WORKING PAPER MASSACHUSETTS

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1 BASEMEN

Systems/ Donald B. g.osenfeld Vstng Assocate Professor M.I.T.

5 HD28.M414 ^5- Dewey ALFRED P. WORKING PAPER SLOAN SCHOOL OF MANAGEMENT Desgn and Control of Mult-Locaton Dstrbuton Systems/ Donald B. g.osenfeld Vstng Assocate Professor M.I.T. Sloan School of Management Senor Consultant Arthur D. Lttle, Inc. Aprl 1985 # MASSACHUSETTS INSTITUTE OF TECHNOLOGY 50 MEMORIAL DRIVE CAMBRIDGE, MASSACHUSETTS 02139

7 ^Desgn and Control of Mult-Locaton Dstrbuton Systems/ Donald B. 5.psenfeld Vstng Assocate Professor M.I.T. Sloan School of Management Senor Consultant Arthur D. Lttle, Inc. Aprl 1985 #

8 M..T.UBRI^nES AUG RECEIVED

merchandse) and the del very of these goods to customers or reta outlets.

9 rm b y n date -I on af ocat I Intr oduct an Ths paper examnes the ssues n the desgn and contra mult-locaton dstrbuton systems. Mu I t ocat dstrbuton systems nvolve the procurement ot merchandse ar rau materals from vendors I the transport of the same to plants) warehouses and dstrbuton centers; the stockng of fnshed goods or merchandse) and the del very of these goods to customers or reta outlets. Some of these dstrbuton systems use dstrbuton centers) whch consoldate and dstrbute merchandse to captalze on the economes of scale n transportaton) and others use warehouses) whch serve to stock goods and pass I conso I de I ver es The desgn and control of these systems nvolve a range of questons nvolvng facltes) nventores) product flows and transportaton. In addton) control of the movements and storage of goods requre a greater level of sophstcaton than smple sngle nstallaton retal outlets or manufacturng operatons. In addton to the obvous operatonal questons of mul t I dstrbuton systems) the basc logstcs choces have mportant strategc mplcatons. The strategc mplcatons of logstcs choces have been examned by Shapra> [1] by ShaprO) Rosenfeld) and Bohn; C23) Shycon and on Sprague and) wth respect to facltes choces) by Hayes and Wheelwrght C4II. A f can ga a compettve advantage usng dstrbuton and ts network of facltes. There are qute clearly sgnfcant strategc dfferences) for example) n operatng a large number of dstrbuton facltes and n operatng a small number of facltes. A f rm mght compete by offerng hgh servce (large numbers of facltes) or low cost (smaller number of facltes.) By understandng the dstrbuton and logstcs optons avalable and the nature of the marketplace) a frm can better desgn ts dstrbuton network

I t es ze y ce on eve I t ona I y - 1 - In usng multple dstrbuton facltes there are a number of mportant questons that must be answered.

coordnaton The number and locatons and szes of both manufacturng and dstrbuton f ac have obvous mpacts on both cost and servce) and the goals for servce are strategcally mportant.

Frms can alternatvely grow smultaneously n all regons of the country) requrng a full-scale dstrbuton network) or grow sequentally regon by regon; requrng on I a staged growth of the dstrbuton and

11 I t es ze y ce on eve I t ona I y In usng multple dstrbuton facltes there are a number of mportant questons that must be answered. These nclude: - number and locaton of facltes - servy I I - s of fac es - assgnment of products and markets to facltes - desgn of system durng growth stage - eche I des gn - nventory control and coordnaton The number and locatons and szes of both manufacturng and dstrbuton f ac have obvous mpacts on both cost and servce) and the goals for servce are strategcally mportant. Once a network s desgned? there are also complex ssues of product and market assgnment. For an expandng frm) there are the mportant ssues of the growth of the logstcs system. Frms can alternatvely grow smultaneously n all regons of the country) requrng a full-scale dstrbuton network) or grow sequentally regon by regon; requrng on I a staged growth of the dstrbuton and manufacturng network. The echelon desgn s a key ssue for servce and nventory management. Many frms have several stages) or echelons; of nventory and dstrbuton. A natonal plant or warehouse may supply a regonal warehouse whch may n turn supply a local warehouse and possbly even a representatves' trunk! Each of these s an echelon. In the computer ndustry) where specfc crtcal spare parts may be requred only occass I ) ndvdual parts may be stored at any one of several echelons. For these types of dstrbuton systems) the number of echelons can be a crucal desgn factor.

I 1 1 es on ch I te M I e ng I t nesses - 2 - The echelon desgn leads to the fnal ssues of nventory allocaton) control) and coordnaton.

How to dstrbute and control nventory among the locatons are mportant desgn and management questons.

