Received: January 6, 2011 Accepted: January 24, 2011 doi:10.5539/jmr.v3n2p66 The research is supported by Zhejiang Provincial Education Department research projects (Y201016421) Abstract Monge-Kantorovich transportation problem in a bounded region of Euclidean space is transferred into a partial differential equations group. And then the explicit formula of the optimal coupling is achieved. The...

Abstract. We address the two-commodity maximum flow problem on undirected networks. As a result of a change of variables, we introduce a new formulation that solves the problem through classical maximum flow techniques with only one-commodity. Therefore, a general strategy, based on this change of variables, is defined to deal with other undirected multi-commodity problems. Finally, we extend t...

We describe techniques for visualizing the Pareto optimal set that can be used if the multiobjective optimization problem considered has more than two objective functions. The techniques discussed can be applied in the framework of both MCDM and EMO approaches. First, lessons learned from methods developed for biobjective problems are considered. Then, visualization techniques for convex multio...

While solution methods are well-known for optimization problems with a single objective function, there are many common real world scenarios in which a single function does not suffice. Multiobjective or multicriteria optimization is the branch of optimization that deals with the case of two or more objective functions. An important example is the biobjective problem that arises in portfolio op...

Dealing with uncertainty on financial markets is very difficult task. The investor’s decision is highly dependent on the selected criteria which should help him to select the best among available investment opportunities. Harry Markowitz, [12], introduced his mean-risk model more than 50 years ago where variance was used as the risk measure. Many other risk measures has been proposed since then...

We consider the question of global convergence of iterative methods for nonlinear programming problems. Traditionally, penalty functions have been used to enforce global convergence. In this paper we review a recent alternative, so-called filter methods. Instead of combing the objective and constraint violation into a single function, filter methods view nonlinear optimization as a biobjective ...

In the literature hardly any attention is paid to solving a fuzzy fixed charge transportation problem. In this paper, we consider the fully fixed-charge transportation problem and try to find both the lower and upper bounds on the fuzzy optimal value of such a problem in which all of the parameters are triangular fuzzy numbers. To illustrate the proposed method, a numerical example is ‎presented.‎

The solid transportation problem is an important extension of the traditional transportation problem. Solid transportation problem with uncertain variables as its parameters is called uncertain solid transportation problem. In this paper, the expected-constrained programming for an uncertain solid transportation problem is given based on uncertainty theory. According to inverse uncertainty dist...