Control policies for two-stage, pull-type production/inventory systems with constrained average cost criterion

We consider a two-stage, pull-type production/inventory system with a known service mechanism at the first stage. Set-ups and start-ups are involved in the operation of the second stage. We develop a production control policy for the second stage, within the class of (R, r) continuous-review policies, that minimizes the long run average number of set-ups and start-ups subject to a constraint on the number of customers that are lost. We use a semi- Markov decision model to obtain an optimal policy for the operation of the second stage. The optimal policy is in the form of a randomized stationary policy. The structure of the optimal policy suggests the use of a suboptimal look-back policy that delays the set-up at the second stage if the buffer lacks sufficient raw material.