Inventory Optimization at Procter & Gamble - CiteSeerX

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informs ®

doi 10.1287/inte.1100.0546©2011 INFORMS

THE FRANZ EDELMAN AWARDAchievement in Operations Research

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

Inventory ToolsIngrid Farasyn

Procter & Gamble Services Company NV, 1853 Strombeek-Bever, Belgium, [email protected]

Salal HumairHarvard School of Public Health, Boston, Massachusetts 02115, [email protected]

Joel I. KahnPS Analytics, The Procter & Gamble Company, Cincinnati, Ohio 45202, [email protected]

John J. NealeBoston University, Boston, Massachusetts 02215, [email protected]

Oscar RosenThe Procter & Gamble Company, Cincinnati, Ohio 45202, [email protected]

John RuarkLogility, Inc., Burlington, Massachusetts 01803, [email protected]

William TarltonThe Procter & Gamble Company, Hunt Valley, Maryland 21030, [email protected]

Wim Van de VeldeProcter & Gamble Services Company NV, 1853 Strombeek-Bever, Belgium, [email protected]

Glenn WegrynThe Procter & Gamble Company, Cincinnati, Ohio 45202, [email protected]

Sean P. WillemsBoston University, Boston, Massachusetts 02215, [email protected]

Over the past 10 years, Procter & Gamble has leveraged its cross-functional organizational structure withoperations 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 thefirst inventory tools installed, they achieved significant savings and established P&G’s scientific inventory prac-tices. Second, P&G’s more complex supply chains implemented multiechelon inventory optimization softwareto minimize inventory costs across the end-to-end supply chain. In 2009, a tightly coordinated planner-ledeffort, supported by these tools, drove $1.5 billion in cash savings. Although case studies show the mathematicsemployed, of equal importance is the presentation of the planning process that facilitates inventory managementand the decision tree that matches a business to the optimal inventory tool depending on the requirements of thebusiness. Today, more than 90 percent of P&G’s business units (about $70 billion in revenues) use either single-stage (70 percent) or multiechelon (30 percent) inventory management tools. Plans are underway to increase theuse of multiechelon tools to manage 65 percent of P&G’s supply chains in the next three years.

Key words : industries: consumer packaged goods; inventory/production: applications, multi-item/echelon/stage; dynamic programming: applications.

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Farasyn et al.: Inventory Optimization at P&GInterfaces 41(1), pp. 66–78, © 2011 INFORMS 67

Procter & Gamble (P&G), founded in 1837, is aleading global consumer products company with

$76.7 billion in sales in 180 countries. Four billiontimes a day, P&G touches the lives of people aroundthe world through its familiar brand names—Tide,Crest, Gillette, Pantene, and more than 200 others.It competes in 26 distinct product-category marketssuch as hair care, paper towels, cosmetics, skin care,oral care, blades and razors, diapers, and fabric care.Inventory management in a company of P&G’s

size, scale, and complexity requires leveraging theright people, organization, and tools. By marrying theappropriate operations research (OR) techniques witha unique planning-organization structure, P&G hasachieved two step-change improvements in inventorylevels. The first improvement came from the broadapplication of spreadsheet-based inventory models;this work produced four tools that locally optimizedifferent portions of the supply chain. The secondimprovement integrated multiechelon inventory soft-ware in P&G’s more-complex supply chains. In 2009,these tools, implemented through a well-coordinatedplanning community, were instrumental in driving$1.5 billion in cash savings, while maintaining orincreasing service levels.This paper details how P&G implemented advanced

inventory optimization technology in more than90 percent of its businesses to reduce its inven-tory investment significantly over the past 10 years.Although case studies show the mathematics emp-loyed, of equal importance is the presentation of theplanning process that facilitates inventory manage-ment and the decision tree that matches a businessto the optimal inventory tool depending on businessrequirements.

