interfaces kellogg

7/29/2019 Interfaces Kellogg

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The Kellogg Company Optimizes Production,Inventory, and DistributionGERALD BROWN Operat ions Research Departmentgbrown @ nps.navy.mi l Nava l Postgraduate School

M onterey, Cal i fornia 93943JOSEPH KEEGAN Kel logg Company, P .O. B ox 3599joe.keegan@kel logg.com Bat t le Creek , Michigan 49017-3599BRIAN VIGUS Kel logg Company, P .O. Box 3423brian.vigus@kel logg.com Bat t le Creek , Michigan 49016-3423KEVIN WOOD Operat ions Research Departmentkwood @ nps.navy.mi l Naval Postgraduate School

For over a decade, the Kellogg Co m pan y has used its p lanningsystem (KPS), a large-scale, multiperiod linear program, toguide production and distribution decisions for its cereal andconvenience foods business. An operational version of KPS, ata weekly level of detail , helps determine w here pro duc ts areproduced and how finished products and in-process productsare shipped between plants and distribution centers. A tacticalversion of KPS, at a monthly level of detail, helps to establishplant budgets and make capacity-expansion and consolidationdecisions. Operational KPS reduced production, inventory,and distribution costs by an estimated $4.5 million in 1995.Tactical KPS recently g uid ed a consolidation of production ca-pacity with a projected savings of $35 to $40 million per year.T he Kellogg Co m pan y has been usin g ing, capacity expa nsion, capacity reassign-a large-scale linear progra m, the Kel- men t, and other similar issue s,logg Planning System (KPS), for more KPS m od els Kellogg's operations in th ethan a decad e to gu ide its operational Un ited States and Canad a, with global(wee kly), prod uction, inventory, and dis- operations under study. These operationstribution dec ision s for breakfast cereal and inclu de the prod uction , inven tory , and


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BROWN ET AL.to distribution centers (DCs) and tocustomers.

Many large companies like Kellogg em-ploy some sort of enterprise resource plan-ning system (ERP) to coordinate raw-material purchases, production,distribution, orders, and forecasted de-mand. Kellogg's ERP is largely a custom,in-house product, and KPS is a customtool to complement that system. Modelslike KPS are also attractive w ithin thecommercially available ERPs of SAP, Ora-cle, JD Edwards, and others. Indeed, theseERP systems offer plug-in features forplanning production, distribution, and in-ventory, for example, SAP's AdvancedPlanner and Optimizer [SAP 2001]. How-ever, even these features may be inade-quate [Hsiang 2001]. For instance, theymay use rule-based heuristics to attemptto meet dem and while ignoring capacityconstraints and then iteratively refine thesolution, using heuristics, to attempt tomeet capacity constraints. These heuristicstake costs into account in their rules bu tdo not minimize costs or maximize profits.

In current vernacu lar, KPS is a poin t so-lution because it is tailored to solve prob-lems for particular functional areas of thebusiness. KPS uses o ptimization to findthe best long-term, cost-minimizing, inte-grated production, inventory, and d istri-bution planwithin the limits of model-ing assumptions and data accuracy. ERPsaccount for the low-level influence of indi-vidual near-term transactions; in contrast,KPS is a high-fidelity, prescriptive mo delthat is ideally suited to evaluating alter-nate systemwide scenarios.

ing producer of convenience foods. In1999, worldwide sales totaled nearly $7billion. Kellogg began with a single prod-uct, Kellogg's Corn Elakes, in 1906 and de-veloped a product line of well-known,ready-to-eat cereals over the years, includ-ing Kellogg's All-Bran (1916), CompleteBran R ak es (1923), Rice K rispies (1927),Variety Pak (1938), Raisin Bran (1942), andCorn Pops (1949). Kellogg continues toManagers modify plans thatdon't quite fit the realities ofthe plant floor.develop and market new cereals, but itsrecent thrust has been in conveniencefoods, best exemplified by Kellogg's Pop-Tarts and Nutri-Grain cereal bars. In addi-tion, Kellogg has recently entered thehealth-food business. Kellogg produceshundreds of products that are sold asthousands of stock-keeping units (skus),and acceptable profit margins depend onproducing these products and packagingthese sku s as efficiently as possible.

