APPLICATION OF INVENTORY CONTROL PROCEDURES TO AN ELECTRONIC PARTS
WAREHOUSE
by
Lowell E. Solien
ARTHUR LAKES LIBRARY COLORADO SCHOOL ol MINES
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A th e sis su b m itted to th e F acu lty an d Board of T ru stees of th e
Colorado School of M ines in p artia l fulfillm ent of th e req u irem en ts for th e degree of M aster of Science (M athematics).
Golden, Colorado D ate Golden, Colorado D ate i C K h i , i W Signed: Lowell E. Solien Dr. R. E. D. Woolsey T hesis Advisor
Dr. Ardel J . Boes, Head D ep artm en t of M athem atics
ABSTRACT
Inventory control in a n in d u stria l organization m u s t an sw er som e fu n d am e n tal q u estio n s in order to perform its assigned ta sk . T hese q u estio n s are
1) w h at to stock? 2) how m u c h to stock? 3) w hen to order ? 4) how m u c h to order?
The p u rp o se of th is th e sis is to analyze th e se choices a n d show how one com pany is applying th e concepts of inventory control to lower costs w hile providing a n acceptable level of cu sto m er service. The su b je ct com pany is a p ro d u cer of television satellite receiver system s in th e D enver area. The com pany’s initial inventory control system w as largely intuitive. The goal is to su g g est so lu tio n s w hich w ould n o t have
u n accep tab le d raw backs w ithin th e com pany. The final p ro d u c t w as politically feasible a n d show s significant im provem ent over th e previous system a s m e asu red b y p re se n t w orth.
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TABLE OP CONTENTS
PAGE
ABSTRACT m
LIST OF TABLES AND FIGURES vi
ACKNOWLEDGEMENTS v«
C h a p ter 1. INTRODUCTION 1
C h a p ter 2. INVENTORY MODEL OPTIONS 4
2.1 A lgorithm s 4
2.2 R eorder Points 9
2 .3 Safety Levels 11
2 .4 Q u an tity D isco u n ts 14
C h ap ter 3. HOUSTON TRACKER SYSTEMS 17
3.1 B ackground 17
3.2 Initial O bservations 19
3.3 Invetoiy P rocedures 22
3 .4 O perating C onditions 24
C h a p ter 4. THE REVISED SYSTEM FOR HTS 38
4.1 Overview 38
4 .2 Revised C osts 39
C h a p ter 5. CONCLUSION 47
REFERENCES CITED 50 APPENDICES
A. G lossary 52
B. V ariable Listing 55
C. E xplanation of P art C ategories 57
D. E xplanation of LOTUS 1-2-3 C ost S p read sh eet 59
E. Use of STORM II a n d QSOM 61
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LIST OP TABLES AND FIGURES
TABLE PAGE
3.1 Sam ple of C andidate Lines to Delete 28
3 .2 Sam ple of Lines to R em ain in Stockage 31
3.3 C osts For Sam ple of R etained Lines 33
3.4 C ost by Category for R etained Lines 35
4.1 Revised C osts For 23 (Retained) Line Sam ple 40 4.2 Safety Stock C arrying C ost a n d Service Level 41
4.3 C ost Projections - Revised System 44
C -1 P a rt C ategories 58
FIGURE
ACKNOWLEDGEMENTS
I w ould like to express m y appreciation to th e m em bers of m y th e sis com m ittee w ho guided m e in th e com pletion of th is endeavor. A special th a n k s to Dr. R.E.D. Woolsey w ho co n stan tly challenged h is stu d e n ts w ith th e applied a sp e c t of education. He h a s b een th e finest academ ic advisor a s tu d e n t could hope for.
M any th a n k s to Prof. William R. As tie a n d Dr. Paul L. A nderson who were in stru m e n ta l in helping m e deal w ith th e sta tistica l asp ects of th is project a n d in m y com pletion of th e CSM cu rricu lu m . I w ould also like to th a n k Dr. R u th M aurer for h e r help a n d advice in research in g th is
problem .
My sin c erest g ratitu d e goes to th e m an ag em en t a n d em ployees of H o uston T racker S ystem s who tolerated m y p e rsiste n t q u estio n s an d p resen ce for n early a year. T heir cooperation w as p a ra m o u n t in th e com pletion of th is d o cu m en t a n d w as indicative of th a t com pany’s com petitive spirit.
I especially w an t to th a n k m y wife, Birgit, for h e r help an d
u n d e rsta n d in g th ro u g h o u t th e com pletion of m y th esis. H er c o n s ta n t en co u rag em en t an d a ssista n c e co n trib u ted m ore th a n all of m y w ork com bined.
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C hapter 1 INTRODUCTION
Inventory is th e stock of an y item or item s u se d in a n organization (Chase a n d Aquilano 1989, 579). Inventories are one of m an y
ex p en d itu res th a t com panies m ake in order to carry o u t th e process of p ro d u ctio n an d m arketing. A lthough frequently tre a ted a s a n
u n im p o rta n t a sp e c t of th e pro d u ctio n process, its value m ay co n stitu te a large portion of th e sales revenue of th e average m a n u fa ctu rer. For
exam ple, d u rin g th e m o n th of April, 1989 to tal sales from U.S. m a n u fa c tu re rs of electronic m ach in ery were $17 .9 billion. O n h a n d inventory for th e m onth, however, w as estim ated to be $ 3 7 .4 billion (Survey of C u rren t B u sin ess 1989, 93). This is over 200% of gross sales for th e m onth. T he carrying or holding cost associated w ith th e value of th is inventory is trem en d o u s a n d will be d iscu sse d la te r in th is
docum ent. N evertheless, controlling th e level of inventory ca n re s u lt in significant cost savings to th e com pany from th e sta n d p o in t of b o th p u rc h a s e a n d carrying costs.
