Correspondence: Erratum: Optimizing Strategic Safety Stock Placement in Supply Chains

In Graves Willems (2000) we consider the problem of finding the optimal placement of safety stocks in a supply chain with bounded demand and guaranteed service times. We develop a dynamic programming algorithm for supply chains that can be modeled as spanning trees. The intent of this note is to correct an error in the algorithm. Ekaterina Lesnaia of MIT and Dr. Salal Humair of Optiant independently discovered the error. We wish to acknowledge and to thank Ms. Lesnaia and Dr. Humair for uncovering the error and for bringing it to our attention; they also have identified how to correct the error. In order to describe the error and its correction, we will repeat part of the algorithm from Graves Willems (2000). The dynamic program evaluates a functional equation for each node in the spanning tree, in which the nodes have been labeled 1, 2, … N by the labeling algorithm in Graves Willems (2000). We define N k for each node k to be the subset of nodes {1, 2, ... k} that are connected to k on the sub-graph with node set {1, 2, … k}. There are two forms for the functional equation. First, the function f k (S) is the minimum holding cost for safety stock in a sub-network with node set N k , where we assume that the outbound service time for node k is S. Second, the function g k (SI) is the minimum holding cost for safety stock in a sub-network with node set N k , where we assume that the inbound service time for node k is SI.