12 I 1 1 es on ch I te M I e ng I t nesses The echelon desgn leads to the fnal ssues of nventory allocaton) control) and coordnaton. Uh multple echelons may not be common) most large busnesses mantan two echelons where central plants and warehouses + ac may supply sate I warehouses. How to dstrbute and control nventory among the locatons are mportant desgn and management questons. In order to provde a focus and framework for addressng the desgn and control of mu I t -I ocat we vew as the four key questons: dstrbuton networks) we focus n ths paper an what - number of dstrbuton facltes - locaton and sze of dstrbuton f ac - deployment of nventory among dstrbuton facltes n a two stage (plant and dstrbuton center) system - control of nventory among f ac Number of facltes s clearly a key desgn ssue. Gven the number of facltes) szng and locaton are dependent on many characterstcs of the busness. These factors nclude sourc es I t es factors) locatons of markets) economes of scale n manufacturng and dstrbuton) and locatons and capactes of exstng facltes for an expandng frm. Inventory deployment and control are crucal because of the nature of manufacturng and dstrbuton. For many natonally or regonally based bus ) the number of manufacturng facltes s less than the number of dstrbuton facltes II4I]. As a result) plants wll generally serve as combnaton plants and dstrbuton centers) wh w n turn supply the addtonal dstrbuton centers. For frms wth extensve dstrbuton networks) there wll hence be two stages or echelons. The key nventory management ssue s the a I locaton of nventory between the two echelons. That s) should nventory be concentrated at the frst) or plant stage) of the system wth modest stock

ng I t I e - 3 - levels at the second stage) or should be nventores be concentrated at the second) or warehouse) stage of the network) wth mnmal stagng stdc< at the plant stage a+ the system.

' Standard methods for control I ng nventory at a sngle locaton) such as order pont systems) may not be suffcent for two-stage networks where there are complex nteractons between the two stages.

13 ng I t I e levels at the second stage) or should be nventores be concentrated at the second) or warehouse) stage of the network) wth mnmal stagng stdc< at the plant stage a+ the system. In addton) once nventory s al located among the two stages* how should t be control led'?' Standard methods for control I ng nventory at a sngle locaton) such as order pont systems) may not be suffcent for two-stage networks where there are complex nteractons between the two stages. Methods such as Dstrbuton Requrements Plannng C5D have been suggested for hand I these more complex systems. In any case) a dfferent framework or approach s requred for a mult-stage network. Ths paper presents an overvew of these four key questons n the desgn and control of mult-locaton dstrbuton networks) and dentfes the dfferent stuatons whch wll cause dfferent frms to approach desgn questons dfferently. Number of Dstrbuton Fac es There are several factors that mpact the choce of the number of dstrbuton facltes. These nclude - dstrbuton costs - customer servce levels - growth patterns of busness - number and locaton of manufacturng facltes There s an obvous relatonshp between the number of dstrbuton facltes and both dstrbuton costs and customer servce. Uth addtonal facltes) customer servce mproves. Uh nventory nvestments and facltes nvestments ncrease; transportaton costs may decrease as descrbed as follows) due to the economes of scale n the costs of ndvdual transportaton loads. Economes of scale dctate that full loads cost less per unt than partal loads. If a manufacturng frm s payng for outbound

ns I t es oads I loads ver loads rm - 4 - transportaton costs (from dstrbuton centers or warehouses to customers ul- ch may be n small loads)) transportaton n consoldated loads to warehouses or

Dth addtonal dstrbuton centers or warehouses^ facltes are> on average) closer to the customer) the nbound porton of the delvery ncreases) and total transportaton costs can decrease.

14 ns I t es oads I loads ver loads rm transportaton costs (from dstrbuton centers or warehouses to customers ul- ch may be n small loads)) transportaton n consoldated loads to warehouses or dstrbuton centers wll gve more economc transportaton to the nbound (to warehouses or dstrbuton centers) porton of the delvery. Dth addtonal dstrbuton centers or warehouses^ facltes are> on average) closer to the customer) the nbound porton of the delvery ncreases) and total transportaton costs can decrease. In a retalng busness) where loads from vendors are typcal ly n sma I and loads from dstrbuton centers to stares are n consoldated I ) a dstrbuton network wth several dstrbuton centers wll provde a smlar economc advantage. In both stuatons) however) as the number of dstrbuton centers substantally ncreases) t may not be possble to del ful I to dstrbuton centers or warehouses (for a manufacturng frm) ar from dstrbuton centers (for reta I ng cha ). In the stuaton where the customer s payng for transportaton from the dstrbuton center or warehouse) faclty and nventory costs qute clearly ncrease as the number of facltes ncreases. Transportaton costs may also ncrease) or they can stay approxmately the same. Wth an ncrease n the number of facltes) some dstrbuton centers or warehouses may be closer to plants (decreasng nbound costs) and some may be farther away (ncreasng nbound costs). The overall effect s n general not clear but costs should not Kary substantally wth the number of facltes. Some specfc quanttatve results for these types of relatonshps are presented below. Corporate growth s another mportant factor n the determnaton of the number of f ac. Companes that are expandng geographcal ly need to add dstrbuton facltes for both economc and servce reasons. A f may expand by slowly expandng ts geographc base or by attemptng to expand smultaneously n several locatons on a small scale. The latter approach may

rms m ted ng I t - 5 - be problematc n terms of economes of scale of dstrbuton costs.

