Control of Yarn Inventory for a Cotton Spinning Plant: Part 1: Uncorrelated Demand. Russell E. King 1 Leigh Ann C. Brain 1 Kristin A.

Transcription

1 Control of Yarn Inventory for a Cotton Spnnng Plant: Part 1: Uncorrelated Demand Russell E. Kng 1 Legh Ann C. Bran 1 Krstn A. Thoney 2 1 Department of Industral Engneerng 2 Department of Textle and Apparel, Technology and Management North Carolna State Unversty Ths research was supported, n part, by the Natonal Textle Center through the U.S. Department of Commerce. ABSTRACT In ths paper, a process control-based nventory control methodology s developed for a yarn spnnng plant. The technque attempts to control the nventory at a specfed level usng separate proportonal/dervatve control equatons for each product (yarn) type. The system s unque n that the controllng varable (number of spnnng frames producng a yarn type) s dscrete whle the output of the control equaton s contnuous. Addtonally, each controller s contendng for a common set of resources (spnnng frames). The approach s compared wth a tradtonal mn/max system va computer smulaton for the case of uncorrelated demand. KEYWORDS: spnnng, proportonal dervatve control, mn max control, nventory control, process control, cotton 1. Introducton In the globally compettve textle ndustry the ablty to meet orders n the lead-tme specfed,.e., servce level s crtcal. Ths s not a new phenomenon. In the late 1980 s Sara Lee Knt Products (SLKP) became unhappy wth ther yarn supplers. The supplers were unable to satsfy SLKP's large demand and the average spnnng machne at ther mlls was 20 years old. Consequently, n 1990, SLKP created Mountan Cty Yarn Mll so that t could reduce ts dependence on external yarn sources. Spnnng ther own yarn 1 resulted n more economcal and hgher qualty yarn (Textle World, June 1992). One approach for yarn supplers to mantan customer satsfacton and to keep customers from spnnng ther own yarn lke SLKP s to mplement a yarn nventory system that holds the optmal amount of yarn; enough to meet demand yet small enough to be cost effectve. In 1978, K. Govndarajulu and R. Nataraj studed the optmal n-process stock to be held n spnnng. The n-process nventory depends upon many factors such as yarn count, type of machnery, etc.

2 Establshng nventory control s a necessty for reducng costs and optmzng the use of lmted resources. Inventory s often the sngle largest asset and s a large porton of the workng captal n a company. Some stock s necessary because of the hghly compettve nature of the textle ndustry, whch can result n rapd deteroraton of ther stocks (Bartnk, 1989). It s also necessary due to machne down tme, mantenance trouble, and qualty problems. Inventory can be excessve as well as nadequate. Excess nventory may result n sellng pressure (Vellangr et al., 1991). Textle mlls whch use modern management scence tools fnd that the most proftable area to optmze and control s nventory (Dudeja, 1981). Some conventonal technques used n the cotton ndustry are stock levels and the economc order quantty (EOQ). Stock levels for safety stock, mnmum and maxmum stock, and reorder ponts avod excess holdng of nventory whle mnmzng stockouts. EOQ optmzes total nventory cost. The optmal level of nventory should consder forecast demand, product lfe, supply, prce, and compettor atttude (Vellangr et al., 1991). Spnnng plants that have routne manufacturng wth the same yarns can be modeled as make-to-stock systems. Wth make-to-stock plants, more emphass and control s requred of producton levels than n a make-to-order plant, but t s often easer to respond quckly to customer orders. The fnal products from the spnnng plant are smply yarn of a gven count and twst. Although a gven product can be used to create a varety of apparel tems, changes n the orgnal demand forecast wth regard to these attrbutes do not affect the spnnng plant. However, the plant must be able to react quckly to changes nvolvng demand n a whole product lne by producng ether more or less yarn of a certan count and twst. Standard technques to determne feedback and correctve acton n make-tostock plants are forecastng, materals requrement plannng (MRP) wth tmephased order ponts, capacty requrements 2 plannng (CRP), I/O control, work center loadng, and daly dspatch reports. Whle these technques are valuable n determnng defcences and surpluses n nventory, they do not determne the allocaton of resources. To do ths, a mult-product lnear programmng (LP) model wth lmted resources may be used. It can determne the amount of product to