How P&G Manages InventoryThe goal of P&G’s logistics planning effort is todelight our consumers and shoppers with world-classproducts that are designed and packaged to suit theirneeds, available wherever they shop, and priced torepresent the best value for them.P&G’s logistics planning workforce consists of

over 5,000 individuals who plan material supply,capacity, inventory, and logistics for the company’s500 supply chains. The total supply chain network

comprises 145 P&G-owned manufacturing facilitiesand 300 contract manufacturers, resulting in over6,900 unique product-category market combinationsserved. Each supply chain requires well-coordinatedefforts based on best-available information, commu-nication, and planning tools. Production batch sizes,planning reaction times, order policies, replenishmenttiming, physical facility restrictions, customer orderpatterns, modes of transportation, new-product intro-ductions, promotions on existing brands, assortmentmanagement, and regulatory requirements combineto present complex challenges and trade-offs.Each of P&G’s three global business units (GBUs),

Beauty & Grooming ($26.3 billion), Household Care($37.3 billion), and Health & Well-Being ($14.4 bil-lion), would be large enough to be placed on the 2009Fortune 200 list. As such, each has an internal sup-port and line organization responsible for planningthat takes into account the unique constraints of thebusiness.To drive scale and efficiency through P&G’s sup-

ply network operations, horizontal process networks(HPNs) (see Figure 1) span across all of P&G. HPNsdefine, manage, and execute standard work processesacross P&G’s business operating units.For example, the category supply planning HPN

is responsible for developing plans that optimize thesupply network’s capability to deliver products asrequired by the customer at lowest delivered cost.This involves balancing numerous constraints againstobjectives that can conflict (e.g., defining capacityrequirements to ensure that targeted utilization ratesare met, while ensuring that sufficient inventories aremaintained in the right quantities and at the rightplace). Planners also must ensure that manufactur-ing resources are planned in a manner that supportsstrategic objectives and delivers against customerrequirements.HPN members include GBU representatives, infor-

mation technology (IT) service managers, and globalbusiness and technical experts such as the supplychain OR group. The teams are responsible for deter-mining the scope of a globally standard solution setconsisting of work processes and tools. The teams alsogovern the use of the solutions—maintaining stan-dards and determining innovation requirements for

Farasyn et al.: Inventory Optimization at P&G68 Interfaces 41(1), pp. 66–78, © 2011 INFORMS

Beauty &Grooming

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Fabric careHome careBaby care

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Figure 1: P&G’s 11 HPNs enable cross-business unit best practices and scalability for P&G.

improving the current solution and supporting thecompany’s growth plans.These global networks provide the backbone to

drive scalability and efficiency for the company andare a primary reason why P&G is ranked as oneof the best-managed supply chains in the world.It has won numerous best-practice awards, includ-ing multiple consecutive top-five placements in AMRResearch’s list. Through the HPNs, planners are con-tinually trained to use planning tools and systemsto help meet business objectives regarding cost, cash,and service management.For a company with P&G’s product depth and

breadth, a one-size-fits-all inventory strategy is notoptimal. Capacity utilization of high-speed papermak-ing operations, in which capital and logistics costsdemand high utilization and turnover for profitabil-ity, differs dramatically from hair-care batch-makingoperations in which many stock-keeping units (SKUs)are made and distributed through a multiple-tier dis-tribution network. Different businesses require differ-ent modeling methods and tools to determine the

correct inventory levels. In recognition of this needfor different inventory models, P&G has deployed aframework (see Figure 2) that assigns the appropri-ate inventory technology to any business based on itsoperating characteristics and complexity. In the nextparagraph, we describe the framework and its appli-cable terms.The primary selection criterion is network com-

plexity—whether or not the planner is setting inven-tory targets at several echelons in the supply chain.As we will show, the majority of supply chains inthe Beauty & Grooming GBU are in this category.These supply chains span multiple echelons and ben-efit tremendously from multiechelon inventory opti-mization. Depending on the workflow defined bythe planner, the technology employed is a third-party software solution from Logility, Inc.—eitherVoyager Inventory Strategy Optimization (VISO) orVoyager Inventory Target Optimization (VITO). Alter-natively, many of the supply chains in the House-hold Care GBU are planned at a single echelon.A single-stage inventory tool has been customized


