The PDF for each paper, if available, is found by clicking on the paper’s bibliographic entry. Each paper’s abstract follows its bibliography entry. If you have any questions about this work, please send me an email.
Mehdi, M. M., L. Wang, and S. P. Willems, “Developing A Maximum Inscribed Rectangle Heuristic To Satisfy Rush Orders For Heavy Steel Plate,” to appear in INFORMS Journal on Applied Analytics (formerly Interfaces), accepted March 2020, 27 pages.
Steel service centers receive rush orders that must be fulfilled on very short notice. Each order only consumes a portion of one steel plate, so plate selection and job placement are the critical factors that affect the service center’s primary performance metric: plate yield. In conjunction with a steel service center, Artco Steel, we model this problem as a two-dimensional online bin packing algorithm. Unique in the online bin packing literature, we calculate the maximum inscribed rectangle (MIR) before and after job placement as the basis for heuristics that assign each job to a plate and position the job on the plate. Our work is the first paper to extend the online two-dimensional bin packing problem to incorporate scrap, rectangular bin sizes, and a finite number of bins. The MIR procedure significantly outperformed Artco’s existing practice of giving priority to the most recently used plate, and the heuristic’s straightforward nature allowed easy adoption in 2010.
Manary, M. P. and S. P. Willems, “Data Set: 187 Weeks of Customer Forecasts and Orders for Microprocessors from Intel Corporation,” to appear in Manufacturing & Service Operations Management, accepted August 2019, 15 pages. Data in CSV format Data in Microsoft Excel format (zipped)
Problem definition: This data set contains 187 consecutive weeks of Intel mi- croprocessor demand information for all five distribution centers in one of its five sales geographies. For every stock keeping unit (SKU) at every location, the weekly forecasted demand and actual customer orders are provided as well as the SKU’s average selling price category. These data are provided by week and by distribution center, producing 26,114 records in total. Academic/practical relevance: The 86 SKUs in the data set span five product generations. It provides years of product evolution across generations and price points. Methodology: As a data set paper, its purpose is to provide interesting and rich real- world data for researchers developing forecasting, inventory, pricing, and product as- sortment models. Results: The data set demonstrates the presence of significant forecast bias, heterogeneity of forecast errors between distribution centers, generational differences, product life cycles, and pricing dynamics. Managerial implications: This data set provides access to a rich pricing and sales setting from a major corporation that has not been made available before.
This paper studies how a manufacturer should engage with a platform retailer and a traditional reseller. Our work is motivated by the emergence of increasingly powerful retail platforms in China’s consumer electronics and appliances markets. The manufacturer pays a slotting fee and a portion of its sales revenue to the platform retailer in exchange for the opportunity to manage its own space within the retailer’s store. The manufacturer can also sell its product to a tradi- tional reseller thereby earning its wholesale price. We first formulate a Stackelberg game where the platform retailer leads by setting the revenue-sharing rate while the manufacturer follows by choosing to sell through one or both channels. We derive the equilibrium channel and characterize each party’s associated sales quantities, prices, and profits. After confirm- ing, it is always beneficial for the platform retailer to determine the slotting fee and revenue-sharing rate simultaneously, we then formulate two bargaining models between the manufacturer and the platform retailer. In the first model, they can negotiate just the revenue-sharing rate and in the second they negotiate both the revenue-sharing rate and the slotting fee. In the second model, a win-win result for the manufacturer and platform retailer is possible. We find that the slotting fee is neither always beneficial to the platform retailer nor always harmful to the manufacturer; it depends on the demand substitution effect between the two retail channels.
This paper documents more than a decade of work to produce an automated in- ventory target-setting process to enable Intel to manage more than $1 billion of finished-goods inventory. What began as a manual pilot project in 2005 has grown into an automated inventory planning process encompassing all forward-staged inventory points in Intel’s global distri- bution network. Key elements in the change transformation include the automatic removal of forecast bias and forecasting based on similar past products. Pivotal to the transformation was first piloting the multiechelon inventory optimization (MEIO) within the existing business process, enabling supply planners to be able to see how MEIO would have been an im- provement over their ad hoc approach and tracking the reasons for their system overrides. The resulting inventory models are run weekly, and over 99.5% of each week’s inventory targets are accepted automatically by the supply planning community. For the four-year period spanning 2014–2017, Intel’s finance organization credits the deployment of MEIO with increasing Intel’s gross profits by over $1.3 billion. As of this writing in 2018, this lights-out process manages approximately 85% of all finished-goods inventory. The breadth of the implementation at Intel is evidence that other companies can implement this process and achieve similar results.