The Kellogg Comp any had long usedspreadsheets and special software for ma-terials requirements planning (MRP) anddistribution resource planning (DRP). Butby 1987 Kellogg realized that its expand-ing product line and geographically dis-persed production facilities required somemeans of systematic, global coordinationand optimization. KPS was the result. Af-ter a year of development, we installedprototyp ic software in 1989. Altho ugh KPSwas intended primarily for operational


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KELLOGGadding a new production facility to ex-pand capacity and extend the product line,and it used KPS to compare the overallcost implications of locating that facility inone existing plant versus another.We installed KPS in 1990 and deve lopedit further over several years. Initially, weused only systemwide average costs foreach plant, basing optimal solutions ondifferentials in transportation costs and onavailable prod uction capacities, ratherthan on differentials in manufacturingcosts at the variou s pro duc tion sites. Thishelped smooth the transition from thethen-current, decentralized production-planning process to a more centralizedprocess guide d by KPS. In particular, us-ing true costs, KPS wo uld have shiftedoverall production patterns dramatically,and actually carrying out this shift wouldhave been impractical. By 1994, how ever,we had introduced true manufacturingcosts into the operational model, and thisproduced savings of $4.5 million in 1995[Scott 1999]. Cu rrently , KPS is in useweekly for operational planning and al-most daily for dealing with tactical issues.Kellogg's Products and Operations

Kellogg operates five plants in theUnited States and Canada: Battle Creek,Michigan; M emphis, Tennessee; Omah a,Nebraska; Lancaster, Pennsylvania; andLond on, On tario. It has seven core DCs insuch areas as Los Angeles and Chicago,and roughly 15 co-packers that contract toproduce or pack some of Kellogg's prod-ucts. Customer demands are seen at theDCs and at four of the Kellogg plants. Inthe cereal business alone, the firm coordi-

tributing over 600 skus at abou t 27 loca-tions (plants, co-packers, or DCs) with atotal of roug hly 90 prod uction lines (in-cluding coaters, puffing towe rs, and cook-ers) and 180 packag ing lines. Optimizingthis many decisions is clearly a formidabletask. The production, inventory, and dis-tribution activities behind getting a pack-age of Kellogg's Variety Pak to m arkethelps to illustrate.

Kellogg's Variety P ak, sku 05337, con-tains 10 small boxes of different cereals,for example Corn Flakes, Rice Krispies,and Froot Loops. The individual boxes (in-dividuals) can be produced and packed atKellogg wants to ship freshproducts.Kellogg plants in Battle Creek, Om aha,Lancaster, or Mem phis. But not all plan tsproduce all individuals. All of the individ-uals at one plant compete for packagingcapacity because they are packed in thesame size box. Many of the basic produc-tion decisions are independent; for exam-ple, Mini-W heats and Corn Pops shareneither materials nor production facilities.On the other hand. Frosted Flakes are es-sentially coated Corn Flakes, and produc-tion constraints dictate that not all CornFlakes in a production run can be coated.Thus, the production of these two prod-ucts must be synchronized.

Variety Paks are assembled only in Bat-tle Creek, so Kellogg m ust coordinateprior production, packaging, and shippingfrom the other three plants with the finalassembly operations in Battle Creek. Each


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BROWN ET AL.at its production location or at an assem-bly site, or it may be used to create an as-sembly directly upon production. To mini-mize costs, the company must account fordifferentials in prod uction , packag ing, in-ventory, and shipping costs. After assem-bling and packaging the Variety Paks intocases, the plant then ships them to one ofthe seven DCs.

This example does not illustrate all ofthe complexities of production and distri-bution at Kellogg. KPS m ust also take intoaccount the following:Some skus are produced and packed byco-packers;A given product and package combina-tion may be packed into several differentcase sizes, each yielding a different sku;Bulk prod uct is sometimes produced atone location and shipped to another forpackaging; and Constituents of certain p rodu cts, for ex-ample, Mueslix, can be produced at onelocation and shipped in bulk to another lo-cation where they are processed togetherwith other con stituents to create a singleproduct. This contrasts with an assemblyof distinct pro du cts like the V ariety Pak.Some constituents may come from Kelloggplants and som e from co-packers. (KPScan model any number of levels of theseintermediate produ cts.)The Basic Operational Linear Program

The operational version of KPS makesproduction, packaging, inventory, and dis-tribution decisions at a weekly level of de-tail. The m odel is based on a linear-costversion of the production-planning modelintroduced by Modigliani and Hohn

uses the now-standard production, inven-tory, and d em and recursion:HOLD, = HOLDi^^ + MAKE, - Demand,

for all time periods (weeks) f,where HOLD, is the inventory for a singleproduct at the end of period t (a decisionvariable), MAKE, is the production of theproduct during time period t (a decisionvariable) and Demand, is the exogenousdemand for the product during period t(data) [Dantzig 1959; Zangw ill 1969]. Thisrecursion is embellished in KPS with mu l-tiple stages of production, multiple prod-ucts and sku s, mu ltiple plants and D Cs,shipping lanes between the plants an dDCs, and various capacity constraints.Johnson and Montgomery [1974, Chapters4.6-7] describe similar models. We assumeall data are deterministic; inventory safetystocks (that is, deterministic lower boundson inventories) help prepare for uncertaindemands and unforeseen production prob-lems. KPS does not model raw materials:We determined early in the mode l's devel-opment that the burden of maintainingdata on raw materials would outweighany improvements provided by theirinclusion.