be produced n a gven perod. However, t assumes a known demand. Its goal s to mnmze costs. The 1- product producton LP model allows projected demand to dffer from actual demand but allows only for one product and has no capacty lmtatons. For a plant to have successful producton plannng, a combnaton of these two,.e., a multproduct, lmted resources model s needed. One approach s to use mn/max control,.e., mantan the level of nventory wthn a specfed range. Wth the mn/max algorthm, the maxmum level of nventory s based on storage constrants and carryng costs, whle the mnmum level s chosen to control stockouts. The nventory level s checked on a user-specfed frequency to see f t s above the maxmum level. If so, producton s stopped untl the nventory falls below the mnmum level. There are two types of parameters that characterze the control. The frst parameter specfes whether or not some frames are dedcated to hgh volume yarns. If so, those yarns whose average demand rate exceeds the producton rate of a frame are assgned dedcated frames. For example, f the daly demand rate for some yarn s 50,000 lbs. and the daly producton rate per frame s 15,000 lbs. then 3 frames would be dedcated to ths yarn yeldng a dedcated capacty of 3*15,000=45,000 lbs./day. The dfference (50,000-45,000=5,000 n ths case) would be made up on the frames not dedcated to some yarn. These frames are referred to as scheduled frames. The second parameter of the mn/max algorthm s the target range. Ths refers to the dfference between the maxmum days of supply target that sgnals a stop n producton of the yarn and the mnmum days of supply target that sgnals resumng producton of the yarn.

3 Scheduled frames are assgned yarns and operate ndvdually. Prorty on these frames s gven to the yarn wth the smallest net nventory poston (NIP). The NIP of a yarn type s the estmated supply n nventory f the yarn s not scheduled to run on ths frame. By regulatng NIP, the algorthm controls the yarn n stock. An alternatve to the mn/max system s to use a sngle target level. In ths paper a proportonal-dervatve (PD) process control-based control algorthm s developed to keep the nventory level for each yarn as close as possble to the target usng the NIP values. It s mplemented usng all frames as scheduled frames. Process control s desgned to control a contnuously rangng system varable usng a contnuously rangng control varable. However, n ths paper, we apply process control usng multple, dscrete control varables, namely number of spnnng frames runnng a gven yarn. Snce each yarn s competng for systems resources (frames), the algorthm must also handle contenton ssues when more frames are demanded than exst n the faclty. Performance of the PD method s compared to that of the mn/max algorthm n controllng the nventory of a smulated spnnng cotton plant and to analyze the robustness of PD process control. 2. The Model To compare the PD algorthm wth a mn/max algorthm, a stochastc smulaton has been developed (Powell, 1993). It models a cotton spnnng plant that produces n dfferent yarn types. Each product s specfed by a gven yarn count. The plant has m spnnng frames each wth s spndles that are operated h hours a day, d days a week. Yarn type s produced on a spnnng frame at a rate of r lbs/spndle/day. Upon doffng, there s a d c day conng/nspecton delay. The yarn s then placed nto nventory and s ready to shp. As prevously dscussed, spnnng frames can be ether dedcated or scheduled. A dedcated frame 3 s assgned a yarn type at the start of the smulaton and produces only that yarn. A scheduled frame s re-assgned a yarn type perodcally (every t tme unts) based on the need at that moment. A changeover delay s ncurred on scheduled frames when swtchng from one yarn type to another. Both dedcated and scheduled frames may be dle or busy. The rate of customer orders arrvng each day s λ. Each order s randomly assgned a yarn type from a yarn mx dstrbuton and an order quantty from an order sze dstrbuton wth average order sze O. There are two types of customer orders: contract orders and spot orders. κ represents the percentage of total orders that are contract orders. Contract orders are placed by the plant's regular customers and arrve once per week. Spot orders are generated by nfrequent customers and arrve at any tme durng the week wth exponentally dstrbuted nter-arrval tmes. Orders are flled each day wth a maxmum of x orders flled per day to reflect shpment capacty. All remanng orders are flled at the end of the week f stock allows. No shppng s done on weekends. Contract orders have prorty over spot orders, and older orders have prorty over newer orders. The plant s operated as make-tostock where the user specfes the average safety stock n terms of days of supply D. From ths, the overall desred yarn nventory level n pounds of yarn, Y, s calculated and a porton of t, y, s assgned to each yarn type. The goal s to satsfy customer orders wthn a target lead-tme, as well as keep the nventory at the user specfed level. 