We consider the maximum flow network interdiction problem. We provide a new interpretation of the problem and define a concept called ”optimalcut”. We propose a heuristic algorithm to obtain an approximated cut, and we also obtain its error bound. Finally, we show that our heuristic is an α-Approximation algorithm for a class of networks. By implementing it on three network types, we show the advantage of it over solving the model by CPLEX.

Capacitated Minimum Spanning Tree Problem (CMSTP), a well-known combinatorial optimization problem, holds the central place in telecommunication network design. This problem involves  nding a minimum cost spanning tree with an extra cardinality limitation on the orders of the subtrees incident to a certain root node. The Balanced Capacitated Minimum Spanning Tree Problem (BCMSTP) is a special case that aims to balance the orders of the subtrees. This problem is an NP-hard one and presents two Approximation algorithms in this paper. By considering the maximum order of the subtrees Q, a (3 􀀀 1Q )-Approximation algorithm was provided to  nd a balanced solution. This result was improved to a (2: 5 +  ) Approximation algorithm (for every given  > 0) in the 2d-Euclidean spaces. Also, a Polynomial Time Approximation Scheme (PTAS) was presented for CMSTP.

Identifying the efficient extreme units in a production possibility set is a very important matter in data envelopment analysis, as these observed, real units have the best performances. In this paper, we proposed a multiple objective programming model, in which the feasible region is the production possibility set under the assumption of variable returns to scale and the objective function consists of input and output variables. As we know, by increasing the dimensions of the problem, the set of efficient points would increase as well; thus, using the multiple objective linear programming problem-solving methods in a decision set would lead to computational problems and it would be much easier to work in the outcome set instead of the decision set. In this research, we show that the efficient points in the outcome set of the suggested multiple objective linear programming problems correspond with the efficient extreme points in data envelopment analysis. An outer Approximation algorithm is presented for production of all efficient extreme points in the outcome set. This algorithm provides us with the equations for all efficient surfaces. In the outcome set, this algorithm would use few calculations to produce all the extreme points. Finally, we demonstrate the presented approach through numerical examples.

In this paper, a numerical method for solving stochastic optimal control problem by using Markov chain Approximation method has presented. The basic idea of the Markov chain Approximation method is to approximate the original controlled process by an appropriate controlled Markov chain on a finite state space.Also, we need to approximate the original cost function by one which is appropriate for the approximating chain. These Approximations should be chosen such that a good numerical Approximation to the associated optimal control problem can be obtained, which means the conditional mean and covariance of the changes in state of the chain are proportional to the local mean drift and covariance for the original process. The finite difference Approximations are used to the construction of locally consistent approximating Markov chain, the coefficients of the resulting discrete equation can serve as the desired transition probabilities and interpolation interval.