Optimizing input rates to manufacturing cells in a production system

A manufacturing system that can produce multiple part types generates inputs, at a given rate R, to a set of m cells. Each cell processes a certain type of parts and has its own production and buffer capacities. The authors study the problem of allocating the production rate R among the m cells, such that the total throughput (over all m cells) is maximized, while the blocking probabilities are kept below a given set of limits. For this problem a model has been formulated, which maximizes a concave function over a convex set. In this paper the authors will present and study a dual Lagrange relaxation approach. Numerical experiences will also be reported.