3. PD Process Control 3.1 The Algorthm The PD algorthm s mplemented every t tme unts. At tme t t calculates yarn 's NIP value, NIP (t), and compares t wth ts target level, y tar,. The dfference s called the error, e. By adjustng the number of frames runnng each yarn, the PD

4 algorthm attempts to allevate the error wthn a user-specfed amount of tme. The algorthm uses process control to regulate the nventory (see Johnson 1984). For each yarn type, NIP (t) s effectvely a contnuous functon of tme, ncludng the current number of frames runnng yarn type, N (t), spndle effcency, E, frame setup tmes, S, and customer order attrbutes, F o, (number of customer orders, order szes, product demand mx),.e., NIP ( t) = F( N ( t), E, S, Fo ). Varaton n these varables s responsble for creatng error (actual level - desred level) n NIP. Because of uncontrollable demand varatons, t s vrtually mpossble for the system to be error-free. Thus, the objectve s to mnmze the error. The number of frames runnng type, N (t), s the controllng varable for NIP (t) because t s the only varable that nfluences NIP (t) that can also be altered by the spnner. There s a separate control equaton for each yarn type. Snce there s a lmted number of spnnng frames, contenton may occur when the total number of frames requred for all yarns exceeds m, the total number of frames. In ths case, frames are allocated ndvdually based on the expected tme untl stockout, whch s a functon of NIP (t) and the average daly demand rate for yarn type. Process control uses a repettve procedure that nvolves feedback. Fgure 1 s a dagram of the steps nvolved. The model attempts to control a contnuous varable (NIP (t)) usng a dscrete, capactated control varable (N (t)). Steps 1 through 4 are repeated every t tme unts and are descrbed below. Fgure 1: Steps n the Control Process 4 Step 1: Measure the Controlled Varable A raw measurement must be taken of the controlled varable. Ths s smply the value of NIP (t) at the tme the algorthm s beng executed. NIP (t) s defned as the current nventory level n terms of pounds of yarn, INV ( t), plus any work n process, WIP ( t) mnus any outstandng orders for yarn, β (t). NIP ( t) = INV ( t) + WIP ( t) β( t) Step 2: Calculate the Error NIP (t) s compared to the target nventory level, y tar,, and the error s calculated. Postve error ndcates that there s too much yarn n nventory, whle the error s negatve when there s not enough yarn. e ( t) = NIP ( t) ytar, Step 3: Compute the New Controllng Varable The error must be translated nto the controllng varable's unts n order to correct the error. In other words, pounds of yarn must be translated nto number of runnng frames. PD (proportonal - dervatve) control s used whch attempts to modulate the nventory by consderng the sze and slope of the error curve. The control formula has a constant, proportonal, and dervatve term. Because the controllng varable s a dscrete varable, ths value s rounded. c () t = c + c () t + c () t o, p, d, Constant Term, c o, : Ths term s the number of frames needed to mantan NIP at the target level when the error s zero. In other words, t s the number of frames needed to meet the expected daly demand and s defned as: where c Op, = λ sr E o

5 λ = expected number of orders/day, O = expected order sze, p = percentage of total demand that s for yarn type, s = number spndles per frame, r = producton rate n terms of lbs./spndle day, and E = spndle effcency. Proportonal Term, c p, : Ths term attempts to correct devatons from the desred level of the controlled varable n amounts drectly proportonal to the error,.e., cp, () t = K p, e() t where K p, s a proportonalty constant for yarn type (wth unts of frames/lbs) 1 K p, =. tc1sr E The larger the absolute error, the more frames that should be allocated/deallocated. Ths term translates the error n terms of pounds of yarn nto the equvalent number of frames requred to make up that error. An nput parameter, c 1, specfes the number of t perods n whch to make up the error. In other words, t determnes how reactve the controller s to the