Scheduling preemptive jobs with precedence constraints on parallel machines

Article Abstract:

An approach was proposed to address the parallel machine scheduling problems. With regards to parallel machine scheduling problems with general precedence constraints, good lower bounds and near optimal solutions can be obtained by transforming the set of constraints into an interval order. Such can be achieved by extending or reducing the set of constraints. Scheduling problems that become NP-hard can be solved by approximating any partial order by an interval order which lessens a certain objective.

Analysis, Scheduling (Management), Heuristic programming

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The balanced linear programming problem

Article Abstract:

A problem enlargement prevention algorithm for the balanced linear programming problem (BLPP) is developed. The algorithm performs steps similar to those in the parametric simplex method and the adaptations to the network flow model reveals that the algorithm may be applied directly to the network without the need for simplex tableu maintenance. The algorithm solves the problem enlargement associated with BLPP transformations to standard linear programming form.

Operations research, Management science, Reports

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Perfect, ideal and balanced matrices

Article Abstract:

Research into perfect, ideal and balanced matrices is presented. There are some cases in which the natural linear programming relaxation produces an optimal solution that is integer, thereby solving the problem. This research considers conditions under which this integrality property holds.

Matrices, Matrices (Mathematics)

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