solving the IMDF in strongly polynomial time. Ultimately, the proposed algorithm, is illustrated by a numerical example on a dynamic network.