A growth strategy also crtcally affects locaton and sze of facltes) and the topc s more extensvely dscussed n the next secton.

15 rms m ted ng I t be problematc n terms of economes of scale of dstrbuton costs. For a broad-scale geographc expanson) Hayes and Wheelwrght dscuss the requrement of establshng "beachhead plants" for the assocated manufacturng network. A growth strategy also crtcally affects locaton and sze of facltes) and the topc s more extensvely dscussed n the next secton. A fourth factor that affects the number of dstrbuton facltes s the nature of the manufacturng network. Dstrbuton facltes are often located adjacent to) or are desgned as part of) a manufacturng plant. The desgn of a manufacturng network s not the focus of ths paper) but t s mportant to note that manufacturng faclty locaton s often based on a dfferent type of analyss than the analyss of the dstrbuton. Ths may nclude manufacturng economes of scale) labor and tax questons) locaton of key supplers or raw materals) and plant focus n terms of products and process. In any case) the desgn of the dstrbuton network needs to take nto account the desgn of the manufacturng network. For most natonally-based manufacturng f > as noted) the deal number of dstrbuton locatons exceeds the deal number of manufacturng locatons. The dstrbuton system desgn ssue s therefore to determne the best number of warehouses or dstrbuton centers gven the I number of manufacturng locatons. In general) the two problems are related) but gven the addtonal ssues nherent n the manufacturng network desgn) a decoup I s often feasble) and we concentrate on the separate desgn of the dstrbuton network To deal wth the varous ssues nherent n the determnaton of the number of dstrbuton facltes) we consder the two prmary questons concernng the number of dstrbuton facltes (dstrbuton centers or warehouses): - How do costs vary wth number of dstrbuton f ac es? - tajhat s the relatonshp between servce and cost as the number of dstrbuton facltes s vared?

To answer these two questons; one can make some s I y ng assumptons about the dstrbuton of demand and the locatons of dstrbuton facltes that) whle not always valdj should not compromse the

16 I number I t I ty es I I be I ty ng /N I not mp f - ^ - The dscourse that follaus s based an a manufacturng frm wth a fxed but sma I of plants. An analogous set of conclusons can be reached for a reta I chan. To answer these two questons; one can make some s I y ng assumptons about the dstrbuton of demand and the locatons of dstrbuton facltes that) whle not always valdj should not compromse the determnaton of the approprate number of facltes. Specfcally) f one assumes that 1) demand s unformly dstrbuted 2) each dstrbuton faclty s located n the center of a regon that t supports and 3) the area of each dstrbuton faclty terrtory s equal) then some general results are obtanable. Consder a network of an arbtrary number of dstrbuton facltes N. Each f ac covers I of the total area of the busness. It fol lows that the outbound transportaton tme (from the dstrbuton centers to customers) wll be proportonal to the square root of l/n) snce ths s the lnear dmenson of area correspondng to each dstrbuton center. These outbound movements wll general ly be LTL movements) and assumng LTL costs are lnear functons of dstance) varable outbound costs wll also be proportonal to the square root of l/n. Uh I e LTL costs often ^ary substantally) n general the lnear assumpton s reasonable Z61. As noted) up to a certan number of dstrbuton facltes nbound costs should not vary wth the number of facltes) snce the average dstance from the central plant or plants w I change. (Wth more f ac I t es some f ac w closer to a central plant) and some wll be farther away.) However) as the number of dstrbuton facltes reaches a certan level) t s not possble to obtan full transt loads nbound. How wll f ac and nventory costs vary as the number of dstrbuton facltes changes? Certan costs ) e.g. admnstratve

th es eve led I ty - 7 - overhead) wll be +xed> regardless of the sze of the faclty. Other costs) partcularly those related to nventory) uu I I exhbt economes of scale.

Whle there are economes of scale n nventores) emprcal studes ndcate that the precse relatonshp vares wth the busness) and that) n general) that) nventores wll ^sry w a power of sales between.5 and 1.