observed error. Dervatve Term: c d, : The dervatve term s based on the tme rate of the change of the error,.e., Kd, ( e( t) e( t t)) cd, () t = t where the proportonalty constant c Kd, = 2 sr E and c 2 s a number relatng how mportant t s for the slope of the error to be zero. (c 2 = 0 mples havng a slope of zero s not mportant, c 2 = 1 mples havng a slope of zero s very mportant.). Ths term s not concerned wth the actual error, but wth the rate at whch the error s changng,.e., the slope of the error functon at the current tme. Ths factor attempts to stablze the nventory level by makng the slope of the error functon equal to zero. Even f the 5 error at the present tme s zero, there may stll be an nfluence due to the momentum of the system. The logc behnd the dervatve term s that f the slope s ncreasng/decreasng there s a hgh probablty that t wll contnue n that drecton and therefore, fewer/more frames should be allocated to account for the observed tendency. Integral Term: An ntegral term may also be ncluded (PID control) that s based on the hstory of the error curve wth the dea of tryng to force the average error over tme to zero. However, ths objectve s not relevant to an nventory system where customer servce s an mportant ssue and thus wll not be consdered further n ths paper. Step 4: Enact the Control Enact the new value of the controllng varable nto the process by reallocatng the spnnng frames so that the determned number of frames, c (t), are runnng yarn. Upon completng step 3, all frames are marked for reschedulng. After each frame has doffed, a reallocaton procedure that determnes the yarn that the frame should produce, based on the latest values of the controllng varables, s nvoked. 3.2 The Target Level The target level, Y tar, s the amount of yarn to keep n nventory to satsfy the demand for a specfed number of days, D tar. The average number of orders per day, λ, s multpled by the average order sze, O, yeldng the number of pounds of yarn requred to meet the average demand for a day. Thus, the target level s Y = λo. tar D tar The overall target level s dvded among each of the ndvdual yarns such that the probablty of a stockout s the same for all yarn types (see Powell 1993). In general, the PD controller yelds average nventory levels that are hgher than the target level. Ths s due to the fact that backorders are ncluded n the error term.

6 The target algorthm seeks an nventory level that s equal to the target level assumng all backorders are flled and all WIP s completed. Snce the shppng of orders s assumed to be spread across the entre week, yarn wll be held n nventory untl t s shpped. Ths wll make the average nventory level hgher than ts target level. 3.3 Choosng a value for t The t value determnes how often the target algorthm s evaluated. It must be set to a value that makes sense wthn the context at hand. For example, assume the plant runs on a sx day week where weekly contract orders arrve on Monday, the frst day of the week. To react quckly to these orders, the algorthm should be called soon after these orders have arrved. Therefore, a t value such that the net nventory poston s evaluated shortly after the arrval of the weekly contract orders s preferred. Spot orders can arrve at anytme. The more often the target algorthm s nvoked, the sooner the controller can react to these orders. Thus, n general, t s better to use smaller values of t. In ths expermentaton t s set to one day. Not only does ths react quckly to customer orders but t s a logcal choce,.e., re-evaluatng the nventory poston and determnng the frame schedule for the day each mornng makes more sense than reevaluatng t, say, every day and a half. 3.4 Determnaton of the c 1 and c 2 values Snce the system exhbts stochastc behavor, determnaton of the optmal parameter values (c 1 and c 2 ) for the algorthm s dffcult. Addtonally, t s desrable that the algorthm be robust,.e., able to work well under a varety of operatng condtons. Therefore, the approach taken here s to fnd good values for the parameters expermentally. Generally n process control, the proportonal term has the greatest mpact n the ablty of the controller to perform well. Ths term can be thought of as a macro 6 tunng knob whle the dervatve term s a fne tunng knob. The c 1 value desgnates the number of t perods n whch to make up the error. The c 2 value desgnates how mportant t s to have the slope of the error curve equal to zero. Ths factor handles the desre to have a constant, predctable nventory wth small standard devaton. In some