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Figure 2: P&G’s OR group has developed a decision tree for its businesses to follow to match the correct inventorytool to the appropriate business conditions. Complex networks, defined by multiple echelons or many SKUs,employ multiechelon inventory optimization models, whereas single-stage settings employ customized single-stage inventory management solutions tailored to the operating environment.

to each echelon’s most important focus—materials(MIM), finished goods held at a P&G plant location(FIM), or at a distribution point with several remotestocking locations (XIM). Custom variations of themodel have been developed for retail customer needs(RIM) and to better predict prebuild inventory levelsfor new products. To demonstrate the breadth of thesetools, we focus on two implementations that corre-spond to the nodes in Figure 2: single-stage inventorymodels in Western Europe and multiechelon modelsin North America.

Single-Stage Inventory ModelsP&G has a long history of applying inventory man-agement techniques. Its use of scientific inventoryplanning dates to the 1970s (Murphy 1975); how-ever, the adoption of distribution requirements plan-ning (DRP) systems in the late 1980s triggered P&G’sdevelopment of simple but robust models for set-ting inventory targets across a distribution network,one echelon at a time. P&G has successfully adoptedsingle-stage inventory models in over 60 percent ofits supply chains. Coverage by region varies from

about 50 percent in the Americas to over 80 per-cent in Europe, the Middle East, and Africa (EMEA)and Asia.The single-stage models were developed by P&G’s

internal OR group and implemented as end-userspreadsheets for use by planners. We refer to Farasynet al. (2008) for a deeper discussion of our single-stageinventory models, including a review of the designchoices, benefits, and weaknesses of spreadsheets asthe technology platform for this type of application.

Business BenefitsStatistical inventory models avoid supply chain plan-ner bias toward excessively high levels of safetystock. Indeed, safety stock at too low a level wouldquickly result in customer service incidents; the plan-ner would fix this issue by choosing higher safetystock targets. However, when a planner manually setsa high safety stock target, no automatic correctionmechanism is available to adjust the safety stock lev-els downward.Across all regions and business units, we see a dra-

matic inventory reduction the first time the modelsare used for a specific supply chain (see Figure 3). For


Global Total inventorybusiness unit Region Model scope Inventory model reduction (%)

Beauty & Grooming North America Skin-care plants FIM −50Household Care Western Europe Amiens, France plant to XIM −12

Germany warehouseHousehold Care Western Europe Mechelen, Belgium plant to XIM −30

UK warehouseMultiple Central and Eastern Europe Regional plants and FIM/XIM −10

warehousesHousehold Care Central and Eastern Europe Moscow central XIM −10

warehouseHousehold Care Asia Pan-Asia Pringles FIM −12Household Care Asia China Pringles FIM −10

Figure 3: Examples illustrate applying single-stage inventory models to various businesses at P&G.

example, the initial implementation of the extendedsingle-stage model, XIM, on the Lenor fabric softenerinventory produced at the plant in Amiens, France,yielded a realized inventory reduction of 12 percent.Figure 3 provides additional examples of the model’sapplication. Although not exhaustive, it provides evi-dence of the model’s robustness across a number ofdifferent business categories and regions.In addition to the quantifiable results, there are

intangible benefits. The single-stage models have cre-ated a common language for inventory discussionsin the supply chain function. Planners have becomemore aware of the role and influence of the variousinventory building blocks (e.g., safety, cycle, transitstocks). Inventory concepts are now an important partof the supply chain function’s curriculum, helpingplanners to manage the complex trade-offs betweencapacity, inventory, and service.

Case Study: Fabric & Home Care, Western EuropeDespite growing business complexity, our single-stage models have enabled the Fabric & Home Care(F&HC) business in Western Europe to reduce itsinventory and maintain high customer-service levels.This business unit comprises approximately 20 manu-facturing and customization centers. Fabric care prod-ucts include laundry granules, liquids and tablets,liquid tablets, bleach, and fabric enhancers. HomeCare includes automatic and manual dish care, sur-face cleaners, and air care products.Figure 4 tracks inventory and customer service

