Push and Pull Systems With External Demands

We examine Push and Pull production control systems under a make-to-order policy with safety stock. We compute the distribution of the waiting time until a demand is satisfied, as well as flow time distributions and service levels for both systems. Work-in-process levels are determined as well. The analysis is carried out under Markovian assumptions and the explicit results on flow times depend on non-overtake conditions that are satisfied for single machine stations.