cases, the contrbuton of ths parameter goes aganst the contrbuton of the c 1 parameter (such as when error s negatve wth an ncreasng slope). Other tmes, c 2 enhances the mpact of c 1 (such as when error s negatve wth a decreasng slope). The Nelder Mead (Olsson 1974 and Olsson and Nelson 1975) optmzaton procedure can be used to fnd a local mnma of a mult-parameter functon. It s an effcent and drect search algorthm that moves towards the smaller values by movng away from hgh functon values. The goal s to fnd values for c 1 and c 2 that perform well over a large range of key nput parameters. A half-factoral desgn was used wth two levels for each of the followng fve factors: Number of Yarns, Capacty Utlzaton, Product Mx, Number of Spnnng Frames, and Target Inventory Level. The functon evaluated at each desgn pont s the percent dfference between the tme weghted NIP value and the target level (percent error), averaged over 16 runs of length T,.e., 16 T 1 1 NIP ( t) ytar, f = dt 16 T y = 1 0 tar, The Nelder-Mead algorthm generates a smplex of v vertces where each vertex s a functon of v-1 varables. In ths case the varables are c 1 and c 2 and the smplex has 3 vertces. Gven a v th order smplex, the algorthm generates another pont that s a reflecton of the pont wth the largest functon value through the mdpont of the other ponts. The objectve s to replace the pont wth the hghest value. Based on the functon evaluaton at the new

7 pont compared wth those n the smplex, a new smplex s generated and the process s repeated. The algorthm s termnated when the dfference between functon evaluatons at the smplex ponts s less than a gven value or when the percent change wthn the ponts themselves s less than a gven value. Usng the Nelder-Mead algorthm t was determned that the best pont s at c 1 =3.075, c 2 = Through roundng ths optmal pont, the smpler values of c 1 =3, c 2 =0 are chosen as those whch wll perform well under a wde range of plant confguratons. Snce the demand s uncorrelated, t s ntutve that the c 2 value goes to zero. If demand was correlated, then t would be expected that the c 2 value would not be zero. The correlated demand case s explored n Kng, Bran and Thoney, Comparson of the Algorthms 4.1 Comparson Crtera As mentoned prevously, the PD algorthm tends to have an average nventory that s slghtly larger than the target level. A mn/max algorthm, on the other hand, tends to keep the average nventory level closer towards the mnmum level. These characterstcs are most obvous n cases wth a large number of yarns (18-36 yarns). Because of ths, the mn/max algorthm cannot be accurately compared to the PD algorthm wth a target level halfway between the mn/max levels. In order to compare performance measures such as percentage of on-tme orders and the varance of the nventory level, only cases that have approxmately the same average nventory level are compared, regardless of ther user-specfed target or mn/max levels. Separate scenaros nvolvng 6, 12, 18, 24 and 36 yarn types were smulated over a 5- year horzon. For each scenaro, the PD control algorthm was evaluated. The results were compared to mn/max control where two levels of target range (1-day and 5-day) were tested wth both dedcated and undedcated frames. In the fgures that 7 follow, the 18-yarn scenaros are representatve. For the sake of brevty, the results below are for the 18-yarn cases unless otherwse stated. In comparng the PD and the mn/max algorthms, the performance measures of nterest are the percentage of on-tme orders, nventory varance, and the number of frame changeovers. The frst relates drectly to servce. Inventory varance s mportant because a plant that has a steady nventory level can more lkely meet demand. Inventory can also be thought of as safety stock for customer orders. Therefore, lower varablty n the nventory allows for lower levels of nventory to be carred wthout sacrfcng customer servce. Frame changeovers relate to the varable component of operatng cost. Achevng low nventory levels wth fewer frame changeovers s more economcally proftable for plants. 4.2 Orders Shpped On-Tme Fgure 2: Percentage of On-Tme Orders vs. Inventory Fgure 2 shows the average nventory levels needed for each algorthm to acheve a certan percentage of overall orders shpped wthn 5 days. Notce that for the mn/max algorthms, the target range has lttle effect, but not dedcatng any frames yelds better on-tme shpments than dedcatng frames. In general, the PD algorthm s able to acheve a gven level of servce wth less nventory than the varous forms of the mn/max algorthm. For