Since com panies u su a lly w a n t to minim ize costs to aid in
m axim izing profits, th e ability of a corporation to lower co sts associated w ith inventory is beneficial. Given th is, it is ironic th a t th e m an ag em en t in m an y inventory holding entities (e.g. corporations, sm all b u sin e sse s, a n d even th e U.S. Army) never feel th a t a problem exists u n le ss th e y are u n a b le to provide th e p a rt or n ec essary m aterial u p o n dem and.
Therefore, cu sto m er satisfactio n becom es th e alarm . The p o in t is th a t th e co sts asso ciated w ith ordering a n d holding inventory (the variable costs)
are largely h id d en a n d m ay be overlooked by m anagem ent. For exam ple, u n its responsible for th e stockage a n d issu e of rep air p a rts in th e U.S. Arm y are driven strictly by th e level of service th ey can provide th eir cu sto m ers. The leadership is totally unco n cern ed a b o u t th e in d irect costs of holding an d ordering stock. However, th ese costs are j u s t a s real an d n ec essary a s capital in v estm en t dollars (Stermole 1974, 144).
W ithin a com pany, different p erso n n el will have different opinions o n inventory control. The a c c o u n ta n t w a n ts to minim ize th e dollar value a t an y given tim e and, therefore, w a n ts inventory levels k e p t low. The p u rc h a sin g d ep a rtm e n t w a n ts to m ake as few p u rc h a s e s a s possible so w ould like to order large lot sizes infrequently. On th e o th e r h a n d , th e inventory m an ag er is literally ab u sed w hen he ca n ’t provide a p a rt an d lives by th e adage th a t m ore (on hand) is b e tte r th a n less. The problem , th en , is to b alan ce th e cost of th e inventory an d cu sto m er service level. In a n u tsh e ll, th is is th e p u rp o se of inventory control. An inventory system ca n th e n be defined as th e controls an d policies for determ ining:
1) th e level of inventory to m aintain; 2) w hen to reo rd er stock;
3) how large orders sh o u ld be (Chase an d Aquilano 1989, 579). M uch w ork h a s b een done in th e a re a of inventory control, resu ltin g in a n u m b e r of lot-sizing algorithm s. The ability to u se m an y of th e se m eth o d s ca n be h in d ered b y two problem s.
1. The algorithm m ay require a relatively ac cu ra te m ethod of forecasting d em an d s by tim e period. R andom or sto c h astic d em an d can m ak e th is very difficult.
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w ho u se it. An extrem ely com plicated algorithm th a t re su lts in lower co sts ca n fail sim ply b ec au se it is n o t un d ersto o d . The u s e rs have to believe in it: sim plicity is a decision criteria.
A n u m b e r of m odels were considered while form ulating th e final recom m endation for th e com pany involved in th is study. T hese m odels are d isc u ssed in detail in th e n ex t ch ap ter. The final recom m endation w as n o t b ase d on a given algorithm ’s ability to produce th e m inim um cost of operating th e inventory. While th is w as a consideration, m ore realistic criteria were:
1) will th e algorithm significantly lower variable costs over th e p re se n t system ;
2) th e type of system required to forecast dem ands;
3) acceptability by m an ag em en t a n d th e u s e rs of th e system ; 4) w h at ca n be econom ically a n d logically in stitu te d .
The bottom line is n o t w h a t system is optim al, b u t w h at can be
realistically im plem ented an d still show im provem ent over th e p re se n t system .
T he following c h a p te rs d o cu m en t how applying basic inventory control p ro ced u res c a n im prove operating conditions w ithin a com pany. The specific a sp ects considered are th e variable costs of operating th e inventory an d th e cu sto m er service level afforded by th e new system . While th e final p ro d u c t is n o t a n optim al solution b ase d on a n n u a l cost, its im plem entation is a n d will re s u lt in significant cost savings for th e com pany involved, H o uston T racker S ystem s (HTS).
C hapter 2
INVENTORY MODEL OPTIONS
Inventory control theory, a s we know it, is prim arily a n invention of th e 2 0 th century. The concept of lot-sizing w as first p u b lish ed in 1915 a n d a m ethod of com puting reo rd er points w as pub lish ed in 1934 by R. H. W ilson (Plossl a n d W ight 1967, 4). A pplication of th e theory w as slow to come a n d probably resu lted from th e w idespread u se of operations re se arc h tech n iq u es after World W ar II. W ith th e advent of th e com puter age, th e ability to apply relatively com plicated algorithm s to large
inventories h a s developed. A few of th ese m ethods are d iscu ssed in th is chapter.
