Virtual and node routing for optimal control of production rates in a flexible manufacturing facility

A production facility has several machines that are used to perform the transformation operations required by several parts. These parts are used to produce a number of final products. In this work we focus on the optimization of the production process, without considering the assembly operations. Our model therefore can be used whether the products are assembled in the same factory or packaged for home assembly. The problem consists in finding optimal input rates per part and routing strategies, in order to maximize the total rate of profit. Two such routing strategies are considered. Under “node routing”, we look for a single routing scheme applied to the operations. Under “virtual routing”, we look for a multiple routing scheme applied to the operations. We discuss the implementation of gradient search methods to construct an adaptive control procedure that will adjust the input rates per parts as well as the routing probabilities, in order to maximize the total long term rate of profit. Using mean flow analysis, we express the gradients in terms of local sensitivities, which can be estimated at each machine