Sean P. Willems

Optimizing Strategic Safety Stock Placement in Supply Chains

Manufacturing managers face increasing pressure to reduce inventories across the supply chain. However, in complex supply chains, it is not always obvious where to hold safety stock to minimize inventory costs and provide a high level of service to the final customer. In this paper we develop a framework for modeling strategic safety stock in a supply chain that is subject to demand or forecast uncertainty. Key assumptions are that we can model the supply chain as a network, that each stage in the supply chain operates with a periodic-review base-stock policy, that demand is bounded, and that there is a guaranteed service time between every stage and its customers. We develop an optimization algorithm for the placement of strategic safety stock for supply chains that can be modeled as spanning trees. Our assumptions allow us to capture the stochastic nature of the problem and formulate it as a deterministic optimization. As a partial validation of the model, we describe its successful application by product flow teams at Eastman Kodak. We discuss how these flow teams have used the model to reduce finished goods inventory, target cycle time reduction efforts, and determine component inventories. We conclude with a list of needs to enhance the utility of the model.

Optimizing the Supply Chain Configuration for New Products

We address how to configure the supply chain for a new product for which the design has already been decided. The central question is to determine what suppliers, parts, processes, and transportation modes to select at each stage in the supply chain. There might be multiple options to supply a raw material, to manufacture or assemble the product, and to transport the product to the customer. Each of these options is differentiated by its lead time and direct cost added. Given these various choices along the supply chain, the configuration problem is to select the options that minimize the total supply chain cost. We develop a dynamic program with two state variables to solve the supply chain configuration problem for supply chains that are modeled as spanning trees. We illustrate the problem and its solution with an industrial example. We use the example to show the benefit from optimization relative to heuristics and to form hypotheses concerning the structure of optimal supply chain configurations. We conduct a computational experiment to test these hypotheses.

Supply Chain Design: Safety Stock Placement and Supply Chain Configuration

Publisher Summary This chapter discusses two approaches to safety stock placement, which are termed as “stochastic-service model” and the “guaranteed-service model.” In the stochastic-service model, each stage in the supply chain maintains a safety stock sufficient to meet its service level target. In this setting, a stage that has one or more upstream-adjacent supply stages has to characterize its replenishment time taking into account the likelihood that these suppliers will meet a replenishment request from stock. In the guaranteed-service model, each stage provides a guaranteed service to its customer stages. In this setting, a supply stage sets a service time to its downstream customer and then holds sufficient inventory so that it can always satisfy the service-time commitment. A key assumption in this model is to assume that demand is bounded for the purpose of making the service-time guarantee. The chapter also discusses how the supply chain can be optimally configured. The notion of options are introduced for each stage in the supply chain, where the options differ in terms of lead-time and cost.

Strategic Inventory Placement in Supply Chains: Nonstationary Demand

The life cycle of new products is becoming shorter and shorter in all markets. For electronic products, life cycles are measured in units of months, with 6-to 12-month life cycles being common. Given these short product life cycles, product demand is increasingly difficult to forecast. Furthermore, demand is never really stationary because the demand rate evolves over the life of the product. In this paper, we consider the problem of where in a supply chain to place strategic safety stocks to provide a high level of service to the final customer with minimum cost. We extend our model for stationary demand to the case of nonstationary demand, as might occur for products with short life cycles. We assume that we can model the supply chain as a network, that each stage in the supply chain operates with a periodic review base-stock policy, that demand is bounded, and that there is a guaranteed service time between every stage and its customers. We consider a constant service time (CST) policy for which the safety stock locations are stationary; the actual safety stock levels change as the demand process changes. We show that the optimization algorithm for the case of stationary demand extends directly to determining the safety stocks when demand is nonstationary for a CST policy. We then examine with an illustrative example how well the CST policy performs relative to a dynamic policy that dynamically modifies the service times. In addition, we report on numerical tests that demonstrate the efficacy of the proposed solution and how it would be deployed.

Accelerating the Profitability of Hewlett-Packard's Supply Chains

Hewlett-Packard (HP) developed a standard and common process for analysis coupled with advancement in inventory optimization techniques to invent a new and robust way to design supply-chain networks. This new methodology piloted by HPs Digital Imaging division has received sponsorship from HPs Executive Supply- Chain Council and is now being deployed across the entire company. As of May 2003, a dozen product lines have been exposed to this methodology, with four product lines already integrating this process into both the configuration of their new-product supply chains and the improvement of existing-product supply chains. The team will highlight the application of these new capabilities within HPs Digital Camera and Inkjet Supplies businesses. The realized savings from these first two projects exceeds

Data Set---Real-World Multiechelon Supply Chains Used for Inventory Optimization

130 million.

Optimizing Strategic Safety Stock Placement in Supply Chains with Clusters of Commonality

This data set describes 38 multiechelon supply chains that have been implemented in practice. These chains exhibit special structure that can be used to inform and test analytical models. Although the data were not collected with the intention of econometric analysis, they may be useful in an empirical study. The data described in this paper are publicly available at the journals website (http://msom.pubs.informs.org/ecompanion.html).

Managing Inventory in Supply Chains with Nonstationary Demand

Multiechelon inventory optimization is increasingly being applied by business users as new tools expand the class of network topologies that can be optimized. In this paper, we formalize a topology that we call networks with clusters of commonality (CoC), which captures a large class of real-world supply chains that contain component commonality. Viewed as a modified network, a CoC network is a spanning tree where the nodes in the modified network are themselves maximal bipartite subgraphs in the original network. We first present algorithms to identify these networks and then present a single-state-variable dynamic program for optimizing safety stock levels and locations. We next present two reformulations of the dynamic program that significantly reduce computational complexity while preserving the optimality of the resulting solution. This work both incorporates arbitrary safety stock cost functions and makes possible optimizing a large class of practically useful but previously intractable networks. It has been successfully applied at several Fortune 500 companies, including the recent Edelman finalist project at Hewlett Packard described in detail in Billington et al. (2004).

Inventory Optimization at Procter & Gamble: Achieving Real Benefits Through User Adoption of Inventory Tools

Many companies experience nonstationary demand because of short product life cycles, seasonality, customer buying patterns, or other factors. We present a practical model for managing inventory in a supply chain facing stochastic, nonstationary demand. Our model is based on the guaranteed service modeling framework. We first describe how inventory levels should adapt to changes in demand at a single stage. We then show how nonstationary demand propagates in a supply chain, allowing us to link stages and apply a multiechelon optimization algorithm designed originally for stationary demand. We describe two successful applications of this model. The first is a tactical implementation to support monthly safety stock planning at Microsoft. The second is a strategic project to evaluate the benefits of using an inventory pool at Case New Holland.

A Periodic-Review Modeling Approach for Guaranteed Service Supply Chains

Over the past 10 years, Procter & Gamble has leveraged its cross-functional organizational structure with operations research to reduce its inventory investment. Savings were achieved in a two-step process. First, spreadsheet-based inventory models locally optimized each stage in the supply chain. Because these were the first inventory tools installed, they achieved significant savings and established P&Gs scientific inventory practices. Second, P&Gs more complex supply chains implemented multiechelon inventory optimization software to minimize inventory costs across the end-to-end supply chain. In 2009, a tightly coordinated planner-led effort, supported by these tools, drove