We generalize the guaranteed-service (GS) model for safety-stock placement in supply chains to include capacity constraints. We first examine the guaranteed-service model for a capacitated single-stage system with bounded demand. We characterize the optimal inventory policy, which depends on the entire demand history. Due to this complexity, we develop a heuristic, namely a constant base-stock policy with censored ordering. This is an order-up-to policy but with its replenishment orders censored by the capacity constraint. We refer to this heuristic as the modified constant base-stock policy (MCBS). We use a numerical experiment to compare the performance of the heuristic policy to the optimal policy. We find that the performance of the heuristic relative to the optimal policy improves with a tighter capacity constraint. We also observe that the performance of the heuristic itself can sometimes be improved by tightening the capacity constraint. We then use the results for a single-stage system to model a multistage serial system that operates with a constant base-stock policy with censored ordering, i.e., an MCBS policy. We show how to adapt the existing dynamic programming algorithm for the unconstrained case to solve for the safety-stock locations and base-stock levels in a capacitated serial system. We describe how to extend this model to other supply chain topologies. We report on numerical tests for serial systems and find that the best MCBS policy in a capacitated system can outperform the best constant base-stock policy in an identical but uncapacitated system.
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