With some variations, we model eachKellogg plant or co-packer as a set of pro-cessing lines that produce products (forexam ple. Corn Flakes, Rice Krispies, andBlueberry Pop-Tarts), which in turn feed aset of packaging lines that pack finishedskus. An sku is defined by product, pack-age size, and case size: For example, sku00122 is a case of 12,18-ounce packages ofCom Hakes. "001" is the product code for


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KELLOGGplaced in inventory or are used to meetdemand assigned to the plant (Kelloggplants can act as their own DCs) or areshipped to another plant or DC. All cus-tomer demand is aggregated by sku andlocation, that is, plant or DC.

For each week of the 30-week planninghorizon, the decision variables associatedwith a plant are the following:MAKEUP,Production of prod ucts on a

processing line and other facilities thatform a production process, for instance,the klbs (pou nds X 10^) of prod uct 015(Frosted Flakes) produced on processingKellogg ru ns KPS eachSunday morning to guideproduction decisions in week2 and beyond.Une LLOl and frosted with sugar on coaterLCOl at the p = Lancaster plant in week .The product 015 and two production fa-cilities LLOl and LCOl form the produc-tion process h. Fvery product requires pro-cessing on one processing line but mayalso consume capacity on other facilities,such as a coater.

PACKjt^p,Packaging of skus on par-ticular pack aging lines, for ex am ple, theklbs of sku k = 00122 packed on packag-ing line m = LP09 at th e p = Lancasterplant in week t.

HOLD^p,Inventories of skus, for ex-ample, the klbs of sku k = 00525 held ininventory at the p = Battle Creek plant atthe end of week t.

SHIP^pp'jShipments of skus to orfrom other plants and DCs, for example,

th e p' = Los Angeles DC. For the m ostpart, we m odel a shipme nt leaving inweek t to arrive in week t -I- 1.

A DC m ay be viewed simply as a Kel-logg plant with no production or packag-ing facilities, and thus a DC incorpo ratesonly inventory an d shipping variables.

KPS currently models Kellogg's ownplants and distribution centers and about15 co-packers. Co-packers are non-Kelloggproduction facilities under contract to pro-duce and package products designed byKellogg an d bearing the Kellogg label orto produce constituents for Kellogg prod-ucts that undergo final processing at Kel-logg plan ts. (Kellogg performs no co-packing for other companies.) A co-packerhas no exogenous demand assigned to it.

W ithin a plant, basic constraints for eachweek require that the system:

(Cl) Does not exceed processing linecapacities;(C2) Does not exceed packaging line

capacities;(C3) Packages all products produced in

a week into skus during that week (theseare flow-balance constraints between pro-cessing and packaging);

(C4) For each sku, balances inventoryfrom the previous week plus current pack-aging plus incoming shipments with out-going shipmen ts, plus consum ption in as-semblies if this is a constituent sku, plusexogenous demand assigned to the plant;

(C5) Satisfies safety stock requirementswith inventory of each sku at each plant;

(C6) Coordinates processing lines andpackaging lines as needed durin g eachtime p eriod. For example, we m ay require


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BROWN ET AL.product from which that sku is derived.

With respect to these constraints, a DCis just a plant without production-relatedconstraints and a co-packer is a just a Kel-logg plant with no exogenous demand.Constraints (Cl), (C2), (C4), and (C5) areimplemented as elastic goals that can beviolated at a price: When an elastic goalconstraint is violated, a linear penalty perunit of violation is assessed. The occur-rence of such an elastic violation may indi-cate that a little overtime is needed, or itmay signal a bottleneck that cannot beavoided. Either way, the model recom-m ends a system wide plan that is opti-mally adjusted to deal with all such pro b-lems over all locations and time periods.