17 th es eve led I ty overhead) wll be +xed> regardless of the sze of the faclty. Other costs) partcularly those related to nventory) uu I I exhbt economes of scale. For example) the so-ca I square-root law hypotheszes that nventores at warehouses ncrease as the square root of the sales covered by the stockng locaton. Whle there are economes of scale n nventores) emprcal studes ndcate that the precse relatonshp vares wth the busness) and that) n general) that) nventores wll ^sry w a power of sales between.5 and 1.0 [73. A hgher power ndcates a hgher degree of correlaton across geographc areas. In ths case the splttng of nventores across several dstrbuton facltes does not substantally ncrease total nventores. Other costs wll be smply proportonal to the total sales volume. Labor costs wll presumably be proportonal to total sales volume) as each unt of merchandse wll requre the same type of materals movement) regardless of how long t sts on the shelf. In summary) nventory and other f ac costs (not ncludng those costs that are proportonal to sales volume) wll be fxed for each locaton or wll vary as a power of sales between.5 and l.d. That S) C = A + KS^ where C = nventory and f ac I ty costs A = f xed costs K = constant S = sa I I I B = constant As the number of facltes ncreases) the cost per faclty decreases) but the total casts ncrease.

ume us ons I t ty onsh tt es ng ps t es I t es t - 8 - cone I These types af general re at can be used to develop an the best number at dstrbuton facltes and the tradeoffs between costs and servce.

(Ths assumes nbound transportaton costs) or those from plant to dstrbuton f ac reman approxmately constant) whle outbound transportaton costs decrease as customers are generally closer to the nearest

18 ume us ons I t ty onsh tt es ng ps t es I t es t cone I These types af general re at can be used to develop an the best number at dstrbuton facltes and the tradeoffs between costs and servce. For example) wth outbound costs pad by the manufacturer; transportaton costs decrease but faclty costs ncrease as the number of f ac ncreases. (Ths assumes nbound transportaton costs) or those from plant to dstrbuton f ac reman approxmately constant) whle outbound transportaton costs decrease as customers are generally closer to the nearest dstrbuton faclty). Wth fxed-faclty costs low (.e. total costs are proportonal to a power of sales) a mathematcal relatonshp can be es derved showng that the best number of dstrbuton facltes s proportonal to a power of total sales volume between D and.5. (The power s when faclty costs are proportonal to sales volume) n whch case there s no premum for spl volume among several f ac I t. A power of.5 results when fac I costs vary as the square root of sales vo I. ) If a frm doubles ts volume) for example) t should ncrease the number of ts dstrbuton facltes between zero and 41%. The curve relatng total costs and the number of facltes (see fgure 1) wll be relatvely flat around the regon of the optmum) but the approach ndcates the nature of the relatonshp between the number of fac I es and sales volume. Perhaps a more mportant queston than cost mnmzaton s the relatonshp between the dstrbuton costs and customer servce) defned as del very tme) as the number of fac I s vared. Assume now that outbound costs are pad by the customer. Hence as the number of facltes s ncreased) the costs ncrease) but outbound delvery tme -k vares as N. Snce both costs and outbound del very tme can be

the power relatonshp (1) between nventory and other facltes costs and sales volume.

19 I ty - ^ - expressed n terms af N; N can be elmnated and dstrbuton casts can be related ta outbound del '^ery tme T. Ue do not present ths dervaton but note that the term n ths relatonshp between the costs a dstrbuton and the del very tme s 2+2B proportonal to T > where T s the del very tme and B s the exponent n the power relatonshp (1) between nventory and other facltes costs and sales volume. For example; f nventory costs are prapartonal to the square root of sales) then costs are nversely proportonal to delver tme. The result s a wde range of cost-delvery tme relatonshps on the effcent fronter) or the most cost-effcent dstrbuton system for a gven level of servce. The general form of ths tradeoff relatonshp can have a sgnfcant mpact on ndustry logstcs structure C2I1. Industres wth relatvely flat curves may offer more feasble alternatves for the varous frms n the marketplace than ndustres wth relatvely sharp turns. In the latter case frms not locatng at the pont of curvatve may offer sgnfcant premums ether n cost or del very tme. In the former case frms can offer alternatve servce levels for modest dfferences n cost. (See fgures 2 and 3). The mportant ssue for number of dstrbuton facltes s the mpact of the nventory-sales parameter B n (1) on the cost-del very tme tradeoff curve. Fgure 4 presents the curves for two dfferent values of B. For the hgher B case of.875) there s hgher correlaton among regons of the country) and splttng nventores among locatons does not sgnfcantly ncrease costs. Indeed) the B =.875 curve s flatter over a wder range of delvery tme values) untl t becomes sharply knked at low values of delvery tme) or very fast delvery tme. Consequently) the nature of demand and f ac economes of scale wll affect the shape of the curve and) n turn) the structure of the ndustry. In ndustres

20 I t - ID - wth hgher B, frms wll generally have many dstrbuton facltes, whle n ndustres wth lower B, there may be a wde range of number of f ac es

nts ocat d ans I ty th mp y - 11 3. La catan and Sze of Faclte s Szng and I questons prmarly consst n+ the fa I lowng - How large are approprate faclty terrtores?

a dstrbuton faclty locaton wll be based on transportaton costs and customer proxmty. The sze wll be s sze requred to servce the terrtory.

