Look-back policies for two-stage, pull-type production/inventory systems

The authors 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. The authors develop a production control policy for the second stage, within the class of (R,r) continuous-review policies, that minimizes the long run average total cost. They use a semi-Markov decision model to obtain an optimal policy for the operation of the second stage. 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. The performance of the system and the average total cost under the suboptimal policy can be obtained approximately using a decomposition algorithm. The authors show examples justifying the use of this suboptimal policy.