KPS does not model raw materials b utdoes model some intermediate products.An intermed iate product is viewed as aconstituent sku that can be shipped toother plan ts wh ere it is further processedor combined and packed with other con-stituent skus to create a finished, assem-bled sku. The Variety Pak described ear-lier is one instance of a co nstituents-to-assembly recipe. Also, semiprocessed RiceKrispies, called bumped rice, are producedat one plant and shipped in bulk totes (la-beled and modeled as an sku) to a co-packer to be further processed and packedinto Rice Krispies Treats. KPS han dles thepackaging of assembled skus by straight-forward modifications of the How-balanceand packaging-line constraints: The assem-bly and packaging of an assembled skuconsumes only packaging capacity an ddraws constituent skus from inventory orconcomitant packaging.

Product and sku codes, product-to-skurelationships, including recipes for assem-bled skus, and case weights;The identities of the processing andpackaging lines at each plant, the productsor skus that can be processed or packedon those lines, nominal yields in klbs perFor its size, KPS is curiouslydifficult to solve.shift, nominal processing or packagingcost for each product or sku in dollars perklb;Inventory costs for each type of sku ateach plant in dollars per case per week;Shipping costs (dollars per case) by laneandVarious per-unit penalties for unmet de-mand, unmet safety stock, and lineovercapacitation.Data that vary by week are:Production and processing line avail-abilities at each plant measured in shifts;Variations in nominal yields or costs toaccount for time-of-year effects (for exam-ple, it may take longer to dry certain prod-ucts during humid summer months) or ef-fects associated with new lines, products,or skus where yields typically improve forthe first few weeks after commencingproduction;Estimated demands, in cases, for skusat Kellogg plants and DCs based on fore-casts made by the marketing department;andDesired minimum inventory levels(safety stocks) at demand locations.The basic objective of KPS is to m ini-


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KELLOGGeludes pena lty terms for violating process-ing and packaging capacities, for notmeeting demand, and for not meetingsafety stocks.

A fundamental assumption behind a lin-ear program is that each decision variablemay take on any value in a continuousrange, but production and packaging deci-sions at Kellogg (and other manufacturers)are not that flexible. For instance , KPSmight suggest that about one third of ashift of a low-demand sku be produced atsome plant in each week of the planninghorizon, but the plant manager requires aone-shift minimum for that sku because ofsetup overhead (production time lost be-cause of required equipment adjustments).Theoretically, it is possible to add binaryvariables to KPS to han dle such situations,but we have not yet done this because themodel has been hard enough to solve as asimple linear program . (Technology is im-proving, however, and a mixed-integerversion of KPS to handle pro duction andpackaging setups is on the drawingboard.) Therefore, managers review KPS-suggested production plans to modifyplans that don't quite fit the realities of theplant floor.Meeting Uncertain DemandForecastsand Safety Stocks

Much uncertainty is associated with thedata for a long-term production-inventorymodel, and for KPS, the greatest uncer-tainty is in actual demands for skus. In thefirst few weeks of a time horizon, demandnumbers may be fairly accurate becausethey are largely based on firm orders fromcustom ers. But even at week three or four

partment's original forecast. Nonetheless,the overarching goal of Kellogg, and thusKPS, is to meet these customer dem ands.

Perhaps KPS should be a multistagestochastic-programming model that di-rectly handles uncertainty in demand, andpossibly uncertainty in manufacturingyields and line availabilities. But such amodel would require an unwieldy amountof data and would be too difficult to solve:As a deterministic model, KPS is largeand can take several hours to run. Astochastic-programming version would re-quire orders of magnitude longer to solve.So KPS simply uses planned safety stocks,that is, m inimu m inventory levels, as abuffer for uncertain demand. A huge bodyof literature addresses safety stocks inproduction-inventory models (for instance.Silver, Pyke, and Peterson [1998, Chapter7] and the 103 references they list), butthese models typically require strongprobabilistic assumptions and do not ex-tend to multistage, capacitated, produc-tion, inventory, and distribution modelslike KPS. KPS uses sim ple rules for settingsafety stocks that have been tuned manu-ally over time: Experience is a goodteacher in this case.

In KPS, safety stocks for an sku are setonly at locations that see demand for thatsku. Nominally, the safety stock for sku sat location p in week t is the sum of de-m ands there in weeks t and t + 1, orsome other function of future demands.However, if an sku is to be promoted in aspecial advertising campaign starting inweek t, the safety stock in week t is set asthe sum of estimated dem ands in w eeks t


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BROWN ET AL.promoted. This extra buffer is kept be-cause the actual demand for a promotedsku is higher and more variable than forone that is not.

