We study a two-stage push–pull system in an assemble-to-order manufacturing environment. Modelling the system as an inventory-queue model, we construct a decision model to determine the optimal stock level of the semifinished base product and the optimal leadtime of the finished products that will minimize the total operational cost. We analytically characterize the structure of the optimal policy. For systems with moderate demand and upstream processing time variabilities, there exists a threshold determined purely by the tradeoff of operational costs so that when the upstream utilization is above the threshold, the push–pull strategy is optimal; otherwise the pure-pull strategy is optimal. When the inter-arrival time or the upstream service time follows a general probability distribution, the optimal policy depends on the demand or process variability at the upstream stage. Our results can be used to guide managers in selecting the right inventory and leadtime strategy to cope with system variability. We find that in comparison of the downstream variability, under some mild condition, the upstream variability has a more significant impact on the choice of the optimal policy, the corresponding inventory, and lead time. Further, the guaranteed/constant downstream processing time does not always benefit the supply chain performance.
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