In this paper, we integrate goal programming (GP), Taylor Series, Kuhn-Tucker conditions and Penalty Function approaches to solve linear fractional bi-level programming (LFBLP)problems. As we know, the Taylor Series is having the property of transforming fractional functions to a polynomial. In the present article by Taylor Series we obtain polynomial objective functions which are equivalent to...

Minimum cost flow problems in infinite networks arise, for example, in infinite-horizon sequential decision problems such as production planning. Strong duality for these problems was recently established for the special case of linear costs using an infinite-dimensional simplex algorithm. Here, we use a different approach to derive duality results when the costs are convex. We formulate the pr...

In this paper we propose a scalable QoS-based inter-domain routing scheme for distributed multimedia applications in a high speed wide area network. The problem of QoS-based routing is formulated as a multicriteria shortest path problem, known as NP-complete 20,29]. Our scheme consists of two phases. In Phase 1, we present a way of mapping the network into a graph that contains a part of the ne...

This paper considers two stochastic models with static and fatigue failures under various situations of availability and slackness of manpower and business. An operating system is exposed to a shock process which causes static or fatigue failures. The static failures are repaired and fatigue failures call for replacement of the entire system when they occur. Considering a continuous time Markov...

This paper addresses combined location/routing problems defined on trees, where not all vertices have to be necessarily visited. A mathematical programming formulation is presented, which has the integrality property. The formulation models a directed forest where each connected component hosts at least one open facility, which becomes the root of the component. The problems considered can also...

Column generation has been intensively used in the last decades to compute good quality lower bounds for combinatorial problems reformulated through Dantzig-Wolfe decomposition. In this paper we propose a novel framework to cope with problems in which the structure of the original formulation, namely the presence of a combinatorial number of decision variables, does not allow for straightforwar...

We generalize the -relaxation method of [14] for the single commodity, linear or separable convex cost network flow problem to network flow problems with positive gains. The method maintains -complementary slackness at all iterations and adjusts the arc flows and the node prices so as to satisfy flow conservation upon termination. Each iteration of the method involves either a price change on a...

There are some specific features of the non-radial DEA (data envelopment analysis) models which cause some problems under the returns to scale measurement. In the scientific literature on DEA, some methods were suggested to deal with the returns to scale measurement in the non-radial DEA models. These methods are based on using Strong Complementary Slackness Conditions in the optimization theor...

We review a class of recently-proposed linear-cost network flow methods which are amenable to distributed implementation. All the methods in the class use the notion of e-complementary slackness, and most do not explicitly manipulate any "global" objects such as paths, trees, or cuts. Interestingly, these methods have stimulated a large number of new serial computational complexity results. We ...

This lecture starts with an LP relaxation of the max sat problem and a proof showing how close the relaxed optimum is to the integral optimum. Then we move on to a definition and proof complementary slackness and use it to establish primal-dual schema and algorithms. We then show an example of using such an algorithm on the set cover problem. The maximum satisfiability problem asks for the maxi...