21 nts ocat d ans I ty th mp y La catan and Sze of Faclte s Szng and I questons prmarly consst n+ the fa I lowng - How large are approprate faclty terrtores? - How senstve s total market share and costs to locaton and sze'7 - How are locatons dentfed as the frm grows Gven a terrtory? a dstrbuton faclty locaton wll be based on transportaton costs and customer proxmty. The sze wll be s sze requred to servce the terrtory. The demand centra d of the faclty) the locaton that mnmzes the weghted average dstance to demand po j wll mnmze average customer proxmty and> assumng transportaton costs are proportonal to dstance) the transportaton cost. The centro can be approxmated ether by weghted coordnate I the average or a coordnate medan. Determnaton of faclty terrtores can be salved on the bass of mnmzng average dstance to the nearest dstrbuton center or warehouse. Generally) ths also mnmzes transportaton cost and delvery tme. For areas of hgh cost (or delvery tme) per mle? dstances should be mare heavly weghted. Intutvely? where demand s denser faclty terrtores should be smaller) but total demand covered by the faclty should be larger. Hence the sze of the f ac should vary nversely w a power of demand densty between D and 1. The precse power s 2/3 [7]. Hence faclty terrtory szes wll decrease by a factor of 4 and total faclty) demand wll double f demand densty ncreases by a factor of 8. Ta best llustrate the senstvtes and growth questons) we present a case study. The study llustrates some conclusons that are applcable

nter m dat on ts n dates - 12 - ta many stuatons. The company nvolved was a major Eastern retaler embarkng on an ambtous growth program.

Three dfferent scenaros for chan sze were of concern: the current chan; the ful ly expanded chan; and an cha n ConsD I economcs plays an mportant role for any logstcs system nvolvng delveres from

who procure goods from hundreds of vendors and delver them to multple assembly p ants > and retalers? who need to transport merchandse from hundreds of vendors to large numbers of stores?

22 nter m dat on ts n dates ta many stuatons. The company nvolved was a major Eastern retaler embarkng on an ambtous growth program. Servce requrements and the economcs of transportaton consoldaton ponted out the need for addtonal dstrbuton centers. Three dfferent scenaros for chan sze were of concern: the current chan; the ful ly expanded chan; and an cha n ConsD I economcs plays an mportant role for any logstcs system nvolvng delveres from many orgns to many destnatons. Wth large numbers of paths of small loads? t s economcal to consoldate loads. The automoble companes? who procure goods from hundreds of vendors and delver them to multple assembly p ants > and retalers? who need to transport merchandse from hundreds of vendors to large numbers of stores? are good examples of ths. Perhaps the most strkng example of ths s Federal Express Corporaton? who conso I almost all of ts delveres at ma hub at Memphs? Tennessee. The key questons for the reta I er were - The senstvty of cost and servce to the utlzaton of ts exstng faclty? and - The stagng of expanson decsons wthn the frm-'s overall growth strategy The utlzaton of the exstng faclty was mportant n that the company had a large faclty n the eastern part of the country that could be expanded or reduced n sze. Hence t was mportant to understand the senstvty of costs and servce to utlzaton of ths faclty n the long-term strategy of the frm. Wth respect to the second ssue? the stagng of decsons as part of the growth strategy? t was mportant to understand how the frm could expand whle at the same tme controllng dstrbuton costs and servces.

I t I t I zat es an I as on I ty ca I projected th I zat I volumes) I e - 13 - Td analyze the ssues > the author develaped a computer model to optmze product flows wthn the dstrbuton network gven the

The upper curve represents a network wth the Eastern locaton and a fxed mdwestern locaton.

zat As the ut I of the exstng fac I ty ncreases j the best second locaton moves further awayj and the cost of a network w a fxed second locaton can rse very sharply.

23 I t I t I zat es an I as on I ty ca I projected th I zat I volumes) I e Td analyze the ssues > the author develaped a computer model to optmze product flows wthn the dstrbuton network gven the utlzaton of each of the dstrbuton facltes. Fgure 5 presents the relatonshps between costs and ut of the exstng f ac for alternatve networks of two dstrbuton centers. The upper curve represents a network wth the Eastern locaton and a fxed mdwestern locaton. The lower curve represents network wth the Eastern locaton and the best second locaton (whch wll K^ary as the utlzaton of the Eastern faclty changes). zat As the ut I of the exstng fac I ty ncreases j the best second locaton moves further awayj and the cost of a network w a fxed second locaton can rse very sharply. The analyss shows that locatons of f ac as we I costs can be very senstve to ut on of gven fac es. The set of optmum dstrbuton networks for dfferent ponts n tme durng the growth stage of the frm dentfed the best mplementaton strategy for new dstrbuton centers. It turned out that best second locaton for the nterm pont of the rapd growth stage was 1) the best second locaton for the ful ly expanded chan and> 2) a part of the best network wth three dstrbuton centers. Uh I e ths result was somewhat fortutousj t supports the concept that a frm should expand nto new geographcal areas sequentally (a fannng out process) rather than expandng smultaneously to a I markets. The latter approach can lead to dsecanomes of scale n dstrbuton) as such an approach wll yeld large geographcal areas wth sma I wh a sequental expanson mght be acheved econom costs II y n terms of dstrbuton

