Optimal service control of a serial production line with unreliable workstations and random demand

The problem considered here is to find the optimal service control policy for a serial production line with n failure-prone workstations and random demand. The processing times of the part in workstations are exponentially distributed, and the service rates are controllable if the workstations are up. The objective function is the expected discounted cost caused by inventories of work-in-process and inventory or backlog of finished products. It is shown that the optimal policy is of bang-bang type and can be determined by a set of switching manifolds. For a given state of the workstations, one manifold determines the optimal decision of one workstation while it is up. The monotonicity and asymptotic behaviors of the manifolds are investigated. The relationship of the manifolds under different workstation states is studied, i.e. the more the workstations are down, the lower the switching manifolds locate in the state space. Based on the structural properties of the switching manifolds, some simple suboptimal policies are proposed, which are quite easy to implement in practical systems. Numeric examples are given to illustrate the results. (C) 1998 Elsevier Science Ltd. All rights reserved.