The project scheduling polyhedron: dimension, facets and lifting theorems

Article Abstract:

Inequality classes regarding the facet-defining properties of the scheduling polyhedron of feasible solutions of the resource constrained project scheduling problem are evaluated. The convex sets of solutions are evaluated, the dimension of the set is calculated and inequalities defining facets are shown. General lifting theorems are then derived for inequalities that do not define facets and are used to obtain general inequalities and facets.

Methods, Scheduling (Management)

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On the design of a finite-capacity queue with phase-type service times and hysteretic control

Article Abstract:

The design of an M/G/1 queue with a finite waiting space, phase-type distribution service times and two-level hysteretic control is proposed along with algorithms for equilibrium probabilities. These algorithms are also used to obtain expressions for features necessary for the design. Results show that the algorithms are capable of efficient search for the optimal combination of trigger points.

Control theory

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Performance bounds for the effectiveness of pooling in multi-processing systems

Article Abstract:

The effect of resource pooling on the performance of multiprocessing and queueing systems is evaluated using performance bounds for different pooling scenarios. Results indicate that pooling tends to degrade the performance of such systems when the variability in the processing requirements of the different customer classes exceeds the minimum average delay.

Multiprocessing

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