2 .1 Algorithms
Several algorithm options were considered while form ulating th e final recom m endation for th e m a n ag em en t of HTS. A lthough optim ality m ay be m easu red by lower to tal a n n u a l cost, th e ability to im plem ent a given system becom es th e real b o tto m line. In th is case, additional c o n stra in ts were: to form ulate a system th a t m an ag em en t could easily g rasp in a briefing w ith o u t atten d in g a g rad u ate level college course an d to acknowledge th a t d em an d s could n o t be accu rately forecast.
T he W agner-W hitin algorithm is probably th e m o st com m on of all m odels th a t are classified a s dynam ic program m ing approaches. It u se s a repetitive pro cess to exam ine all alternatives for ordering to satisfy
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low est to tal controllable cost (Tersine 1982, 341). While W agner-W hitin does re s u lt in a n optim al solution from th e cost stan d p o in t, it h a s som e serio u s draw backs. Since it exam ines all alternatives for cost
com parison, W agner-W hitin rapidly becom es com putationally expensive a s th e total n u m b e r of item s stocked increases. Additionally th e
algorithm req u ires a relatively ac cu ra te dem and forecast for several periods into th e fu tu re. In th is case, th e ability to forecast d em an d s by period w as questionable a t b e s t an d w ould probably have resu lted in freq u en t recalculation of ordering schem es for th is algorithm .
Two p o p u lar h eu ristic m eth o d s were developed by E dw ard Silver a n d H arlan Meal. T hese m eth o d s are very sim ilar except th a t one allows
reo rd ers a t an y tim e while th e o th e r req u ires th a t rep len ish m en ts be m ade a t th e beginning of discrete tim e periods (Tersine 1982, 341-342). T he Silver a n d Meal h e u ristic s a tte m p t to minim ize th e average cost p er period a s m e asu red by holding an d carrying costs. While n o t optim al, th e se m eth o d s yielded total co sts w ithin 1% of th o se obtained w ith W agner-W hitin in te s ts cited by W inston (W inston 1987, 819-821). The Silver a n d Meal algorithm s also require less com putational effort th a n W agner-W hitin. The p rim ary draw back is still th e req u irem en t for a relatively good forecast of d em an d s for m ultiple periods in th e future.
P art-period b alan cin g eq u a tes order cost an d holding co st derived p art-p erio d s to generated part-periods. A part-period is th e q u an tity of a given item held in inventory m ultiplied by th e n u m b e r of periods th e p a rts are held (Tersine 1982, 346). The m ethod eq u ates order an d
holding co sts in te rm s of p art-p erio d s by ad ju stin g th e order horizon. The order horizon is th e n u m b e r of tim e periods of forecasted d em an d for
w hich a n order will be placed. While th is m ethod will n o t perform as well a s Silver a n d Meal or W agner-W hitin, th e re su lts are generally b ette r th a n econom ic order quantity, w hich will be d iscu ssed later. The problem is th a t part-period balan cin g is also d ep en d en t on a forecast of dem and by period, m ultiple periods into th e future.
An in terestin g alternative to com plicated algorithm s is lot-for-lot ordering. T his m ethod sim ply orders b ased on th e forecasted d em an d s in upcom ing periods by th e exact q u a n tity required for each period.
Therefore, one order is lau n ch ed for th e q u an tity forecasted for each period (Tersine 1982, 341). While th is m ethod effectively m inim izes holding costs, it totally ignores th e cost to order an d an y available price b re a k d iscounts.
The econom ic order q u an tity (EOQ) m odel is probably th e m o st com m only u se d th ro u g h o u t in d u stry today. It is also one of two m odels cu rren tly u se d by th e U.S. Army (D.A. 1984). While it is frequently referred to a s th e W ilson EOQ model, th e classic m odel w as actually developed in 1915 by F. W. H arris of W estinghouse C orporation (Winston
1987, 682). The EOQ algorithm essentially a ttem p ts to m inim ize th e cost of carrying or holding inventory a n d th e cost to place orders. By picking th e p o in t a t w hich th e se cost curves intersect, variable costs have
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The to tal cost of stocking a n item th e n becom es
T C = R P + ^ - + £ f - (2.1)
w here
TC = to tal a n n u a l co st of stocking a n item or line of inventory, R = a n n u a l dem an d in u n its,
P = p u rc h a se cost of a u n it, C = order cost p er order,
H = PF = holding cost p e r u n it p er year, Q = lot size or order q u a n tity in u n its,
F = a n n u a l holding co st a s a fraction of u n it cost.
T he te rm (RP) is th e to tal a n n u a l p u rc h a se cost for th e inventory line. (CR)/Q is th e fixed co st of ordering on a n a n n u a l b a sis for th e line. This term is d ep en d en t on th e order co st p er order (C). The cost c o n s ta n t (C) is in d e p en d en t of order size an d co n sists of su c h expenses a s
bookkeeping, h an d lin g costs, a n d generic costs of generating a n d
receiving a n order. (QH)/2 re p re se n ts th e holding or carrying cost for th e inventory line b ased on th e theoretical average inventory level of Q /2 . T his term is d ep en d en t on th e holding cost (F) w hich is th e co st of capital to th e com pany, taxes, in su ran c e, th e cost of storage, breakage,
obsolescence, a n d th eft expressed a s a fraction. It am o u n ts to a charge for p u ttin g a dollar in inventory in ste a d of o th er investm ent
opportunities.
hold, a n d order item s for inventory, no m ention is m ade of th e cost for n o t having a n item w hen it is needed. This term is com m only called th e sto c k o u t or p en alty cost. While th is is a very real cost to m o st
corporations, it is also u su a lly very difficult to quantify an d frequently left o u t of th e to tal cost equation. The EOQ algorithm does n o t tak e into ac c o u n t th e pen alty cost so it h a s b ee n om itted from equation (2.1).