Safety stocks also attenuate undesirableend effects in KPS. In particular, a cost-minim izing, finite-horizon, produc tion-inventory model will always try to driveinventories to zero at the end of the plan-ning horizon. Even in a mod el with safetystocks, we do not trust a finite-horizonm odel's prog nostications in the last fewtime periods ; without safety stocks, thenum ber of periods of untrustw orthy re-sults would be even greater.The Rolling Horizon and SolutionPersistence

Kellogg uses KPS in setting a rolling ho-rizon [Schrage 1999, pp. 187-188]:Multi-period models are usually used in a roll-ing or sliding format. In this format, the modelis solved at the beginning of each period. Therecommendations of the solution for the firstperiod are implemented. As one period elapsesand better data and forecasts become available,the model is slid forward one period. The pe-riod that had been number 2 becomes number1, etc., and the whole process is repeated.

KPS has one difference, however: Pro-duction and packaging decisions in thefirst week are fixed, and it is largely thesecond w eek 's decisions that are set inmotion at the beginning of week 1. Themain reason for this is that it takes time toget raw materials and packaging materialsin place for prod uction, bu t KPS does notmodel such materials. Thus, at the begin-ning of week 1, the production and pack-aging plan is locked in place, having beenmade the week before or earlier alongwith orders for any materials that may not

enforcing solution persistence [Brown,Dell, and Wood 1997]. That is, we requirethat the solution of KPS covering, say,weeks t through t -\- 29, persist to somedegree with respect to last week's solutioncovering weeks t - 1 through t -\- 28. Ifthe time lag in ordering certain ma terialsis longer than a week, variables may alsobe fixed in weeks beyond the first week ofthe horizon.

Fixing variables to given values is astrong form of persistence; KPS also usesless coercive techniques, such as requiringa variable to lie within a specific range orpenalizing deviations of the variable froma target value. For instance, it is com monfor a plant manager, with guidance fromKPS, to decide that his plant will pack acertain sku in week 3, say, of the planninghorizon. However, he will let the modeldecide (for now) exactly how much of thissku to produ ce above a specified mini-mum level. We m ay also view safety-stocklevels and penalties for not achievingthem as a form of solution persistence. Ingeneral, KPS exploits persistence to (1)han dle lead times of raw materials, (2) re-duce volatility in suggested productionand distribution plans as the model hori-zon rolls ahead, and (3) incorporate mana-gerial knowledge into the production planthat is too complicated to model moreexplicitly.The Tactical Linear Program

Even though we originally envisagedKPS as only an operational model, wehave also developed a tactical version ofKPS for long-range plann ing, on the orderof 12 to 24 months. Kellogg uses long-


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KELLOGGnew DC locations for cost savings, and soon. The tactical model is identical to theoperation al one except that (1) time pe-riods consist of four-week blocks calledm onth s, (2) transpo rtation is typicallytreated as instan taneo us, and (3) a specialtime-cascade solution technique helps dealwith the limited product shelf lives.

Aggregating data and changing trans-portation delays is straightforward, buthan dling shelf lives is not. Kellogg w antsto ship fresh products and, as a rule, prod-ucts should reach customers (retailers)within four or five months of productionEstimated savings of $4.5million per year accrued fromfollowing the model'srecommendations.so that they have plenty of shelf life re-maining. Shelf life can essentially be ig-nored in a 30-week operational model, butit cannot be ignored in a 16-month tacticalmodel: If solved as a monolith, a 16-monthversion of KPS could, conceivably, call forproducing an sku in month 1 to meet a de-mand in month 16, and this would not berealistic.

Conceptually, it is not hard to model aprodu ction, inventory, and distributionsystem that tracks the age (or the use-before date) of inventory: If the useful lifeof a product is x periods, create T copies ofthe inventory balance constraints, inven-tory variables, and shipping variables, andindex them by the vintage of the p roductthey represent. Unfortunately, this wouldincrease the size of tactical KPS nearly

time w indow.To implement the sliding window, we

generate the standard mo del, solvemonths 1 throug h 5, fix the first m on th'svariables, solve m on ths 2 thro ug h 6, fixthe second month's variables, solvemo nths 3 through 7, and so on. In thisway, the model solution cannot see de-mand beyond five months in the futureand therefore will not try to produce anyproducts meant for sale more than fivemonths in the future. This is a heuristic,but users are convinced that it works well.An added benefit is that the tactical KPS iseasier to solve than the operational ver-sion, and this is impo rtant w hen running alarge num ber of what-if scenarios. (Brown,Dell, and Wood [1997] give more details.)Operational KPS in Action

Planning personnel meet for a half dayabou t six weeks p rior to the start of aquarter to schedule production and pack-aging for that upcoming quarter. They willchange the schedule produced many timesas the start of the q uarter gets closer anddata estimates are revised. But having along-rang e, visible target is im po rtant inman aging the purchase of raw materialswith long lead times, and for making ad-justments to plant capacities to satisfydemand.