All too often, companies do not rigorously calculate service levels. Instead, they arbitrarily set service levels by employing a top-down mandate. They employ this arbitrary approach because they have difficulty in quantifying the economics of a specific service level; the primary difficulty these companies encounter is quantifying the cost of not satisfying demand. Intel’s Customer Fulfillment and Logistics Group has developed a data-driven approach to calculate customer service levels. The major breakthrough in this work is a simple three-step process that diverse functions across the supply chain can employ to agree on the costs associated with a given service level.
Design-and-development buyers sourcing new supply chains and strategic sourcing analysts making outsourcing decisions for existing supply chains are in different organizations but share a common problem. Both determine whether an existing part should be replaced. Relative to the existing part, new candidates could be cheaper with longer leadtime, or more expensive with shorter leadtime. Further- more, a longer leadtime part could be buffered with inventory and this could be cheaper than paying more for a shorter leadtime part.
To derive analytical insights into the nature of this problem, we restrict our scope to a two-stage serial line supply chain. This restriction is consistent with sourcing analysts that consider sourcing a single part from different vendors and different transportation alternatives. The resulting two-stage supply chain configuration model jointly determines the chosen option and inventory stocking level at each stage to minimize cost of goods sold, pipeline stock cost and safety stock cost.
We prove it is preferable to synchronize the supply chain by employing the same type of option, either low cost long leadtime or high cost short leadtime, at both stages. We prove that the selection threshold for high cost short lead time options is lowest at just the downstream stage, highest for just the upstream stage, and between these extremes if such a candidate is selected for both stages. If a part’s cost-time relationship follows a functional form, we establish conditions when it is optimal to choose the lowest cost, longest leadtime, option available.
Effective inventory management is one of the most significant challenges facing today’s global supply chains. Businesses are observing significant profitability gain by optimizing their inventory. This paper optimizes safety stock inventory in a two-stage serial line supply chain, inspired by real-life Cisco supply chains, under guaranteed-service safety stock model assumptions. We analytically show that the optimal safety stock levels depend on the cost and leadtime parameters of the supply chain. Intuitively, it is only worthwhile to hold safety stock inventory at the upstream stage when cost at the upstream stage is relatively low or its leadtime is relatively long. We also show that total supply chain safety stock cost can be reduced when cost allocated at the upstream stage is reduced or leadtime at the upstream stage is increased.
Seasonal demand for products is common at many companies including Kraft Foods, Case New Holland, and Elmer’s Products. This study documents how these, and many other companies, experience bloated inventories as they transition from a low season to a high season and a severe drop in service levels as they transition from a high season to a low season. Kraft has termed this latter phenomenon the “landslide effect.” In this study, we present real examples of the landslide effect and attribute its root cause to a common industry practice employing forward days of coverage when setting inventory targets. While inventory textbooks and academic articles prescribe correct ways to set inventory targets, forward coverage is the dominant method employed in practice. We investigate the magnitude and drivers of the landslide effect through both an analytical model and a case study. We find that the effect increases with seasonality, lead time, and demand uncertainty and can lower service by an average of ten points at a representative company. While the logic is initially counterintuitive to many practitioners, companies can avoid the landslide effect by using demand forecasts over the preceding lead time to calculate safety stock targets.
Part obsolescence is a common problem across industries, from avionics and military sectors to most original equipment manufacturers serving industrial markets. When a part supplier announces that a part will become obsolete, the OEM can choose from a number of sourcing options. In practice, the three most commonly adopted mitigation strategies are: (1) a lifetime, or life-of-type (LOT), buy from the original supplier; (2) part substitution, which finds a suitable alternative; and (3) line redesign, which modifies the production line to accommodate a new part. We first develop a framework incorporating fixed cost, variable cost, leadtime, demand uncertainty and the discount rate to directly compare and characterize these three sourcing strategies in a static context. We next formulate an integrated sourcing approach that starts with a bridge buy and may continue with part substitution or line redesign when the originals parts are depleted. Through numerical studies, we identify the joint impact of the problem parameters on the static and integrated sourcing strategies and the optimal choice among them. While the integrated sourcing approach outperforms the static ones in many cases it is not a dominant strategy.
Many real-world supply networks source required materials from multiple suppliers. Existing multiechelon inventory optimization approaches either restrict their scope to multiple supply sources in two-echelon systems or single suppliers in multiechelon systems. We develop an exact mathematical model for static dual supply in a general acyclic N -echelon network structure, which builds on the guaranteed-service framework for safety stock optimization. It is assumed that the suppliers are allocated static fractions of demand. We prove that for normally distributed demand an extreme point property holds. We present a real example from the industrial electronics industry consisting of five echelons and three dual-sourced materials. This example forms the basis for a numerical analysis. Compared with the only previously published approximate solution, our exact approach results in considerable cost savings because the exact model captures inventory pooling in a way that the approximation is unable to do. For a set of test problems, total safety stock cost savings are 9.1%, on average.