The econom ic lot size to order (Q) is found by tak in g th e derivative of eq u atio n (2.1) a n d settin g it equal to 0.
Solving for Q yields
By tak in g th e second derivative of th e to tal cost equation, we have
This confirm s th a t we have found a m inim um .
Since th e to tal p u rc h a s e cost over a y ea r sh o u ld be c o n sta n t
reg ard less of th e lot-sizing schem e used, th is te rm w ould logically n o t be u se d in th e lot-size calculation. C o n sisten t w ith th is, th e p u rc h a se cost
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(R P) goes to 0 w hen th e derivative is ta k e n an d does n o t a p p e ar in th e com putation of Q. From th is
2 .2 R eorder P o in ts
In th e m o st sim plistic sen se of EOQ, rep len ish m en t is assu m e d to be in sta n ta n e o u s a t th e tim e th e req u irem en t is know n. W ith th is in m ind, th e o n -h an d b alan ce could always be allowed to go to 0 before a rep len ish m en t is initiated. The obvious reality is th a t th e re is a lead tim e asso ciated w ith ordering a n d receiving m o st item s stocked for a n
inventory. Generally, th ere is also a pen alty or sto ck -o u t co st associated w ith n o t having a p a rt o n -h an d u p o n dem and. The solution th e n
becom es to calculate th e expected u sag e d u rin g lead tim e a n d se t th e reo rd er p o in t equal to th is value. The equation th e n becom es
w here
n = expected n u m b e r of orders du rin g th e y ea r an d
w here
R 0 P = U (2*3)
w here
ROP = reo rd er point, L = lead tim e in m o n th s, R = a n n u a l dem and, or
R O P = % (2.4)
w here
L = lead tim e expressed in w eeks.
The previous calculation will w ork well a s long a s th e cycle tim e does n o t exceed th e lead tim e for replenishm ent. W hen lead tim e is greater th a n cycle tim e, th e reorder p o in t will exceed th e m axim um q u an tity o n -h an d . T his is b ecau se th e calculated order q u an tity (Q) will n o t la s t th e lead tim e required for rep len ish m en t. Hence, th e o n -h an d q u an tity will always be below th e reo rd er point. An alte rn a te reorder p o in t
calculation p resen ted by N ahm ias (Nahm ias 1989, 150) can be u se d in th is situ atio n .
1. Form th e ratio L/T. U nits m u s t be co n siste n t in th e fraction. 2. M ultiply th e fractional rem ain d er of th is ratio by th e cycle tim e to convert b a c k to th e b a se u n it.
3. M ultiply th e re s u lt from step 2 by th e d em and ra te to o btain th e reo rd er point. Again c o n siste n t u n its m u s t be u se d th ro u g h o u t th is
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calculation.
As a n exam ple, consider a n item th a t h a s a calculated Q of 25, a n a n n u a l d em and of 500 u n its, a n d a lead tim e (L) of 6 w eeks. The cycle tim e (T) is 2 5 /5 0 0 = .05. Applying th e above algorithm :
1. L /T = (6 /5 2 )/.0 5 = 2.31. Notice th a t lead tim e h a d to be converted to a n a n n u a l b a sis to be co n siste n t w ith th e cycle tim e. The 2.31 in d icates th a t every order h a s to be initiated 2.31 cycles in advance.
2. (.31)(.05) = .0155
3. ROP = (.0155)(500) = 7.75 or 8
2 .3 S a fety L evels
One of th e a ssu m p tio n s in th e basic EOQ m odel a s well a s th e o th er m odels d isc u ssed is th a t fu tu re d em an d s are relatively co n tin u o u s an d know n w ith certainty. T his condition is u su a lly referred to a s
determ inistic dem and. A ctual dem and, as in th e case of HTS, is
frequently u n k n o w n or m ore ran d o m in n a tu re . The problem is to p ro tect ag a in st a sto ck o u t d u rin g u n k n o w n dem and. One solution is to do
n o th in g a n d atte m p t to satisfy abnorm ally large d em an d s by expediting orders a s required. T his n o t only forces th e com pany to b e a r th e cost of a sto c k o u t b u t also to in c u r th e added cost of expediting delivery w hen necessary.
A nother ap p ro ac h is to m a in ta in safety stock in anticipation of flu ctu atio n s in dem and. If th e safety level is well chosen, th e re su lt can be greatly im proved service to th e custom er. The dow nside is th a t a s th e safety level in creases to offer g reater protection a g a in st a stockout, th e
carrying cost also increases. This carrying cost can become significant quickly. Referring to equation 2.1, th e carrying or holding cost associated w ith Q is
f
The carrying cost for safety stock, however, is calculated a t full value. This assu m es th a t th e safety stock is never u sed an d theoretically it is not. The cost of stocking th e safety stock th e n becom es
(s)(H)or(sHP)(F) (2.6)
w here
s = th e n u m b er of item s held a s safety stock.