To prepare for the quarterly meeting,we solve a weekly model with a 30-weekhorizon using a starting point projectedfrom the end of the current quarter'sschedule. Planners then deve lop detailed,implementable schedules for each process-ing and packaging line using K PS's pro-duction and packaging quantities as tar-


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BROWN ET AL.If KPS show s a proce ssing line beingheavily utilized for a particular product,planners will enforce a regular schedulewith prod uction every week on that lineusing a whole number of shifts;If KPS shows consistent, low levels ofproduction on a line, they will aggregateproduction into a sequence of larger pro-duction runs, in a whole number of shifts,once every few weeks; andIf KPS shows u nm et de ma nd for a par-ticular sku, planners may schedule week-end overtime for production and packag-ing of that sku.

The scheduled produ ction at each plant,by product and totaled over the quarter,usually conforms closely to that suggestedby KPS. How ever, KPS might source aparticular product at Battle Creek rather

When Kellogg completes thisproject, it estimates thesavings w ill be betw een $35and $40 million annu ally.than Omaha because of a very small costdifference, a difference that planners real-ize is negligible. In this case, plannersmight schedule Omaha for that product tocreate a more flexible or balanced schedu lefor the plants or to make the schedulemore closely follow budgetary guidelinesestablished months before using tacticalKPS.

As time passes, planners com pare theschedule against a weekly run of KPS inorder to adjust process quantities and tim-ing and to identify any approaching risksof unmet demand; planners may look sev-

flexibility to change the schedule, they re-view only large dev iations from the KPS-suggested packaging plan for potentialmodification.

Kellogg runs KPS each Su nday mo rning(the end of week 0) to guide productiondecisions in week 2 and b eyond. Mostmodel variables for week 1 are fixed: BySunday, it is too late to make changes toproduction plans for week 1 because rawmaterials and packaging materials forweek 1 are already at the plant or on theway.Data for the weekly run of KPS comefrom a variety of sources. Demand datacomprise a combination of forecasts fromthe marketing department and firm or-ders. Structural data on line capacities,yields, and the like are averages compiledover time, with data on new lines takenfrom engineering estimates. New or over-hauled lines wiU have start-up curves as-sociated with them . That is, yields will im-prove for several weeks as operators gainexperience with the lines and productchangeovers become sm oother. Add itionaldata come from conferences with plantman agers: For example, a packaging line,BP25, at Battle Creek unexpectedly may bescheduled for maintenance in weeks 3through 5, or a run of at least 200 klbs ofproduc t 123 mu st be mad e in week 4 be-cause raw materials are reaching age lim-its and must be processed, or the yield onprocessing line OLOl at Omaha must bereduced in weeks 2 through 4 because ofprojected humid weather.

A typical m odel h as rou ghly 100,000constraints, 700,000 variables, and 4 mil-


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KELLOGGtwo to four hours on a DEC Alpha com-puter with 512 megabytes of RAM or inless than 20 minutes on a 500 MHz Pen-tium III laptop. For its size, KPS is curi-ously difficult to solve, and we hav e d on eresearch to find out w hy. K ellogg's systemhas scant slack capacity; small changes inplans affect many facilities and time pe-riods; and about 70 percent of the model'sconstraints are taut at optimality. Theseare tough linear programs.

One key to solving KPS efficiently is theX-System's generalized-netwo rk factoriza-tion [Brown and Olson 1994; McBride1985]. In particular, a selection of up to 95percent of constraints Cl, C3, and C4 willhave at most two no nzero elements percolumn and thereby form a largegeneralized-network subm odel. Such asubmodel is easily identified, and substan-tial computation savings accrue becausean explicit basis inverse (or other explicitbasis factorization) need not be m ain-tained for that submodel.

Once KPS is solved, results are loa dedinto a database and checked for consis-tency. If data problems are revealed, theycan be corrected and the model rerun be-fore central plan ners receive the resu lts onMonday or Tuesday.

