Strategic Safety-Stock Placement in Supply Chains with Capacity Constraints

Abstract

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 multi-stage serial system that operates with a constant base-stock policy with censored ordering, i.e., a 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.

Planning capacity and safety stocks in a serial production–distribution system with multiple products

“…There are few studies that propose GSA models with capacitated stages. Graves and Schoenmeyr (2016) considered stages with a fixed capacity, and modified the base stock policy in a way that a stage never places an order to its upstream stage, which is greater than the available capacity. They show that the dynamic programming algorithm proposed by Graves and Willems (2000) can be modified to solve the capacitated case.…”

“…They show that the dynamic programming algorithm proposed by Graves and Willems (2000) can be modified to solve the capacitated case. Graves and Schoenmeyr (2016) made the assumption that lead times are fixed, independent of utilization, which is restrictive in the presence of congestion effects due to variability (Hopp and Spearman, 2011). Lemmens et al (2016) and Kumar and Aouam (2018b) present models that capture the relationship between the capacity, batch size, and lead times using queuing theory.…”

The trade-off between inventories, lead time and capacity: application to vaccine supply chain design

“…The authors use simulation to estimate a correction factor to obtain the same stock-out probability as in the uncapacitated case. Graves and Schoenmeyr (2016) published an extension of the GSA model (Graves and Willems (2000)) to include capacity constraints and analytically characterized the necessary base stock levels. The authors show how existing dynamic programming algorithms for the uncapacitated case can be modified to the capacitated case.…”

Performance Measurement of a Rotavirus Vaccine Supply Chain Design by the Integration of Production Capacity into the Guaranteed Service Approach

“…The authors use simulation to estimate a correction factor to obtain the same stock-out probability as in the uncapacitated case. [Graves and Schoenmeyr, 2016] published an extension of the GSA model ( [Graves and Willems, 2000]) to include capacity constraints and analytically characterized the necessary base stock levels. The authors show how existing dynamic programming algorithms for the uncapacitated case can be adapted to the capacitated case.…”