Several m ethods of calculating a n appropriate safety level are available. One m ethod is to select a level based on days of supply (DA
1984, 271). This is the m ethod currently used by th e U.S. Army for repair p a rts stockage. The safety level using th is m ethod th e n becom es
s = (SLD)(D) (2.7)
where
SLD = safety level days,
D = average daily dem and.
While th e days of supply m ethod is extremely sim ple an d easy to com pute, it’s ability to protect ag ain st a stockout condition is
ARTHUR LAKES LIBRARY COLORADO SCHOOL o£ MINES
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questionable. This follows since th e selection of the SLD is n o t related statistically to fluctuations in dem and.
A m ore commonly accepted safety level com putation involves
selection of th e custom er service level and sta n d a rd deviation of dem and (Tersine 1982, 140). This m ethod assu m es th a t dem and is norm ally distributed; however it can also be adapted to a poisson distribution. The com putation of safety level now becom es
s - Z g- Zgd^ L (2.8)
where
Z = sta n d a rd norm al deviate,
a = estim ated sta n d ard deviation of lead tim e dem and, L = lead time,
gd = estim ated sta n d a rd deviation of dem and.
T hroughout th is thesis, th e sta n d a rd deviation is estim ated from the m ost recent 52 weeks of dem and history.
One of th e m any advantages to th is m ethod is th a t it can be adapted to a desired custom er service level. In th is case, custom er service is
defined as th e probability of n o t incurring a stockout during lead time (Nahmias 1989, 201). By choosing a desired service level, we effectively define the percent of the area u n d e r th e sta n d ard norm al curve to trap. The appropriate Z value is th e n tak en from a sta n d a rd norm al table to trap th is area. As an example, for a custom er service level of 97.5%, the
corresponding Z value w ould be 1.96 (Scheaffer a n d McClave 1986, 610). As a w ord of caution, th e s ta n d a rd deviation m u s t be calculated from
d a ta in th e sam e u n its a s th e lead tim e.
2 .4 Q u an tity D isco u n ts
C om panies can frequently p u rc h a se a t a d isco u n t by buying in quantity. Two m eth o d s of doing th is are th ro u g h in crem en tal q u an tity d isc o u n ts an d all-u n it d isco u n ts. Increm ental quan tify d isc o u n ts would offer, for exam ple, th e first 100 u n its a t one price, th e n ex t 1,000 u n its a t a lower price , a n d p erh ap s th e n ex t 5,000 u n its p u rc h a se d a t still a lower price. In th is m an n er, th e d isco u n t is increm ented over th e
q u a n tity p u rch ased . A ll-unit d isc o u n ts apply to all th e u n its p u rch a sed u n d e r one requisition. If a d isc o u n t is offered for buying over 500 u n its of a n item , all th e u n its p u rc h a se d are discounted a n d n o t j u s t th o se over 500. We will concern ourselves w ith th e all-u n it discount; a s it ap p ears to be th e m o st com m on a n d is th e type offered by th e vendors of HTS.
The concept of all-u n it d isc o u n ts is b e s t p rese n ted by T ersine th ro u g h th e following verbal algorithm (Tersine 1982, 88).
1. C alculate th e to tal co st for each p rice-break quantity. This is done u sin g eq u atio n (2.1). A price-break is defined a s th e low est q u an tity th a t th e d isc o u n t is available for.
2. C alculate th e EOQ for each u n it price u sin g equation (2.2). 3. C alculate th e to tal co st for each valid EOQ u sin g equation (2.1). A valid EOQ is one greater th a n th e price-break quantity. The price-b reak q u an tity is 0 for u n its w ith no q u an tity discount.
T -3850 15
4. The low est cost is in cu rred by picking th e q u an tity w ith th e low est to tal cost found in 1 or 3 above.
The following exam ple is p resen ted by Tersine: w here R = 8,000 C = $ 3 0 .0 0 / order F = 30% p e r u n it co st p e r y ear P = $1 0 .0 0 for Q < 500 = $ 9 .0 0 for Q >= 500 Step 1. TC = 8000(9) + = $73> 155.00 Step 2. „ ^ 12(30)8000 _ .
Qw = V~L
0(
30r =400“mtt
„ ^ 12(30)8000 . a = V “ i0 ( W =422m mThe EOQ w ith $ 9 .0 0 is invalid since it is unavailable for order q u an titie s less th a n 500. The EOQ w ith $ 1 0 .0 0 is valid. The total cost for th e valid EOQ follows in step 3.
Step 3.
r c = 8000(10)+ M + M ^ = $81.20000
HUU «
Step 4.
The co st order q u an tity is 500. This is found by com paring th e to tal costs for th e valid EOQ a n d th e price b re a k quantity.
This c h a p te r serves a s a brief p resen tatio n of th e concepts applied in th is th esis. It is n o t in ten d ed to be a com prehensive d iscu ssio n of th e th eo ries of inventory control. The n ex t ch a p te r will serve to a c q u a in t th e re ad e r w ith th e original inventory system in u se a t H ouston T racker System s.