It is difficult to quantify the savings Kel-logg obtains by using KPS rather than ear-lier manual methods. However, when wefirst introduced KPS for weekly planning,management decided that productioncosts should be equalized across plants.That is, average production costs wouldbe used at all plants so that no plantwould be likely to have a severe increase

differentials. After planners became com-fortable with KPS and verified data, theyintroduced actual costs into the model. Atthat time, 1994, it was estimated that sav-ings of $4.5 million per year accrued fromfollowing the model's production, inven-tory, and distribution recommendations[Scott 1999].Tactical KPS in Action

KPS is just as important for tacticalplanning as it is for operational planning.Some representative examples d emo n-strate its value in the tactical arena.Prior to the start of each fiscal year,planners po pulate the KPS database w ithestimated plant-cost and throughput dataand forecasted demands for the fiscal yearplus six mo nths. We run the model to de-termine the optimal sourcing of produ c-tion to satisfy the forecasted demand forthe fiscal year; the extra six months of datamediate undesirable end effects in the so-lution. The firm uses the information onKPS has saved the KelloggCompany millions of dollarssince the mid-1990s.production volumes to then establish fi-nancial budg ets within the plants, inven-tory space requirements within the DCnetwork, and equipment projections foreach transportation lane.

KPS plays an integral role in evaluatingproduction capacity. By investigating theutilization of variou s processing lines,planners can identify opportunities for im-provement. If they see that the utilizationof the lines that make certain products is


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BROWN ET AL.utilized, they may seek additional capac-ity. Also, if a product is produced on mul-tiple lines at different locations with somelines operating at less than capacity, butwith the low-cost location operating at ca-pacity, a capacity increase at that locationmay be justified. Managers must evaluatethe potential savings in variable costs us-ing KPS and compare them w ith the costof the capital improvements.

A recent con solidation project exem pli-fies the use of KPS for capacity planning.A combination of declining sales and in-creasing yields of certain products on cer-tain lines was leading to underutilizationof other processing lines, and managersconjectured that they could make savingsby closing dow n som e of the un der-utilized lines.

Multiple plants produced the relevantprodu cts, and no single line was com-pletely idle. Initial runs of KPS also re-vealed that simply removing one of thelines with low utilization would be un-wise, because the remaining lines wouldhav e too little capacity to fully sup po rt thebusiness . So, we u sed KPS to explore setsof alternatives for shutting down a subsetof the lines and increasing capacity on oth-ers. We undertoo k the study in two stages,first determining which lines to shut downand then deciding where to increase ca-pacity. Ideally, we would look at both setsof decisions simultaneously, but the largenumber of combined options necessitatedthis ad hoc decomposition. We identifiedreasonable alternatives for shutting downHnes by running KPS with data covering18 m onth s, with different com binations of

these alternatives off for more detailed fi-nancial and engineering analyses. Thoseanalyses, combined with an accounting offixed and variable cost implications for thescenarios, led to a decision about whichlines to close. Then managers had to de-cide how to increase capacity.

By using KPS, we determined the re-quired overall capacity increase and gavethat figure to Engineering. Engineeringgenerated a list of implementable optionsthat could deliver this increase and theircosts. W e then incorpo rated capacity information so that we could m easure variable-cost impacts of the va rious scenarios.Combining this with the capital requiredfor each option enabled m anagers to m akea financial comparison and select the bestoption.

Having selected the consolidation planto follow, we created a transition plan forimplem enting it. KPS helped us answe rthese questions:When could Kellogg take the lines tar-geted for capacity increases out of serviceand install new equipment? (Engineeringprovided information regarding the timerequired and start-up curve estimatesupon completion.)When should production cease on thelines being eliminated?How much inventory should Kelloggbuild to support the business during thetransition?

W hen Kellogg com pletes this project, itestimates the savings will be between $35and $40 million annually.

Kellogg also uses KPS to d eterm inewhere to produce new products, to assist


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KELLOGGcost impacts of various projects. For itsNorth American cereal business, we runKPS about 30 times a month to answerthese types of what-if questions.ConclusionsAfter more than 10 years, KPS is still indevelopment: Business never stops chang-ing. Global operations will require som erefinements and more flexible inputs. Wewill introduce binary variables to more ac-curately model the realities of line sched-uling. We will more accurately model pro-duction and packaging operations that aretightly coupled; this should result in im-proved solution quality and possiblyspeed. We may also model some criticalraw materials with long lead times.

