This paper discusses an Interval Quadratic Programming (IQP) problem, where the constraints coefficients and the right-hand sides are represented by interval data. First, the focus is on a common method for solving Interval Linear Programming problem. Then the idea is extended to the IQP problem. Based on this method each IQP problem is reduced to two classical Quadratic Programming (QP) proble...

this paper studies the hybrid flow shop scheduling where the optimization criterion is the minimization of total tardiness. first, the problem is formulated as a mixed integer linear programming model. then, to solve large problem sizes, an artificial immune algorithm hybridized with a simple local search in form of simulated annealing is proposed. two experiments are carried out to evaluate th...

Linear programming problems with alternate solutions are challenging due to the choice of multiple strategiesresulting in the same optimal value of the objective function. However, searching for these solutions is atedious task, especially when using mixed integer linear programming (MILP), as previously applied tometabolic models. Therefore, judgment on plurality of optimal m...

In 1951, Dantzig [3] showed the equivalence of linear programming and two-person zero-sum games. However, in the description of his reduction from linear programming to zero-sum games, he noted that there was one case in which his reduction does not work. This also led to incomplete proofs of the relationship between the Minmax Theorem of game theory and the Strong Duality Theorem of linear pro...

Abstract The maximum clique problems calls for determining the size of largest in a given graph. This graph problem affords number zero-one linear programming formulations. In this case study we deal with some these We consider ways tightening carry out numerical experiments to see improvements tightened formulations provide.

In this work, we study continuous reformulations of zero–one programming problems. We prove that, under suitable conditions, the optimal solutions of a zero–one programming problem can be obtained by solving a specific continuous problem.

Phasor Measurement Units (PMUs) are in growing attention in recent power systems because of their paramount abilities in state estimation. PMUs are placed in existing power systems where there are already installed conventional measurements, which can be helpful if they are considered in PMU optimal placement. In this paper, a method is proposed for optimal placement of PMUs incorporating conve...

This paper presents the results of experimentation on the development of an efficient branch-and-bound algorithm for the solution of zero-one linear mixed integer programming problems. An implicit enumeration is employed using bounds that are obtained from the fractional variables in the associated linear programming problem. The principal mathematical result used in obtaining these bounds is t...

In practice, there are many problems which decision parameters are fuzzy numbers, and some kind of this problems are formulated as either possibilitic programming or multi-objective programming methods. In this paper, we consider a multi-objective programming problem with fuzzy data in constraints and introduce a new approach for solving these problems base on a combination of the multi-objecti...

There are varieties of QFD combination forms available that can help management to choose the right model for his/her types of problem. The proposed MOCC-QFD-FMEA model is a right model to include variety of objectives as well as the risk factors into the model of the problem. Due to the fact that the model also takes into consideration the concept of Fuzzy set, it further allows management...