measures over the 10-year period from fiscal year

(FY) 1999–2000 through FY2009–2010. Inventory isnormalized on a 100-unit scale, and service is mea-sured as case fill rate. Implementing the initial single-stage model (FIM) in the F&HC Western Europebusinesses resulted in a 29 percent inventory decreasein the first five years. In subsequent years, in whichthe next-generation, eXtended Inventory Model (XIM)was introduced, an additional 10 percent inventoryreduction was realized.Following the initial dramatic improvement as

a result of introducing the single-stage tool inFY1999–2000, service has remained stable and theF&HC business in Western Europe has achieved its99.5 percent case fill-rate objective.F&HC Western Europe realized this improve-

ment in spite of growing complexity. Over the past

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Figure 4: By implementing single-stage inventory models in F&HCWestern Europe, total inventory decreased 36 percent; service roseabove 98.5 percent.


10 years, it has had to deal with significant prod-uct proliferation—partly because of acquisitions andpartly driven by new-product introductions and inno-vations. Although its number of finished goods hasdoubled (i.e., from under 2,500 to over 5,000) duringthese 10 years, inventory levels have held steady.

Multiechelon Inventory Optimizationin P&G’s Beauty & Grooming GBUOf P&G’s three GBUs, Beauty & Grooming’s prod-ucts have the most complex supply chains. Severalfactors drive this complexity, all of which increase thebenefits derived from multiechelon inventory opti-mization. In comparison to the other GBUs, it hasmore finished goods SKUs, both for everyday itemsand promotional items. It also commonly customizespackaging to match a customer’s unique require-ments. In general, customized packaging has a lowerunit volume per item, a higher sales price per item,and more echelons in the supply chain. Raw materi-als are often turned into intermediate products usinga batch manufacturing process; these products thenbecome many different finished goods, which thenreceive specialized packaging and pass through mul-tiple tiers of distribution, depending on the region ofthe world. Figure 5 shows an example of a Beauty &Grooming supply chain modeled in Logility’s VISOsoftware.To properly set inventory targets across the supply

chain, the supply chain must be modeled at the levelof complexity consistent with the production plan-ning system. Therefore, it is modeled as a network inwhich a stage represents a specific SKU at a locationand arcs denote precedence between the stages; thiscorresponds to SAP’s classification for raw materials(ROH), semifinished products (HALB), and finishedproducts (FERT). The mapping must be one-to-one toimplement the optimization results.From a mathematical perspective, the need for mul-

tiechelon inventory optimization is driven by reviewperiods, demand pooling, cost accrual, and net-work complexity. Although production runs each day,many SKUs are reviewed and replenished weeklyor monthly, thus introducing important dependenciesbetween stages. The demand at upstream stages is acomplex function of downstream demand, and prop-erly defining how adjacent stages transmit demand

information is necessary. Bossert and Willems (2007)discuss the complexity of review periods.The costs and demand uncertainties differ signif-

icantly at various echelons of the supply chain. Ona relative basis, packaged finished goods are sig-nificantly more expensive than semifinished goods,which are more expensive than raw materials. Fur-ther, because demand is aggregated at fewer locationsas it is passed up the supply chain, its relative uncer-tainty decreases. Combined, these present a tremen-dous postponement opportunity.The supply chain in Figure 5 is a relatively sim-

ple representation; an average network modeled byBeauty & Grooming has 4,000 to 5,000 stages and6,000 to 10,000 arcs. Models of this size involveapproximately 500 finished goods across the supplychain. Although the supply chain in Figure 5 is sig-nificantly more modest in size, it presents a complexacyclic network. The use of common components thatrange from bottles to chemicals to cardboard, andmultiple sources of supply to downstream stages, cre-ate a network without any predictable structure. Fig-ure 6(a), which reduces the network from 45 nodesand 52 arcs to 26 nodes and 33 arcs, simplifies Fig-ure 5 to show its network complexity.Prior to the research we present in the appendix

and document in Humair and Willems (2011), thesupply chain in Figure 6(a) could not be solved tooptimality. Existing exact solution techniques, suchas Humair and Willems (2006), require partitioningthe network into disjoint bipartite subgraphs; Fig-ure 6(b) shows that this is not possible. Other tech-niques that rely on linear programming (LP) relax-ations require concave stage costs. Because plannersrequire the problem to be solved exactly, these kindsof relaxations were not acceptable to the planningcommunity. In effect, the planners were already usingsingle-echelon tools; they would only adopt new toolsthat were demonstrably superior.To demonstrate the value of multiechelon inventory

optimization at P&G, we present the implementationprocess that began with the North America Cosmeticsunit and now spans the entire Beauty business unit,which consists of cosmetics, deodorants, hair care,personal cleansing, prestige fragrances, and skin-careproducts.