In both its tactical and operational roles,KPS has saved the Kellogg Com pany mil-lions of dolla rs since the mid-1990s. Kel-logg is introducing KPS into Latin Am er-ica to improv e op erations there, and it isstudying a global model. The advent ofthe European U nion has simplified cross-border operations in Europe, and the eastcoast of the United States and the coasts ofEurope are getting closer all the time.Acknowledgments

The authors are grateful for the supportof Don Scott of the Kellogg Company, andthank Richard Powers of INSIGHT, Inc.,who has shepherded this application sinceits inception. They also thank tw o an ony-mous referees for a careful review of thepaper and the resulting improvements.APPENDIXThe following linear program is a didac-tic specimen of the Kellogg Planning Sys-tem. The constraints and variables corre-spond to a generic location. Kellogg plants

production and packaging, and co-packershave no exogenous demands.Indices/food (product).kstock-keeping unit (sku).pplant (or distribution center).ttime period./processing line (for foods).mpacking line (for skus).hproduction process.fih)the food produced by process h.H(l, p)processes h that use line / atplant p.K{m, p)skus k that are packed on linem at plant p.H{f, p)processes h that produce food /at plant p.K{f, p)skus k that are packed fromfood / at plant p.K'ik, p)skus k' that are assembledfrom (constituent) sku k at plant p.M(fc, p)packing lines m that pack skuk at plant p.Data and [Units]ai,ip,fractional shifts used on process-ing line / to produce one klb of food f(h) atplant p during time period t [shifts/klb].Ptepffractional shifts used on packingline m to pack one klb of sku k at plant pduring time period t [shifts/klb].Jkk'pfractional klbs of sku k used tomake one klb of sku k' [klbs/klb].d^p,demand for sku k at plant p dur-ing time period t [klbs].holdup,safety stock for sku k at plant pduring time period t [klbs].W/p,capacity of processing line /, plant

p , time period t [shifts]."mpfcapacity of packing line m, plantp , time period t [shifts].holdi^pQinitial inventory of sku k, plantp [klbs].Decision VariablesMAKEf,p,klbs of product f(.h) pro-duced using process h at plant p duringtime period t.


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BROWN ET AL.p,klbs of sku k in inventory atplant p at the end of time period t.SHIP^pp.,klbs of sku k shipped fromplant p to plant p' at the beginning of timeperiod t (nominally arriving in period t -\-

1).Constraints(Cl)( C 2 ) E ^ , ^ p , ,

ksK(m,p)Vm, p, t.

(C3) ^ MAKEhp, -

\/l,p,t.

keK(f,p) msMik,p)= 0 V/, p, t.(C4)

k'sK'(k,p) m+ HOLDUP,,_, - HOLD^,2 2= dkp, Vfc, p, t.

(C5) HOLDUP, > holdup, VJt, p, t.(C6) (...additional constraints omitted.)(C7) HOLD,po - ^oW^o Vfc, p, t.(C8) All variables non nega tive.ObjectiveMinimize production costs + packingcosts -I- inventory costs + shipping costs-I- penalties for processing line capacityviolations, packaging line capacity viola-

tions, unmet demand, and unmet safety-stock requ irements.Constraints (Cl) and (C2), respectively,constrain shifts of activity on each process-ing line and on each packaging line ineach plant during each period. The rela-tional operators "


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KELLOGGScott, D. 1999, "Custom optimization modelsprovide competitive advantage in the supplychain planning process," Paper presented atthe Council of Logistics Management AnnualConference, Toronto, Ontario, C anada, O cto-ber 17-20.Silver, F. A.; Pyke, D. F.; and Peterson, R. 1998,

Inventory Management and Production Planningand Scheduling, John Wiley and Sons, NewYork.Wagner, H. M. and Whitin, T. M. 1958, "Dy-namic version of the economic lot sizemodel," Management Science, Vol. 5, No. 1,pp. 89-96.Zangwill, W. I. 1969, "A backlogging modeland multi-echelon model of a dynamic lotsize production systemA network ap-proach," Management Science, Vol. 15, No. 9,pp. 506-527.Don J. Scott, Vice President, North

Am erica Logistics, Kellogg Co m pan y, O neKellogg Square, Battle Creek, Michigan49016-3599, writes, "The development ofthe Kellogg Planning System (KPS) 12years ago which is described in the paperentitled The Kellogg Company OptimizesProduction, Inventory, and Distribution'was a major improvement to Kellogg'ssupply-chain planning capabilities. KPSreplaced our existing MRP and DRP Sys-tems as well as enhanced our long-rangecapacity planning capabilities for Kellogg'sUSA business. KPS's ability to gua ranteeoptimized detail production and deploy-ment plans by simultaneously consideringcost and capacity for manufacturing, ware-housing and deployment was a significantimprovement over the traditional planningsystems that it replaced. Early in the life ofKPS, we w ere able to docum ent m ulti-million dollar operating savings that weredriven from improved week-by-week opti-

have continued to enhance KPS's capabil-ity and expand its use across all businesschannels. KPS's planning capabilities haveplayed a vital role in Kellogg's ability tocontinually reduce costs and inventorylevels while improving service and capac-ity utilization throughout our total supplychain."


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