te te n te I e ng 1 -ec o -eche dated led) -I on I t es - 14-4.

Each echelon or stage feeds the succeedng stage wthn the network. Whle the fve ar sx stage systems for feld servce n many hgh-tech busnesses are n the mnorty?

24 te te n te I e ng 1 -ec o -eche dated led) -I on I t es D eployment of Inve ntory u th a Mu 1 h e I n Inventory Sys tem The thrd key ssue n the desgn and control of a mu I t dstrbuton network s nventory deployment tor a mu I t I ocat on system. Each echelon or stage feeds the succeedng stage wthn the network. Whle the fve ar sx stage systems for feld servce n many hgh-tech busnesses are n the mnorty? many frms operate a large number of dstrbuton f ac. Snce the lmted number of manufacturng locatons nvarably act also as stockng locatons) these dstrbuton systems are defacto two-echelon nventory systems. The stuaton s depcted n fgure h. The deployment of nventores between the two stages of the systems s a complex queston. Indeed; when one starts nvestgatng alternatve methods of deployng nventores n a two stage system? there are very dfferent mplcatons for faclty capactes and buffer stocks. In general? there are two sensble methods for deployng nventores between the two echelons of the system. One method concentrates nventores at the central locaton or locatons (a central system)? whle the second method concentrates nventores at the second stage? or the satel I locatons of the system (a satel I te system) CBD. LJth a central system? the satellte warehouses carry stocks to protect aganst lead tme only? wh the central locaton or locatons carry large buffer stocks to protect aganst the producton of procurement lead tme. Wth a satellte system? the satellte warehouses carry larger buffer stocks to protect aganst both transt and producton lead tme. Under ths type of approach) the warehouses assocated wth the central plant ar plants act manly as a stagng and marshal I areas for conso I shpments to the satel I warehouses. In a satel I system) merchandse s pushed (ar pu I out to the satellte locatons as much as possble. In a central system) some nventory

I te ty -eche on I te tes I - 15 - s held back ar protect on) thereby reducng requrements at the sate! I to a sgnfcant degree.

locaton). Obvously) the type of organzaton and nformaton system u) I I affect the relatve desrab I of the two types of systems.

Theoretcans have not been able n general to characterze the best nventory deployment strateges for these mu 1 1 I systems.

25 I te ty -eche on I te tes I s held back ar protect on) thereby reducng requrements at the sate! I to a sgnfcant degree. The exact nventory levels can then be based on standard approaches for calculatng buffer stocks gven the approprate lead tmes (transt tme for the sate I locatons and the producton tme tor the central locaton). Obvously) the type of organzaton and nformaton system u) I I affect the relatve desrab I of the two types of systems. Each type of deployment strategy wll requre a specfc type of control system) whch s dscussed n the next secton. Theoretcans have not been able n general to characterze the best nventory deployment strateges for these mu 1 1 I systems. However) the only two reasonable optons are the two deployment strateges outlned above. The choce between the two optons) moreover) can have an enormous mpact on faclty requrements. Ths latter pont s also best llustrated by a case study. The author was nvolved n a locaton study for a major consumer goods manufacturer. At the tme of the study) the East coast factory and warehouse servced SD7. of the country) and the west coast sate I servced 20% of the country. The purpose of the study was to evaluate and recommend addtonal locatons for warehouses. One of the keys to the analyss was that the product was a hgh-value> low-weght product for whch nventory costs were domnant. It became clear farly early n the analyss that the dstrbuton cost analyss would requre dentfcaton of the specfc nventory deployment strategy. Ue then smulated the nventory levels of each and every product of the company for both a central and satellte nventory deployment strategy. The results of the smulaton are presented n Table 1. Note that wh the net nventores of the two approaches are not vastly dfferent) there are very dfferent allocatons of nventory. These allocatons wll requre

apment y? - 16 - dfferent faclty capactes and are hence crtcal n the deve I of a strategc dstrbuton plan.

Table 2 shows whch system s favored for several dfferent characterstcs of the system C9].

