Optimal control of a two-server flow-shop network

In this paper we suggest a new, intuitive, and simple method for scheduling jobs in a two-server flow-shop network (FSN) with the minimum makespan objective. Multiple types of jobs with corresponding constant service times arrive at the network at various times over a finite time interval. An analog fluid network is proposed and its optimal fluid control policy determined. We make use of this optimal control policy to suggest a new method for scheduling jobs in the original discrete FSN and prove its asymptotic optimality. The method is particularly attractive because it falls into the class of easy-to-implement and computationally inexpensive on-line algorithms. Numerical simulations are used to evaluate the performance of the suggested method and show that it performs optimally in almost all simulated instances. Some additional properties of the network are discussed and illustrated.