T-3850 17
C hapter 3
HOUSTON TRACKER SYSTEMS
3 .1 Background
H ouston T racker S ystem s (HTS) is a wholly owned su b sid iary com pany of E chosphere Corporation; b o th are located in Denver,
Colorado. HTS officially m a rk e ts a variety of television satellite receiver sy stem s u n d e r th e n am es of HTS a n d E chosphere for d istrib u tio n in N orth A m erica an d E urope. The com pany’s p ro d u ct is th e decoder box. All o th er com ponents of th e system are p u rc h ase d off th e shelf a n d
packed w ith th e decoder to m ake a receiver system . E chosphere a n d HTS offer 12 different m odels of decoder boxes u n d e r th e two com pany
n am es. T hese m odels are available in a m u ltitu d e of c o n fig u ratio n s/se ts to d istrib u to rs or th e individual decoder box m ay be p u rch ased .
HTS does n o t produce th e ir p ro d u ct b u t co n tra cts for it’s pro d u ctio n from one or m ore com panies in th e O rient. They do, however, design th e p ro d u ct in th e ir engineering d ep artm en t. The ability of th e se overseas facilities to produce a quality p ro d u c t ready for sale h a s come u n d e r q u estio n an d th is, com bined w ith lim itations on technology th a t can be shipped overseas (such a s video ciphers), h a s forced HTS into opening p o st-p ro d u ctio n facilities in D enver a n d H olland. T hese facilities serve a s final boxing an d te s t cen ters, a n d a s facilities to perform in tricate
m odifications, assem bly com pletion, an d an y rep airs necessary.
C onsequently, every receiver sold is processed th ro u g h one of th e se two facilities. The D enver p ro d u ctio n facility em ploys approxim ately 100
perso n n el who are involved w ith th is process (not including th e corporate h ead q u arters). Over h a lf of th e se people are hired th ro u g h tem porary agencies.
The com pany is organized u n d e r S u b ch ap ter "S" of th e Internal Revenue Code. T his m e a n s th e corporate incom e c a n be d istrib u ted directly to th e com pany sh a re h o ld ers a t th e ir individual ta x rate, thereby avoiding th e corporate ta x (Downs an d G oodm an 1987, 408). The ow ners of th e com pany are a ssu m ed to be in th e 33% effective ta x bracket. One c a n theorize th a t th e ir motive for organizing u n d e r c h a p te r S is related to th e ta x tre a tm e n t afforded su c h a com pany. HTS is profitable. The
m a rk -u p on it’s p ro d u c t is approxim ately 77%. An estim ate from one inform ed individual is th a t th e com pany will realize a 22% -30% after ta x re tu rn on invested capital for ta x y ea r 1989. The sam e individual
classified 1989 a s a ra th e r flat year.
HTS m a in ta in s a rep air p a rts stockage th a t serves a variety of p u rp o ses. The stockage initially consisted of over 1,700 sep a rate item s (as of D ecem ber 1989) a n d w as valued a t roughly $ 2 .8 4 million. This stockage feeds th e pro d u ctio n facility in Denver a n d serves a s th e su p p ly source for all HTS a n d E chosphere rep air cen ters in N orth America. It also su p p lies th e in te rn a l R esearch a n d D evelopm ent (R a n d D)
d e p a rtm e n t a n d individual cu sto m ers. This m ean s th a t d em an d s are determ ined by th e pro d u ctio n schedule, R an d D efforts, an d th e failure of u n its in th e field. The com pany does n o t have a good system of
forecasting pro d u ctio n req u irem en ts so com bined d em and te n d s to be highly ran d o m a n d unknow n.
T-3850 19
inventory m anager, two w arehousem en, a n d a tem porary d a ta en try clerk w ho also perform s th e function of a w arehousem an. This staff a p p e a rs able to h an d le w ork req u irem en ts for an y given day.
3 .2 In itia l O bservations
The a u th o r first becam e involved w ith th e HTS inventory in A ugust of 1989. R esearch revealed a wide range of problem s to include a n inventory control system th a t w as m anaged largely by intuition. T h a t is to say, stockage levels were se t by th e inventory m an ag er b a se d on intuitive g u ess a n d n o t by a sta n d a rd algorithm . There were indications th a t th e com pany’s cost to m a in ta in th e inventory w as too high. In a n in d u stry w here obsolescence ca n re n d er a n inventory line u se le ss quite rapidly, holding co sts ca n be considerable du e to th e inability to liquidate stock. The com pany can have dollars locked u p in obsolete inventory lines th a t have no salvage value. In th is situ atio n , th e holding cost co n tin u es to accrue. A review of th e HTS Bill of M aterials list d ated
0 9 /1 5 /8 9 revealed th a t of 1,726 lines listed, 620 h a d no dem an d histo ry in th e la s t 18 m o n th s. Of th e 620 lines, 271 show ed q u an titie s on h an d . M any of th e rem aining 1,106 lines showed extrem ely high o n -h an d q u an titie s a s d em o n strated by m ultiple y ears of stock on-h an d .
In A u g u st 1989 th e re were initially 2 p a rts stockages h o u se d in ad ja ce n t room s; one for HTS to serve th e production line a n d HTS service cen ters a n d a second to serve E chosphere service centers. An early
sim ilar p ro d u ct lines. This h a s b een com pleted. The a m o u n t of
duplication betw een th e se w areh o u ses w as trem en d o u s although th e E chosphere w areh o u se w as m iniscule com pared to th e HTS stockage.
