Optimal control of dynamic flowshops

Abstract

In this chapter, we consider the problem of controlling the production rate of a stochastic manufacturing system consisting of m ≥ 2 machines in a flowshop configuration (Fig. 2.1) in order to meet the demand for a single product facing the system at a minimum cost. The stochastic nature of the system is due to the machines that are subject to breakdown and repair and to the uncertainty in demand. The machine capacities and demand processes are assumed to be finite state Markov chains. The control variables are the input rates to the machines. We take the number of parts in the buffer of the first m - 1 machines and the surplus at the last machine to be the state variables. Since the number of parts in the internal buffers between any two machines needs to be nonnegative, the problem is inherently a state-constrained problem. Our objective is to choose admissible input rates to various machines in order to minimize a sum of expected discounted inventory/backlog costs and production costs over the infinite horizon.