Development of Production Scheduling Model With Constraint Resources and Parallel Machines

In this paper, a production scheduling model with constraint resources and parallel machines has been investigated. This problem is proposed as a multi-product production problem. Shortage is not allowed and the production horizon is indefinite. The objective is to maximize the level of resource usage and support the management’s standpoint (delays reduction). In this paper, this problem is modeled as the popular Knapsack problem in 0 and 1 programming. Then due to being NP-hard type for this kind of problems to obtain an optimal solution, A heuristic approach has been used to obtain the acceptable solution. By using the branch-and bound method, a near optimal solution is provided. Finally, resultant solutions by the proposed approach have been compared with the optimal solutions of some real-world problems and it has been observed that deviation from the optimal solution is negligible that indicates the accuracy of the proposed approach

SEMIDEFINITE PROGRAMMING BASED ALGORITHMS FOR THE SPARSEST CUT PROBLEM

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)In this paper we analyze a known relaxation for the Sparsest Cut problem based on positive semidefinite constraints, and we present a branch and bound algorithm and heuristics based on this relaxation. The relaxed formulation and the algorithms were tested on small and moderate sized instances. It leads to values very close to the optimum solution values. The exact algorithm could obtain solutions for small and moderate sized instances, and the best heuristics obtained optimum or near optimum solutions for all tested instances. The semidefinite relaxation gives a lower bound C/W and each heuristic produces a cut S with a ratio c(S)/omega(S) where either cs is at most a factor of C or omega(S) is at least a factor of W. We solved the semidefinite relaxation using a semi-infinite cut generation with a commercial linear programming package adapted to the sparsest cut problem. We showed that the proposed strategy leads to a better performance compared to the use of a. known semidefinite programming solver.45275100Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP

An approximation algorithm for scheduling two parallel machines with capacity constraints

AbstractWe consider the problem of scheduling n independent jobs on two identical parallel machines, with a limit on the number of jobs that can be assigned to each single machine, so as to minimize the total weighted completion time of the jobs. We study a semidefinite programming-based approximation algorithm for solving this problem and prove that the algorithm has a worst case ratio at most 1.1626