Browsing by Subject "Linear Programming"

Now showing 1 - 3 of 3

Open Access
Joint cell loading and scheduling approach to cellular manufacturing systems
(Taylor & Francis, 2011-01-31) Akturk, M. S.
A hierarchical multi-objective heuristic algorithm and pricing mechanism are developed to first determine the cell loading decisions, and then lot sizes for each item and to obtain a sequence of items comprising the group technology families to be processed at each manufacturing cell that minimise the setup, inventory holding, overtime and tardiness costs simultaneously. The linkage between the different levels is achieved using the proposed pricing mechanism through a set of dual variables associated with the resource and inventory balance constraints, and the feasibility status feedback information is passed between the levels to ensure internally consistent decisions. The computational results indicate that the proposed algorithm is very efficient in finding a compromise solution for a set of randomly generated problems compared with a set of competing algorithms.
Open Access
Parallelization of an interior point algorithm for linear programming
(1994) Simitçi, Hüseyin
In this study, we present the parallelization of Mehrotra’s predictor-corrector interior point algorithm, which is a Karmarkar-type optimization method for linear programming. Computation types needed by the algorithm are identified and parallel algorithms for each type are presented. The repeated solution of large symmetric sets of linear equations, which constitutes the major computational effort in Karmarkar-type algorithms, is studied in detail. Several forward and backward solution algorithms are tested, and buffered backward solution algorithm is developed. Heurustic bin-packing algorithms are used to schedule sparse matrix-vector product and factorization operations. Algorithms having the best performance results are used to implement a system to solve linear programs in parallel on multicomputers. Design considerations and implementation details of the system are discussed, and performance results are presented from a number of real problems.
Open Access
Solution of feasibility problems via non-smooth optimization
(1990) Ouveysi, Iradj
In this study we present a penalty function approach for linear feasibility problems. Our attempt is to find an eiL· coive algorithm based on an exterior method. Any given feasibility (for a set of linear inequalities) problem, is first transformed into an unconstrained minimization of a penalty function, and then the problem is reduced to minimizing a convex, non-smooth, quadratic function. Due to non-differentiability of the penalty function, the gradient type methods can not be applied directly, so a modified nonlinear programming technique will be used in order to overcome the difficulties of the break points. In this research we present a new algorithm for minimizing this non-smooth penalty function. By dropping the nonnegativity constraints and using conjugate gradient method we compute a maximum set of conjugate directions and then we perform line searches on these directions in order to minimize our penalty function. Whenever the optimality criteria is not satisfied and the improvements in all directions are not enough, we calculate the new set of conjugate directions by conjugate Gram Schmit process, but one of the directions is the element of sub differential at the present point.