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Communications of the ACM

Communications of the ACM

Occurrences of cycling and other phenomena arising in a class of linear programming models

An investigation into the average queue size for a certain class of queues has resulted in the formulation of linear programming problems which are ill-conditioned in some cases. In attempting to solve these linear programming models, using IBM's MPS package, instances of cycling were encountered. Small perturbations in the input data resulted in problems which did not cycle. This fact, plus several other observed phenomena suggest that the primary reason that cycling is not known to occur more frequently is that round-off errors in the computations perturb the problem sufficiently to prevent cycling (or at least to prevent indefinite cycling). In one case maximizing and minimizing an objective function subject to the same constraint set was attempted, but MPS solved only one of these while giving an indication of infeasibility for the other.

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