Each dynamic job shop can be represented as a network of queues, in which each service station indicates a machine or a production department. Now, assume that the service rates of these service stations can be controlled. In this paper, a new model is developed for bicriteria Optimal control of service rates of all service stations in a class of Jackson networks, in which the expected value of the shortest path of the network and, also, the total operating costs of all service stations of the network, per period, are minimized. The expected value of the shortest path of such a network of queues is equal to the expected value of the time that the first product is completed.This is an important factor in production systems, because, related to design and manufacture of a new product, the first manufactured product often has the maximum flow time, in effect, which can be minimized through the model. The networks of queues analyzed in this paper, have all the specifications of Jackson networks, except for not containing M/M /C queueing systems.