The com pany h a s 4 co m p u ters th a t are operated an d m anaged by th e MIS group; 1 - Vax 8600, 1 - Vax 8700, an d 2 - Altos 2086
superm icrocom puters. The A ccounting D ep artm en t u se s a Vax for m any of it’s needs, w hich include m ain tain in g one of it’s versions of th e Bill of M aterials. A second Bill of M aterials is k ep t on th e Altos an d produced by th e A ccounting D ep artm en t for invoicing procedures. The Inventory
Control section also m ain tain ed it’s tra n sa c tio n s on th e Altos. However, Inventory Control m a in tain ed an d accessed a different d a ta b ase an d therefore, produced a th ird version of th e Bill of M aterials. This so called Bill of M aterials w as actu ally a stockage list collated in p a rt n u m b e r sequence. The program s in u se served to u p d a te th e on h a n d b alan ce s of each stocked line a n d track ed dem an d h isto ry for each line by week. T here w as no com p u tatio n al algorithm in u se for lot-sizing or reorder p o in t calculation. By F eb ru ary of 1990, th e various d a ta b a se s h a d b een consolidated to produce one stockage list.
T his system of parallel h ard w are an d softw are ap p e a rs to be a
p ro d u c t of com pany developm ent. The Vax co m p u ters are u se d prim arily by th e p a re n t com pany, E chosphere. The Altos su p erm icrocom puters are utilized by HTS. The M anagem ent Inform ation S ystem s (MIS) G roup is in th e p rocess of consolidating program s to elim inate som e of th is
parallelism . The inventory program s a n d dem an d h isto ry d a ta b a se are p a rt of th is consolidation effort.
T-3850 21
As previously sta ted , inventory m an ag em en t w as perform ed on a n intuitive b asis. A reorder level w as set, an d w hen th e on h a n d balance w en t below th is level a "quantity to order" w as p rin ted in a se p arate
colum n to initiate bringing th e b alan ce b ack u p to th e reorder level. No m axim um q u an tity to stock w as established. Therefore, th e com puter in terp reted th e reorder level also a s th e q u an tity to stock. The re s u lt w as th a t w hen one item w as u se d from a line a t th e reorder level, th e n ex t ru n of th e Bill of M aterials w ould reflect th a t a q u an tity of one sh o u ld be ordered. Following th is w ould have initiated rep len ish m en t orders after each issu e. C onsequently rep le n ish m e n t orders were really being placed w hen a glance in th e storage location indicated th a t th e on h a n d b alan ce w as low.
O n h a n d b alan ce s on th e Inventory Control Bill of M aterials were also found to be unreliable. T he Bill of M aterials u p d a te program w as designed for daily u p d a te s a n d could be considered a perpetually u p d a te d system . A lthough th e c u rre n t em ployees in Inventory Control were extrem ely conscientious a b o u t doing daily u p d ates, it w as a p p a re n t th a t p a s t perso n n el h a d n o t alw ays perform ed th is ritu a l accurately. On h a n d b alan ce s were frequently w rong by large factors. Additionally, secu rity w ithin th e w areh o u se a re a w as initially ra th e r lax. T hese problem s were adequately corrected by th e end of y ea r inventory perform ed in D ecem ber 1989.
W hen th e com pany moved to D enver from H ouston in D ecem ber 1987, it b ro u g h t m o st of it’s existing inventory. M ost of th ese item s were stocked "carte blanch" in ste ad of being periodically reviewed. M any of th e se lines h a d a low or no d em an d histo ry over th e previous 18 m o n th s
(the approxim ate length of th e c u rre n t d a ta base), possibly du e to obsolescence an d lack of periodic review. The bottom line w as th a t no periodic review system or criteria for stockage were in place.
3 .3 In ven tory P rocedures
As previously sta ted , th e original inventory control system a t HTS w as largely b ased on in tu itio n a n d therefore very personality dependent. O rders were initiated w hen a n alert stock clerk determ ined th e storage b in w as low. Additionally, m an y orders were n o t prom ptly lau n ch ed due to shortcom ings w ithin th e P u rch asin g D epartm ent. T his effectively in creased lead tim e by som e u n k n o w n factor. In late 1989, a p u rch asin g ag en t w as hired w hose sole responsibility w as p u rch a sin g for inventory control. This experienced individual h a s effectively c u t th e in tern a l tim e to initiate a p u rc h a se order to one day or less. Since th en , th e track in g of all open p u rc h a se orders h a s b een formalized. In sh o rt, th e p re se n t
p u rc h a sin g system ap p e a rs extrem ely efficient.
P arts req u irem en ts (dem ands) were identified eith er by a n
u n p ro cessed invoice or verbally to th e w arehouse clerk, depending on th e source of th e req u est. A lthough p a rts were issu ed d u rin g th e day a s needed, th e a tte m p t w as to p rocess all invoiced p a rts th a t h a d to be shipped in th e m orning. T his allowed deprocessing of receipts in th e afternoon. P a rts req u irem en ts b ased on invoice were packed for sh ip m e n t a n d a copy of th e invoice w as retain ed for d a ta in p u t in th e afternoon. Those item s issu e d b ase d on verbal d em an d were issu ed an d signed for by th e receiver on a local form. Issu es on th is form were th e n
T-3850 23
in p u t in th e afternoon to u p d a te th e d a ta base. By S eptem ber 1989, it w as m y observation th a t th e Inventory Control personnel were extrem ely conscientious a b o u t p a rts issu e p rocedures an d th e daily u p d ate.