Effective end-to-end supply chain management and network inventory optimization must account for service levels, demand volatility, lead times, and lead-time variability. Most inventory models incorporate demand variability, but far fewer rigorously account for lead-time variability, particularly in multiechelon supply chain networks. Our research extends the guaranteed service (GS) model of safety stock placement to allow random lead times. The main methodological contribution is the creation of closed-form equations for the expected safety stock in the system; this includes a derivation for the early-arrival stock in the system. The main applied contributions are the demonstration of real stochastic lead times in practice and a discussion of how our approach outperforms more traditional heuristics that either ignore lead-time variability or consider the maximum lead time at each stage.
Intel’s Channel Supply Demand Operations (CSDO) organization is responsible for satisfying the boxed processor demands of Intel’s vast customer network of distributors, resellers, dealers and system integrators. In 2005, CSDO began a multi-echelon inventory optimization (MEIO) pro-ject to improve its efficiency and effectiveness by optimizing inventory levels and locations across CSDO’s end to end supply chain. This paper describes the executed project plan, the de-fined workflows and the implemented results. One year after implementation, total inventory le-vels were reduced by over 11% while service levels were eight points higher than products that were not modeled using the MEIO process. The MEIO process continues to be in place to this day, leading to sustained reductions in inventory levels, average service levels exceeding 90%, and more than an order of magnitude reduction in the number of expedites.
Motivated by the sourcing of integrated circuits in the electronics industry, we study sourcing strategies for short-lifecycle products with two substitutable parts. The first part, referred to as the fast part, is highly responsive while having negligible fixed cost but high variable cost. The second part, referred to as the slow part, is opposite in these properties. We build models starting with the fast part to target the initial market, then switching to the pre-ordered slow part for volume production, and eventually transitioning back to the fast part until the product’s end of lifecycle. Assuming an optional second order for the slow part, we model the sourcing process by a two-stage stochastic program. The thresholds for the fixed costs and the optimal ordering policies for the two orders are exactly derived. Assuming the demand throughout the product lifecycle as a multivariate Normal distribution, we approximately compute the policy parameters and expected profit for the two-order problem. In comparison to the fast-part only strategy and one-order slow part strategy, the second order of the slow part could be of great value if the demand correlation across time is high and/or the cost difference between the two parts is large. We also study the joint impact of fixed cost and leadtime as well as demand variation on the sourcing strategies.
In a manufacturer–retailer system with private retail cost information, we find that a set of incentive-compatible contracts consisting of wholesale and buyback prices can coordinate the channel for any retail cost. We then design two wholesale-buyback contracts by imposing a cutoff point on the retail cost. The first contract maximizes the manufacturer’s expected profit while ensuring the channel is coordinated. The second contract assumes the same contractual structure without considering the effect on the channel. Both contracts are exactly solved. We find from numerical study that the manufacturer in the first contract can perform closely to the second one in many cases, and cases exist where both the manufacturer and the channel can do better in the first contract versus the second one.
In this paper, we propose an iterative approach to jointly solve the problems of tactical safety stock placement and tactical production planning. These problems have traditionally been solved in isolation, even though both problems operate in the same decision making space and the outputs of one naturally serve as the inputs to the other. For simple supply chain network structures, two stages and one or many products, we provide sufficient conditions to guarantee the iteration algorithm’s termination. Through examples, we show how the algorithm works and prove its applicability on a realistic industrial-scale problem.
Humair, S. and S. P. Willems, “Technical Note: Optimizing Strategic Safety Stock Placement in General Acyclic Networks,” Operations Research, May/June 2011, Vol. 59, No. 3, pp. 781-787. Online supplement
We present two significant enhancements to the guaranteed-service (GS) model for multi-echelon safety stock placement. First, we let each stage’s expected inventory cost be a generalized non-concave non-closed form function of its incoming and outgoing service time. This allows the GS model to incorporate important phenomena such as variable stage times and non-nested review periods, which previous GS literature has not allowed. Second, we optimize the generalized cost GS model for directed acyclic networks, rather than assembly/distribution networks or trees. For the resulting NP-hard optimization problem, we present a provably optimal algorithm that runs within minutes for 29 chains from a data-set of 38 real-world supply chains ranging from 8 to 2025 stages. We also present two significantly faster yet near-optimal heuristics. One heuristic is motivated by the structure of the formulation’s dual space, while the other heuristic simply terminates the optimization algorithm after a fixed number of iterations. As a performance benchmark, on the 38 chains the first heuristic has an average optimality gap of approximately 1.1% and average run-time of 88 seconds, while the second heuristic has an average optimality gap of 2.8% and an average run-time of 5.9 seconds.