Figure 5: Real-world supply chains at P&G Beauty & Grooming span multiple echelons and have significantcomponent commonality as modeled in this view from Logility’s VISO software. Note: The text associated witheach stage is intentionally blurred to protect confidential information.

Leveraging North America Cosmetics’ SuccessAcross the Beauty & Grooming GBUThe Cosmetics supply chain in North America posesa significant challenge to inventory optimizationbecause it supplies the market with over 1,300 stan-dard SKUs and 400–500 promotional SKUs per year.

The supply chain uses over 4,000 unique materialsfrom more than 100 vendors. Despite this complexity,Beauty & Grooming was able to leverage its inter-nal supply chain mastery, coupled with single-stageinventory tools, to reduce its cosmetics inventory byhalf from 1999 to 2004. Improved capabilities and


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Figure 6: Figure 6(a) simplifies Figure 5 to its underlying acyclic network. Figure 6(b) further reduces 6(a) byrepresenting its largest cluster as a single cluster node, C1.

responsiveness in manufacturing and distribution,real-time information and planning systems, andend-to-end integration from suppliers to retailers allcontributed to this success. However, continuing toreduce the leaner inventory became increasingly dif-ficult. Although results reached a plateau in 2005, thebusiness need to continue to free up cash and reducethe risk of obsolescence did not subside. Supply chainleaders decided to replace the single-stage inventoryoptimization toolset with multiechelon optimizationtechnology.Figure 7 is a simplified Logility VISO multiech-

elon model of one product family (liquid makeup)within the total North America cosmetics supplychain. The chain consists of eight unique raw materi-als (plus another 50 shared with other products thatare not shown), 10 blank uncolored work-in-process(WIP) materials, 24 colored WIP materials, 150 pack-

aging materials, 18 intermediate subassemblies (i.e.,partially assembled finished goods), and 75 finishedgoods that move from finished packaging to US andCanada distribution centers, and ultimately to retailcustomers. Intermediate subassemblies also must sat-isfy demand for promotional items.The model incorporates existing service policies

(e.g., service level target of 99.5 percent case fill rate),material lead times (generally ranging from 7 daysto 8 weeks), production times (1 to 2 days), reviewperiods (7 to 28 days), transportation and movementtimes (1 to 7 days), quality assurance durations (1 to5 days), and costs added at each location. Demandcharacterization (mean and standard deviation) foreach finished-goods SKU was based on the previous13 weeks of actual shipments and forecast, and thefuture 13 weeks of forecast.


Raw materials

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Intermediatesubassemblies

PromotiondemandFinished good

packing Ship to US DC

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customerdemand

Figure 7: In this screenshot of the multiechelon inventory model for liquid makeup, all 75 finished goods aremodeled in a network that has 500 stages and 700 arcs. A stage represents an SKU at a location; an arc capturesthe bill-of-materials goes-into relationship between SKU locations.

Applying Logility’s multiechelon optimization algo-rithms to the cosmetics liquid-makeup portion ofthe supply chain yielded a change in level andplacement of inventory safety stocks, while ensuring

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Figure 8: Multiechelon inventory optimization shifted safety stock to thework-in-process echelon, reducing inventory at downstream finishedgoods locations in the United States and Canada. Raw materials inventorywas also reduced.

that the target 99.5 percent service level was protected.Figure 8 provides an overview of the change insafety-stock days on hand across the four majorsafety-stock inventory echelons—materials, WIP, fin-ished goods in the US distribution center, and finishedgoods in the Canada distribution center. Safety-stockdays decreased in materials and finished goods, andincreased in WIP.Most importantly, Figure 9 provides the safety

stocks in dollars. The total investment in safety stockfor this supply chain was reduced by 17 percentbecause the dollar reduction in finished goods andmaterials far outweighed the dollar increase in workin process.Application of the multiechelon technology to the

entire North America cosmetics supply chain yieldedeven better results, with the total inventory reductionreaching 7 percent. During the implementation, thecosmetics supply chain team also identified a poten-tial four percentage points of incremental reduction bydoing “what-if” analyses of current operating policies.


