Abstract
Abstract A set of independent machines dedicated to different production processes and sharing, one common resource is modelled as a set of M/M/1 queueing systems whose service rates are subject to a linear constraint. We consider a cost function which depends on the service rates of the queueing systems and on a set of time parameters, the lead times. After proving that there exists a set of service rates and lead times which minimize the cost function, we suggest a method to find it through the solution of a sequence of. auxiliary problems.
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