8 example at about 80% on-tme shppng, the PD algorthm requres over 20% less nventory than any form of the mn/max algorthm. However, at on-tme levels above 90% the non-dedcated frame verson of mn/max outperforms the PD algorthm. Ths s acheved at the expense of frame changeovers and s dscussed n secton Inventory Standard Devaton The PD algorthm results n sgnfcantly lower nventory varance. Fgure 3 shows the average standard devaton of the nventory level for each of the fve algorthms tested. The PD algorthm has lower varance at any nventory level than any varaton of the mn/max algorthm. The standard devatons for the mn/max algorthm wth no dedcated frames were smlar regardless of the target range. The same s true for the mn/max algorthm wth dedcated frames. frame algorthm to acheve ts better shppng performance? And what does fewer changeovers mean to the PD algorthm n terms of shppng statstcs? To answer these questons, Tables 1 and 2 were constructed showng 95% confdence ntervals of the dfference between the PD algorthm and the varous mn/max algorthms. Operatng wth an average nventory of about 456,000 lbs., the mn/max algorthm wth a 1 day target range and nodedcated frames can acheve wth 95% confdence at best a 4.3% ncrease n ontme orders over the PD algorthm but at a cost of an extra 14.5 to 24.1 frame changeovers per day. At a hgh average nventory level of about 738,000 lbs, the mn/max algorthm wth a 5 day target range and no-dedcated frames can acheve at best a 2.09% ncrease n on-tme orders over the PD algorthm but at a cost of an extra 11.0 to 19.1 frame changeovers per day. Fgure 3: Inventory vs. Inventory Standard Devaton 4.4 Frame Changeovers The no-dedcated frame versons of the mn/max algorthm show better shppng performance compared to the PD algorthm at hgh levels of servce requrement. However, as shown n Fgure 4, the PD algorthm has fewer changeovers at all levels of nventory. What changeover costs are ncurred by the mn/max no-dedcated 8 Fgure 4: Inventory vs. Frame Changeovers Table 1: Confdence Intervals of the Dfferences Between the PD Algorthm and Mn/Max Algorthms wth Dedcated Frames

9 Table 2: Confdence Intervals of the Dfferences Between the PD Algorthm and Mn/Max Algorthms wth No Dedcaton 5.1 Impact of the Inventory Target Level The results from smulatons usng the PD algorthm were examned to determne the mpact of the target level on the performance parameters. Fgure 5 shows a nearly lnear relatonshp between the actual nventory level and the target nventory level. At smaller nventory levels, there s a slght curvature n the graph because the target level was not suffcent to meet demand. Ths mples that a certan level of nventory s needed to meet demand and the algorthm wll produce that level even though t s hgher than expected. After that level s acheved, the ncrease n nventory s proportonal to ncreases n the target level of nventory as shown by the lnear relatonshp. 5. PD Senstvty Analyss Whle the expermental desgn used to test the performance of the PD algorthm encompassed nput parameters such as number of frames, number of yarns, product mx and utlzaton, t s mportant to determne the mpact of the ndvdual parameters. Thus, algorthm performance s examned for robustness across a varety of nput parameters. Factors consdered n ths secton are target nventory level and the yarn to frame rato. A plant manager must know the potental consequences on performance when consderng changes n the system such as ntroducng new yarns or lowerng the nventory level. The lmts of applcablty and performance of the PD algorthm are explored. An expermental desgn consstng of 16 runs was used for each target level between 1 and 15 days. Results for key output parameters were averaged over the 16 runs to compute a value for the gven target level. 9 Fgure 5: Target Level vs. Inventory The absolute error between the actual level of nventory and the desred level of nventory decreases as the target level ncreases as shown n Fgure 6. There are fewer customer backorders as nventory level ncreases snce there s more nventory n the system to satsfy demand. Thus, the slope of the error curve begns to level off. Fgure 6 shows ths occurrng around a target nventory of ten days. No matter what the target level, there wll always be a certan amount of error n the system. Ths s due to the fact that demand occurs nstantaneously (orders arrve as a group) whle the producton rate s fnte. Thus, t takes some tme to make the stock to return the nventory to ts target level.