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Figure 9: Multiechelon inventory optimization reduced safety stock cost bymore than 17 percent, equating to a 5 percent reduction in total inventorycost.

Implementation of the multiechelon model in NorthAmerica Cosmetics provided 7 percentage points ofthe 9 percent inventory investment reduction thatwas achieved from FY 2005–2006 to 2006–2007 (seeFigure 10), while maintaining its customer servicelevels above target; that is, multiechelon inventorytechnology was credited with 77.8 percent of theinventory savings at North America Cosmetics. Inaddition, the technology has been a key enabler ofsubsequent annual reductions of 2–3 percent since theinitial implementation. The most significant changewas reducing some review periods in finished-goodsinventory. The planners could understand the impact

NA cosmetics care supply chain results

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Figure 10: Total inventory in North America Cosmetics decreased9 percent during the multiechelon implementation process. Multiecheloninventory optimization was credited with 78 percent of this reduction. Withthe technology established as a backbone of the inventory planning pro-cess, sustained reductions of 2–3 percent have been achieved.

of these changes because the supply chain echelonswere linked.It is worth noting that these financial savings were

achieved on top of an already strong base of inventoryreductions that had been achieved by implementingthe single-stage inventory models. These savings wereat a site that was a sophisticated consumer of single-stage inventory models—not at a site new to inven-tory optimization.As the Logility technology was rolled out beyond

P&G Cosmetics to the other Beauty & Grooming sup-ply chains worldwide, a standard multiechelon workprocess using the P&G standard SAP platform (Fig-ure 11) was developed. The process ensures consis-tent data visibility and accuracy. Data are extractedfrom the SAP system modules, passed through aninternally developed database for formatting andmanipulation, and then passed into the Logilitymultiechelon software, which automatically mapsand ultimately optimizes the model. As part of amonthly workflow, planners review the resulting rec-ommended safety stocks and upload them back intothe appropriate SAP systems.P&G Beauty & Grooming also set up a global

support structure (Figure 12) for its multiechelontechnology to enable maintenance of current imple-mentations, user skill development, expansion to newsupply chains (e.g., acquisitions), expansion of modelscope (e.g., into suppliers), and further exploitationof the technology into more strategic applications(e.g., sensitivity and what-if analysis). Key usersat each business site own the supply chain modeland interface with planners in their supply chainto maintain, apply, and leverage their multiechelonmodel. Regional leaders in Asia, Latin America, NorthAmerica, and Europe, who are part of P&G’s ProductSupply organization, provide training and supportfor the site key users, lead new implementations intheir regions, identify unique regional requirements,and implement work-process enhancements. A globalProduct Supply leader supports the regional lead-ers, identifies global enhancements, maintains work-process standardization across regions, and providesoverall strategic direction. These leaders receive ITsupport from the Supply Network Solutions (SNS)organization, which is within P&G Global Busi-ness Services, to maintain hardware and softwarecapabilities.


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Figure 11: As part of the multiechelon inventory process, P&G implemented a standardized interface between itssupply chain related systems and the Logility software. This allows the automatic creation of inventory modelsand targets for planner approval.

Applying multiechelon technology to the NorthAmerican Cosmetics supply chain, although one ofthe most complex in P&G, is only one of 31 successfulimplementations in P&G’s Beauty & Grooming (seeFigure 13). Multiechelon models are in place in everygeographic region; associated work processes areexecuted as frequently as biweekly. As of February

Global BeautyIT Leader

GlobalPS Leader

RegionalIT Leader

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Site KeyUser

Site-IntegratedPlanners

MarketPlanners

MaterialsPlanners

Figure 12: A global workflow structure has been implemented to support multiechelon decision making acrossBeauty & Grooming.

