This paper suggests an algorithm to solve a three level large scale linear programming problem with fuzzy numbers, where all coefficients of the objective functions are symmetric trapezoidal fuzzy numbers. A three-level programming problem can be thought as a static version of the Stackelberg strategy. The suggested algorithm uses a linear ranking function at each level to define a crisp model ...

The computational solution of large scale linear programming problems contains various difficulties. One of the difficulties is to ensure numerical stability. There is another difficulty of a different nature, namely the original data, contains errors as well. In this paper, we show that the effect of the random errors in the original data has a diminishing tendency for the optimal value as the...

We discuss interior point methods for large-scale linear programming, with an emphasis on methods that are useful for problems arising in telecommunications. We give the basic framework of a primal-dual interior point method, and consider the numerical issues involved in calculating the search direction in each iteration, including the use of factorization methods and/or preconditioned conjugat...

this paper uses the l1−norm and the concept of the non-dominated vector, topropose a method to find a well-dispersed subset of non-dominated (wdsnd) vectorsof a multi-objective mixed integer linear programming (momilp) problem.the proposed method generalizes the proposed approach by tohidi and razavyan[tohidi g., s. razavyan (2014), determining a well-dispersed subset of non-dominatedvectors of...

in some data envelopment analysis (dea) applications, some inputs of dmus have negative values with positive cost. this paper generalizes the global cost malmquist productivity index to compare the productivity of dierent dmus with negative inputs in any two periods of times under variable returns to scale (vrs) technology, and then the generalized index is decomposed to several components. th...

data envelopment analysis (dea) is a technique used to evaluate the relative efficiency of comparable decision making units (dmus) with multiple input-output. it computes a scalar measure of efficiency and discriminates between efficient and inefficient dmus. it can also provide reference units for inefficient dmus without consideration of the decision makers’ (dms) preferences. in this paper, ...

Numerical approaches are developed for solving large-scale problems of extended linear-quadratic programming that exhibit Lagrangian separability in both primal and dual variables simultaneously. Such problems are kin to large-scale linear complemen-tarity models as derived from applications of variational inequalities, and they arise from general models in multistage stochastic programming and...

Delay-constrained area optimization is an important step in synthesis of VLSI circuits. Minimum area (minarea) retiming is a powerful technique to solve this problem. The minarea retiming problem has been formulated as a linear program; in this work we present techniques for reducing the size of this linear program and e cient techniques for generating it. This results in an e cient minarea ret...

‎Linear semi-infinite programming problem is an important class of optimization problems which deals with infinite constraints‎. ‎In this paper‎, ‎to solve this problem‎, ‎we combine a discretization method and a neural network method‎. ‎By a simple discretization of the infinite constraints,we convert the linear semi-infinite programming problem into linear programming problem‎. ‎Then‎, ‎we use...

We show that random projection, the technique of projecting a set of points to a randomly chosen low-dimensional subspace, can be used to solve problems in VLSI layout. Specifically, for the problem of laying out a graph on a 2-dimensional grid so as to minimize the maximum edge length, we obtain an O(log3:5 n) approximation algorithm (this is the first o(n) approximation), and for the bicriter...