26 apment y? dfferent faclty capactes and are hence crtcal n the deve I of a strategc dstrbuton plan. Whch of the two types of approaches should be adopted general I There s no drect answer and each of the two approaches must be evaluated separately. Table 2 shows whch system s favored for several dfferent characterstcs of the system C9]. The analyss of many of these factors can be based on a very general prncple of nventory management: hold nventory before the hgh value-added step. That sj f delvery to the fnal echelon s a hgh value-added step n terms of a II costs; hold the nventory central ly n the central system. Ths prncple can be llustrated by ts applcaton to the characterstc of the number of remote warehouses. Uth a large number of remote warehouses > the fnal echelon n aggregate adds a great deal of value) through addtonal nventory; to the product. It s hence benefcal to store ths nventory before the hgh value-added step n a central system. A large number of remote warehouses hence favors a central system.

I te ng e- -Eche ocat o ce on -eche I mu ocat 1 -eche on -eche ons on - 17-5.

The dependences of demand) for example^ from satellte locatons to central locatons) requre more sophstcated types of control than the smpler types of approaches for sngle locatons.

27 I te ng e- -Eche ocat o ce on -eche I mu ocat 1 -eche on -eche ons on Co ntrol of Inve n tory n a Mu 1 1 I n System Mult-stage dstrbuton systems pose ssues of nventory control as well as deployment. The dependences of demand) for example^ from satellte locatons to central locatons) requre more sophstcated types of control than the smpler types of approaches for sngle locatons. In the past several years) Dstrbuton Requrements Plannng) or DRPj has been proposed as an approprate means of controllng nventory wthn a mu I t Ion envronment. DRP uses demands; ether actual or forecasted) at the satellte locatons to determne replenshment requrements at the satellte I > and n turn to determne a requrements schedule at the central locaton or locatons. The approach) lke ts manufacturng analog materals requrements plannng) or MRP) uses a requrements schedule to develop a precse schedule of producton and procurements at the central locaton. DRP s desgned to deal wth some of the problems of coordnaton between central locatons and sae I locatons n a mu 1 1 I system. DRP) however) s not always the system q-^ c! lu for a I 1 I systems. For two-stage systems) the most typcal system for a manufacturng frm) there are actually three dfferent approaches for nventory control: Separate smple systems DRP Allocaton control Separate systems nvolve separate control systems for each locaton. Order-pont control s the most typcal. In ths type of approach) each locaton controls ts nventory ndependently usng order ponts and order quanttes characterstc of s I I nventory systems. When there are sgnfcant nteractons among locatons) for example when several satellte locatons smultaneously make large orders) an order-pont system can lead to

nventores. An echelon nventory conssts of the nventory at a sngle nstallaton as well as a I the nventory at succeedng locatons.

28 I of I te locaton lev I as th - la - problems. DRP s desgned to deal wth these problems through better schedulng of requrements at the central locaton. Smple control systems such as order-pont systems; however) can also be tormulated n terms ot echelon nventores as we I n terms of nventores at the specfc locaton) whch are referred to as nstallaton nventores. An echelon nventory conssts of the nventory at a sngle nstallaton as well as a I the nventory at succeedng locatons. For a two-stage system w a sngle central warehouse) for example) the echelon nventory for the central locaton conssts of the entre nventory n the entre system. Replenshment at the central locaton would therefore be based on total system nventory. Ths type of approach when assocated wth perpetual target nventores) s also known as a base stock approach and can a I late some of the problems of a smple order-pont systems. The fnal type of control system) the allocaton control system) s based on the concept of smultaneously replenshng groups of satellte locatons. When such a jont order reaches the central warehouse stage of the network) t s allocated and pushed out to the satellte locatons as expedtously as possble. The central locaton acts as a stagng area and hence the system s desgned for a satellte nventory deployment strategy. The best choce of nventory control for a mult-stage system depends on the means of nventory deployment and other characterstcs. Table 3 presents the control system approprate for the three man scenaros of two-stage nventory systems. For a satellte nventory deployment system) the central locatons are by defnton stagng areas and nventory s pushed out to the sate I locatons. An a I system s approprate here. For a central

I e I ty. th th gh 1 te th I sate - 19 - nventory deployment system w a moderate number of satellte warehouses) there are sgn+ leant dependences between the demands of the satellte warehouses.

However; w a central nventory deployment system w a large number of sate I warehouses or wth sma I I I te warehouses) demand at the central warehouses acheves a certan level of stab For example?

Ulhen demand at the central locaton s stable) the advantages of DRP are reduced) and a system such as order-pont control s suffcent.