2010, over 85 percent of all SKUs in Beauty & Groom-ing are being modeled using the multiechelon inven-tory process. Similar to the North America Cosmeticsexample described above, these 30 supply chains areachieving total inventory reductions in the 3–7 per-cent range and are maintaining service levels at orabove target.+


Average Average Average Key areaNumber of number of number of number of of model

Region models echelons model nodes model arcs complexity

North 10 5 5�000 7�500 SKUs andAmerica materials

Asia 8 8 3�500 10�000 Distributionnetwork

Europe 10 6 4�000 6�000 SKUs andmaterials

Latin 3 6 2�000 6�500 DistributionAmerica network

Figure 13: As of February 2010, 31 multiechelon inventory models are inproduction in Beauty Care; 85 percent of Beauty & Grooming’s SKUs aremodeled in the multiechelon inventory process.

ConclusionBy marrying the tools of inventory optimization withthe people in P&G’s horizontal planning networks,P&G has defined an inventory management pro-cess that has significantly reduced its total inventoryinvestment. The work began with single-stage inven-tory models designed by P&G’s OR group and imple-mented in spreadsheets that planners can use directly.To this day, these spreadsheet tools drive 60 percent ofP&G’s business. For more complex supply chain net-works, multiechelon inventory models have replacedthe single-stage models, producing additional averageinventory reductions of 7 percent. These multiechelonmodels now drive 30 percent of P&G’s business.P&G’s work on inventory optimization is not stand-

ing idle. We assume that another 40 percent ofthe single-stage models will migrate to multiechelonmodels in the next three years. Beauty Care has alsospearheaded a closed loop of inventory optimizationin which tactical inventory models are used to gen-erate more rigorous strategic analysis that can thenfeed the next-generation design of the supply chain.Furthermore, P&G continues to work in related areas,such as improving the forecast through point-of-sale-based demand sensing.

Appendix. Multiechelon ModelingFrameworkThe guaranteed service (GS) model of inventory place-ment forms the underpinnings of the multiecheloninventory optimization (MEIO) tool. Graves andWillems (2003) summarize the specifics of the GSframework and compare it to other MEIO approaches.

Guaranteed Service Model FormulationIn the GS framework, the supply chain is defined asa network with node set N and arc set A. Each nodecorresponds to a stage in the supply chain. A stageis a processing activity for a given SKU and locationin the supply chain, such as manufacturing an item,transporting an item from one location to another,or packaging an item. Arcs denote the precedencerelationship between stages. To put this in a systemcontext, if one is using a system (e.g., SAP), stagescorrespond to raw materials (ROHs), semifinishedproducts (HALBs), and finished products (FERTs).The arcs correspond to the bill-of-materials (BOM)routes that convert ROHs to FERTs.In its simplest form, the GS model requires very lit-

tle data. Tj is the lead time at stage j ; this is the timerequired to complete the processing requirements ofstage j , assuming that all its raw materials are avail-able. sj is the maximum outgoing service time atstage j ; this is the longest time that stage j can taketo fulfill demand after it receives an order. There aretwo decision variables at each stage: incoming servicetime and outgoing service time. The outgoing servicetime, Sj , is the delivery time stage j quotes its adjacentdownstream stages. The incoming service time, SIj ,is the longest outgoing service time from upstreamadjacent stages quoted to stage j .Each stage has a cost function, cj SIj� Sj �, which is a

function of its incoming and outgoing service times.The cost function represents the cost of holding inven-tory at the stage in all its various forms.The GS model can be formulated as the following

mathematical program P:

P min�N �∑

j=1cj SIj� Sj �

s.t. Sj − SIj ≤ Tj ∀ j ∈N

SIj − Si ≥ 0 ∀ i� j� ∈A

Sj ≤ sj ∀ j �k ∈N � j� k� ∈A

Sj� SIj ≥ 0� integral ∀ j ∈N�

The objective function minimizes the total stagecost. The first constraint imposes a rational operatingconstraint on a stage’s outgoing service time: a stage’soutgoing service time cannot exceed the longest ser-vice time quoted to the stage plus its own lead time.


