Papers by Keyword: Bound

Abstract: This paper addresses a single-machine large-scale rescheduling problems with efficiency and stability subject to machine breakdown. Partial rescheduling (PR) strategy is used to cope with the computational complexity. Two kinds of objective functions of PR sub-problem, where the global dual objectives are reflected to an extent, are designed respectively for the procedural PR horizon and the terminal PR horizon. The PR problem is solved by a branch and bound algorithm. Lower bound and upper bound procedures as well as dominance rules are developed for the branch and bound algorithm. An extensive experimentation was conducted. The computational results show that the branch and bound can solve PR sub-problems with certain scales and the partial rescheduling procedure developed can greatly improve the stability of schedule with little sacrifice in efficiency and provide a reasonable trade-off between solution quality and computational cost.

Abstract: Advanced manufacturing concepts such as cellular and flexible manufacturing may require the formation of part families and machine cells. Many algorithms have been proposed for this and cluster identification (CI) is one such approach. The original CI approach is effective only for perfectly separable cases. Followup efforts use a branch and bound framework to make the CI approach work in partially separable cases. Although the branch and bound framework is useful, it may still produce infeasible solutions. In this paper, we adopt an improved branching scheme to deal with the problem. Computational results are also reported.

Abstract: We consider the Saint-Venant torsion problem of composite shafts. Two different kinds of imperfect interfaces are considered. One models a thin interphase of low shear modulus and the other models a thin interphase of high shear modulus. The imperfect interfaces are characterized by parameters given in terms of the thickness and shear modulus of the interphases. Using variational principles, we derive rigorous bounds for the torsional rigidity of composite shafts with cross-sections of arbitrary shapes. The analysis is based on the construction of admissible fields in the inclusions and in the matrix. We obtain the general expression for the bounds and demonstrate the results with some particular examples. Specifically, circular, elliptical and trianglar shafts are considered to exemplify the derived bounds. We incorporate the cross-section shape factor into the bounds and show how the position and size of the inclusion influence the bounds. Under specific conditions, the lower and upper bounds will coincide and agree with the exact torsional rigidity.

Abstract: This paper deals with an optimal method for solving a 2-stage flexible flow shop scheduling problem with group constraint, batch released dates. This problem is known to be NP-hard. In this paper, first of all, we construct a mathematical model for the problem. Then, we develop a branch and bound method with heuristic algorithm for the optimal solution of the problem. During the initialization, we use a heuristic algorithm H’ as the initial solution. We propose two branching algorithms in the branching procedure and two algorithms for the lower bound. We also propose a set of instances for this type of problem. The results are shown that our branch and bound method is effective for small and medium-sized problem but large-sized problem.

Abstract: In this technical note, we develop an approach to globally solve a class of optimization problems in system engineering based on the recent paper ([1]). Actually the problem we investigated is more general, since we extend numerators and denominators of linear ratios to generalized polynomial functions. And we give a new linear relaxation method for obtaining the lower bound of problems. Our approach is easy to be implemented, since it need not additional special program to the upper and lower bound for numerator and denominator of each generalized polynomial ratio.

Abstract: In this paper, we proposed an algorithm to globally solve a class of mathematical problems in mechanical system. Firstly, by utilizing equivalent problem and linear relaxation technique, a linear relaxation programming of original mathematical problem is established. Secondly, by using branch and bound theory, a feasible algorithm is proposed for globally solving original problem. Finally, the convergence of the proposed algorithm is proven, and numerical experiments showed that the presented algorithm is feasible.

Abstract: In this paper, we develop an algorithm to globally solve a class of mathematical models in system engineering. Firstly, by utilizing equivalent problem and linear relaxation method, a linear relaxation programming of original problem is established. Secondly, by using branch and bound technique, a determined branch and bound algorithm is proposed for globally solving original problem. Finally, the convergence of the proposed algorithm is given and numerical examples showed that the presented algorithm is feasible.