Over the past ten years, Procter & Gamble has leveraged its cross-functional organization structure with operations research to reduce inventory investment significantly. Savings were achieved in a two-step process. First, spreadsheet-based inventory models locally optimized each stage in the supply chain. Since these were the first inventory tools installed, they achieved significant savings and established P&G’s scientific inventory practices. Second, P&G’s more- complex supply chains implemented multi-echelon inventory optimization software to minimize inventory cost across the end-to-end supply chain. In 2009, a tightly coordinated planner-led effort, supported by these tools, drove $1.5 Billion in cash savings.
While case studies reveal the mathematics employed, of equal importance is the presentation of the planning process that facilitates inventory management and the decision tree that matches a business to the optimal inventory tool depending on the business’ requirements. Today, more than 90% of P&G’s business units (about $70 billion in revenues) utilize either single-stage (70%) or multi-echelon (30%) inventory management tools. Plans are underway to grow the use of multi-echelon tools to 65% in the next three years.
In 2007, Intel’s Channel Supply Demand Operations (CSDO) launched an initiative to improve its supply chain performance. In order to ensure success, the process had to fit within CSDO’s existing planning processes. In practice, this meant that the setting of service level targets and inventory targets needed to become part of the structured decision making process, since previously they were both external inputs to the process. While Intel previously achieved success implementing a multi-echelon inventory optimization (MEIO) model, the boxed processor environment posed some unique challenges. The primary technical challenge involved in this initiative required correcting for the impact of the forecast bias, non-normal forecast errors, and heterogeneous forecast error. This paper documents the procedure and algorithms developed by Intel to counter the impact of forecast imperfections. This process has been in place since early 2008 and at any given time is applied to CSDO’s 20-30 highest volume boxed processors determining an inventory commitment of roughly 2 million CPUs.
Many companies experience nonstationary demand due to product lifecycle effects, 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 originally designed for stationary demand. We describe two successful applications of this model. The first is a strategic project to evaluate the benefits of an inventory pool at CNH. The second is a tactical implementation to support monthly safety stock planning at Microsoft.
Inventory target setting within Intel’s embedded devices group historically consisted of management-determined inventory targets that were uniformly applied across product families. Achieving and maintaining these inventory targets at the individual product level proved to be a difficult task. To better align inventory resources and improve customer service levels, Intel employed a multi-echelon inventory optimization (MEIO) model to set inventory targets. However, the company could not implement the model’s initial recommendations because of the presence of bias in the sales forecast data. Managing the forecast bias by directly modifying the raw sales forecast data was not an option because Sales and Marketing controlled and loaded the data into the manufacturing resource planning (MRP) system before the planning organization received it. Therefore, the average forecast demand, with its bias present, was already in the system; the only adjustment that the planning organization could make was to change the inventory target. This paper describes the inventory optimization problem in Intel’s embedded devices group and the adjustment procedure that we developed to produce appropriate inventory targets in the presence of forecast bias.
Graves, S. C. and S. P. Willems, “Strategic Inventory Placement in Supply Chains: Nonstationary Demand,” Manufacturing & Service Operations Management, Spring 2008, Vol. 10, No. 2, pp. 278-287. online supplement
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 six to twelve-month life cycles being common. Given these short product life-cycles, product demand is increasingly difficult to forecast. Furthermore, demand is never really stationary as 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 non-stationary 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 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 non-stationary for a constant-service-time policy. We then examine with an illustrative example how well the constant-service-time policy performs relative to a dynamic policy that dynamically modifies the service times. In the on-line appendix we report on numerical tests that demonstrate the efficacy of the proposed solution and how it would be deployed.
Willems, S. P., “Data Set: Real-World Multi-Echelon Supply Chains Used for Inventory Optimization,” Manufacturing & Service Operations Management, Winter 2008, Vol. 10, No. 1, pp. 19-23. Online appendix Data in Excel format Data in Microsoft Access format Data in Microsoft Excel format
This data set describes 38 multi-echelon 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, it is possible that they could be useful in an empirical study. The data described in this paper are publicly available at the journal’s web site http://msom.pubs.informs.org/ecompanion.html.
We extend the guaranteed service, supply chain modeling framework to allow for an arbitrary, integer review period or ordering frequency at each stage. We define a notation for the cyclic inventory dynamics that review periods introduce and generalize inventory-balance equations to accommodate three different periodic-review operating policies—constant base stock, constant safety stock, and adaptive base stock. As a form of validation, we apply the model to the Celanese acetic acid supply chain and show that inventory metrics of the new model differ by more than 30 percent from those derived through the simpler modeling approach of aggregating a review period into lead time.
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).
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.
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 HP’s Digital Imaging division has received sponsorship from HP’s 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 HP’s Digital Camera and Inkjet Supplies businesses. The realized savings from these first two projects exceeds $130 million.
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.