29 I e I ty. th th gh 1 te th I sate nventory deployment system w a moderate number of satellte warehouses) there are sgn+ leant dependences between the demands of the satellte warehouses. Ths requres a h Uh level of coord naton n replenshment. a base stock system can be desgned to deal wth ths; a DRP system s clearly the system of choce. However; w a central nventory deployment system w a large number of sate I warehouses or wth sma I I I te warehouses) demand at the central warehouses acheves a certan level of stab For example? no sngle warehouse wll make batch orders that wll domnate demand at the central locaton or locatons. Ulhen demand at the central locaton s stable) the advantages of DRP are reduced) and a system such as order-pont control s suffcent. Uth a hundred satellte locatons wth ndependent demands) for example; t s not neccessary to tabulate detaled forecasts of satellte orders. There s a certan statstcal but stable pattern of demand at the central locaton) and the control parameters of the nventory control system can be adjusted for ths pattern. The mportant ssue for nventory control s that as servce) through addtonal facltes) s mproved) there s a certan level of coordnated control of nventores that s requred. As a frm expands from a sngle dstrbuton faclty or a small number of ndependently operated facltes) smple control systems must evolve to more sophstcated ones.

us o I t I e - 2D - ^ Ca ne I n there are a large number of ssues to address n the desgn and development of a

Ths artcle attempts to dentfy some of the key ssues n the dstrbuton part of the network.

cost and servce and ther senstvty to the number of f ac es - the desre for smaller terrtores but hgher volume

30 us o I t I e - 2D - ^ Ca ne I n there are a large number of ssues to address n the desgn and development of a manufacturng and dstrbuton network. Ths artcle attempts to dentfy some of the key ssues n the dstrbuton part of the network. Uh there s no one prescrbed method of system desgn and control) busnesses should be aware of - the tradeoff between cost and servce and ther senstvty to the number of f ac es - the desre for smaller terrtores but hgher volume coverage n areas wth greater demand dens ty - the senstvty of costs and locatons to exstng capactes durng the frms growth phase - how nventores can be allocaton between echel ons - the mportance of more sophstcated control n an expanded network.

- 21 - cat ans ley) References 1. R. ShapIrO) "Get Leverage from Logstcs") -ar'^'ard Bu sn e ss R e veuj ) May-June ) 1984. 2. R. ShaprQ) D. Rosenfeld) and R.

Bpraguej "Put a Prce Tag on Your Customer Servcng Levels") l-larvard Bu sn e ss R e ve u) 53 ) No. 4) p. 71-78. 4. R. Hayes and S. Wheelwrght). Re s torng our Compettve E d ge ) U 1984. 5. J.

31 cat ans ley) References 1. R. ShapIrO) "Get Leverage from Logstcs") -ar'^'ard Bu sn e ss R e veuj ) May-June ) R. ShaprQ) D. Rosenfeld) and R. Bahnj "Imp at Cost-Servce Tradeoffs on Industry Logstcs Structures"; to appear n Interfaces 3. H. Shycan and C. Bpraguej "Put a Prce Tag on Your Customer Servcng Levels") l-larvard Bu sn e ss R e ve u) 53 ) No. 4) p R. Hayes and S. Wheelwrght). Re s torng our Compettve E d ge ) U J. Magee) U). CopacnO) and D. Rosenfeld) Mo dern Lo gstcs Managem ent) Uley) 1985) Chapter ID. 6. ) Chapter A. Martn) Dstrbut o n Requrements Pla n nn g) Prentce-Hall) a. R. G. Brown) S tatstcal Forecast n g for Inv e ntory Control ) McGraw-H New York, I I) 9. M. Hamovch and T. Magnant ) "Extremum Propertes of Hexagonal Parttonng and the Unform Dstrbuton n Eucldean Locaton". Workng Paper OR ) Operatons Research Center, MIT, January) ID. D. Rosenfeld and M. Pendrock > "The Effects of Warehouse Confguraton Desgn on Inventory Levels and Holdng Costs )" Sloan Manag em ent Rev ew, Summer, 198D 11. See Rosenfeld and Pendrock for an explanaton of each.

te - 22 - Table 1 Smulaton far Central and Satellte Inventory

32 te Table 1 Smulaton far Central and Satellte Inventory Deployment Strateges Centra 1 Central Strategy Sate! I Strategy

me I te - 23 - Table 2 Factors Favorng Central or Sate I System System Favored as Fac tor Fa c tor Lev el Increa ses Value Added Central Number of

33 me I te Table 2 Factors Favorng Central or Sate I System System Favored as Fac tor Fa c tor Lev el Increa ses Value Added Central Number of Remote Warehouses Central Trans t T Sate Mte Procurement Tme Central Demand Correlaton among Regons Sate I I te Transshpment Costs Sales Level Central Satellte

th - 24 - Table 3 Inventory Control Strateges Approprate far Dfferent Scenaros Deploym ent See nar o Central wth

34 th Table 3 Inventory Control Strateges Approprate far Dfferent Scenaros Deploym ent See nar o Central wth numerous sate I I tes Central w lmted number of sate I I tes Sate I I te Bes t C o ntrol System orde po D.R.P. A I I ocat on nt