00

20

40

60

80

100

120

140

5 10 15 20

Net replenishment lead time (days)

Exp

ecte

din

vent

ory

leve

l(u

nits

)

25 30 35

Stage B Stage A Stage C

Figure A.1: Generalized stage cost functions occur in the presence ofadvanced supply chain dynamics (e.g., review periods).

The second constraint defines the incoming servicetime at a stage to be at least as large as the longest out-going service time quoted to the stage. The third con-straint enforces an upper bound on a demand stage’soutgoing service time; the final constraints require ser-vice times to be nonnegative and integer.More complex forms of the GS model capture

advanced supply chain dynamics, such as nonnestedreview periods (Bossert and Willems 2007) or non-stationary demand (Neale and Willems 2009). Theseadvanced dynamics require more data to fully specifythe model; however, the general structure is similarin form to P.

Novelty of Solution ApproachIf the model incorporates dynamics such as reviewperiods or batching, the stage cost function is neitherconcave nor monotone. Figure A.1 illustrates whystandard GS optimization approaches cannot be usedfor generalized cost functions, because they assumeeither an extreme-point property of the optimal solu-tion or piecewise linearity of the cost function.This figure also demonstrates why standard noncon-vex optimization approaches fail—because of theirassumptions about the structure of the objective func-tion (e.g., submodularity or quasi concavity). Searchalgorithms also typically either require an objectivefunction structure (e.g., conjugate gradient methods)or use an unstructured strategy (e.g., genetic algo-rithms) and are usually less efficient.

Therefore, we based our approach to constructingan algorithm on two simple observations: first, thatthe spanning tree algorithm from Graves and Willems(2000) could handle these complicated cost structureselegantly with a minor reformulation; second, that thesolution to a well-chosen spanning tree relaxation ofa general network was very often (when we observedit qualitatively) close to the true optimal solution. Theproblem was how to move from the relaxed solutionto the network-optimal solution.The answer was not obvious, because the span-

ning tree algorithm cannot be used to get an optimalsolution by bounding a single variable, as Humairand Willems (2011) discuss. By observing the exis-tence of another relationship between the inboundservice times and network partitioning, we were ableto construct an algorithm that could move efficientlyfrom the relaxed solutions to the network-optimalsolutions. The efficiency of the resulting algorithmwas surprising, and its attractive property was itsprovable optimality. Humair and Willems (2011) pro-vide details.

ReferencesBossert, J. M., S. P. Willems. 2007. A periodic-review modeling

approach for guaranteed service supply chains. Interfaces 37(5)420–435.

Farasyn, I., K. Perkoz, W. Van de Velde. 2008. Spreadsheet modelsfor inventory target setting at Procter & Gamble. Interfaces 38(4)241–250.

Graves, S. C., S. P. Willems. 2000. Optimizing strategic safety stockplacement in supply chains. Manufacturing Service Oper. Man-agement 2(1) 68–83.

Graves, S. C., S. P. Willems. 2003. Supply chain design: Safety stockplacement and supply chain configuration. A. G. de Kok, S. C.Graves, eds. Supply Chain Management: Design, Coordination andOperation. Handbooks in Operations Research and Management Sci-ence, Vol. 11. North-Holland Publishing Company, Amsterdam,95–132.

Humair, S., S. P. Willems. 2006. Optimizing strategic safety stockplacement in supply chains with clusters of commonality. Oper.Res. 54(4) 725–742.

Humair, S., S. P. Willems. 2011. Optimizing strategic safety stockplacement in general acyclic networks. Oper. Res. Forthcoming.

Murphy, R. A. 1975. Inventory control with gamma demand andgamma lead times. Internat. J. Systems Sci. 6(1) 81–85.

Neale, J. J., S. P. Willems. 2009. Managing inventory in supplychains with nonstationary demand. Interfaces 39(5) 388–399.

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