10 Fgure 6: Target Level vs. NIP Error Fgure 7 shows how order leadtmes are affected by target nventory level. As target nventory ncreases, order leadtmes decrease. The largest mpact s seen n the smallest nventory levels. Fgure 7: Target Level vs. Order Lead-Tme 5.2 Impact of Yarn/Frame Rato Two-year smulaton runs were performed varyng the number of frames from 6 to 60 and the number of yarns from 6 to 36. The yarn to frame rato has a drect mpact on the on-tme orders and order leadtme. Fgure 8 shows an approxmately lnear relatonshp between ths rato and the order lead-tme. At small ratos, the leadtme s almost varance free. As t clmbs above 1, the varance ncreases. Thus, a plant manager can determne the number of machnes needed gven a target lead-tme and the number of yarn types to produce. It also shows that producton varety can be harmful to performance. Fgure 8: Yarn to Frame Rato vs. Order Lead-Tme 6. Conclusons The PD algorthm performs much better than the mn/max algorthm n terms of shppng performance, nventory varance, and frame changeovers. Ths algorthm results n an average nventory that s larger than the desred target level. The PD algorthm s relatvely stable when consderng the mpact of capacty utlzaton, percentage of contract orders, and demand mx on overall on-tme shppng performance. A target level of reasonable sze (dependng on the number of yarns) should be chosen to ensure a small error term as well as good shppng statstcs. If the target level s too small, the percentage of on-tme orders wll suffer. Much of the PD senstvty analyss yelded expected results and thus verfes the correctness of the model. One mportant aspect uncovered was the mportance of the yarn-to-frame rato on performance. In the scenaro used, models wth a yarn-to-frame rato under 0.75 experenced deal performance. Whle the number of frames and yarns are mportant parameters ndvdually, together ther rato s a determnng factor of the system s performance. Wth ths n mnd, the value of ths expermentaton s not just n the numbers and graphs presented, but n the fact that plant managers should not necessarly focus on one parameter, but on the possble nteracton of two or more parameters. 10

11 In part 2, a comparson of the mn/max and PD-based controllers s presented under the assumpton of correlated and seasonal demand processes. Bblography Anon. (1992), Mountan Cty: Oh, What a Yarn Mll!, Textle World, June, pp Bartnk, Z. T. (1989), Focus on Inventores, Textle Asa, February, pp Dudeja, V. D. (1981), Inventory Control n Textle Mlls, The Indan Textle Journal, August, pp Author Informaton: Russell E. Kng Department of Industral Engneerng Box 7906, NCSU Ralegh, NC kng@ncsu.edu Legh Ann C. Bran Cary, NC Krstn A. Thoney Department of Textle and Apparel, Technology and Management Box 8301, NCSU Ralegh, NC krstn_thoney@ncsu.edu Govndarajulu, K., and Nataraj, R. (1978), Optmum Process Stock n Cotton Mlls, Indan Journal of Textle Research, 3, September, pp Johnson, C.D. (1984), Mcroprocessor-Based Process Control, Prentce-Hall, Inc., Englewood Clffs, N.J. Kng, R.E., L.C. Bran, and K.A. Thoney (2001), Control of Yarn Inventory for a Spnnng Plant: Part 2: Correlated Demand and Seasonalty, workng paper. Lord, P.R. (1978), Spnnng: Converson of Fber to Yarn, School of Textles, N.C. State Unversty. Powell, K.A. (1993), Interactve Decson Support Modelng for the Textle Spnnng Industry, Master of Scence Thess, Industral Engneerng Department, N.C. State Unversty. Vellangr, A., and Dheenadayalu, N. (1991), Inventory Management n Cotton Textle Industry, The Indan Textle Journal, December, pp