W hen a p a rt w as unavailable for issu e (either th e line w as 0 b alan ce or n o t stocked), a b ac k order w as initiated. If th e item could be obtained from a statesid e vendor, it w as ordered by th e p u rc h a sin g d ep a rtm en t an d shipped by a n express freight com pany, su c h a s "Federal Express" or "United Parcel Service". The priority of sh ip m en t w as d ep en d en t on th e cu sto m er (i.e. a field service req u irem en t w ould w a rra n t a n expedient shipm ent). M any item s were b o u g h t from a sole source su p p lier in th e Hong Kong; th e m a n u fa c tu re r of th e decoder boxes. The expedited sh ip m e n t of s u c h a n item could becom e very expensive, a s HTS w as paying $ 1 .3 9 /lb for priority air sh ip m en ts. This w as th e case for m an y item s w hich added to th e co st of stockouts. The new p u rch a sin g ag en t is now attem p tin g to find alternative vendors for th ese item s.
Receipts for stockage or to fill b a c k orders could be received an y tim e d u rin g th e day, b u t w ere generally received in th e late m orning. T hese item s w ere th e n deprocessed (either placed in th e appro p riate
stockage b in or shipped o u t a g a in st a n existing b ac k order). The receipt do cu m en ts were th e n held an d in p u t in th e daily com puter u p d a te to change th e on h a n d qu an tities. D eprocessing receipts w as a p a rtic u la r problem b ecau se each HTS su p p lier invariably shipped p a rts u n d e r its own p a rt n u m b er, w ith no cross-reference list enclosed. Therefore if th e w areh o u se m an did n o t recognize th e p a rt by sight, he h a d to access a cross-reference program to perform th is before th e receipts could be posted in th e daily u p d a te an d w arehoused. This could be veiy tim e
consum ing for a n inexperienced w arehousem an. The HTS w arehouse p erso n n el were very com petent a t th is an d th e ir o th er d u ties a n d m u s t be appropriately credited here.
As previously m entioned, daily d a ta in p u t of receipts an d issu e s w as perform ed. T his essentially gave a perpetually u p d a te d inventory system alth o u g h th e on h a n d q u an titie s w ere frequently in error. The u p d ate program only am ended on h a n d q u an tities an d determ ined if th e on h a n d b alan ce h a d p en e trate d th e reorder level. The m axim um or authorized q u an tity w as tre a ted a s th e reorder level, so w hen th e on h a n d b alan ce reached one below th e reorder level, th e program
recom m ended ordering one u n it to get b ack u p to th e reo rd er level. If th e o n -h an d q u an tity exceeded th e reo rd er level, a negative q u a n tity to order w as printed. Again, a lot-size w as n o t com puted.
3 .4 O perating C on d ition s
In m o st inventories, probably th e two m o st im p o rta n t operating conditions are th e cost of stocking th e inventory, a n d th e cu sto m er service level it provides. HTS h a d no m ethod of track in g eith er of th e se values. Additionally, records h a d n o t been k ep t to allow for th e ir direct com putation.
Interviews w ith th e Inventory M anager, th e D irector of Production, a n d th e Service C enter M anager show ed th a t cu sto m ers generally felt th e service level w as betw een 75% a n d 80%. T hese were, of course, b e s t gu esses. F u rtherm ore, th e co n se n su s w as th a t th e goal for th e service level needed to be a t le a st 95% or b etter. The ju stificatio n for th is level of
T-3850 25
service w as in th e potential cost of a stockout. In m an y cases, th e cost of a sto ck o u t w as very difficult to m easu re su c h a s a n unfilled dem and from a field service center. However, th e sto ck o u t cost w as easy to estim ate-w hen a sto ck o u t stopped production. The p roduction problem always centered aro u n d th e decoder box in th e system . The com pany’s in v estm en t p er box w as approxim ately $373 .0 0 (as charged from th e vendor). It w as sold to th e d istrib u to r for $660.00. Therefore, th e
inability to produce cost th e com pany approxim ately $287 .0 0 p er box in delayed profit, w here th e re h a d already been a n initial investm ent of $373.00. The inventory of decoder boxes tu rn e d over in excess of 14 tim es p e r year, so carrying costs were negligible u n le ss production stopped. This situ a tio n w as com plicated b ec au se a b o u t 66% of th e com pany’s pro d u ctio n w as sold before it w as shipped. In sh o rt, th e cost of n o t being able to com plete th e pro d u ctio n goal w as high. Generally, th e targ e t w as to produce 500 to 600 u n its p er day in order to satisfy dem and.
The c u rre n t cost of stocking th e inventory w as also n o t know n by th e inventory m a n ag er or u p p e r level m anagem ent. However, it w as generally felt th a t th e co st w as too high. T hrough conversations w ith v ario u s individuals, to include th e A ccounting Controller, a n ordering cost (C) of $ 7 5 .0 0 p e r order a n d a n a n n u a l holding cost of 25% were agreed upon.
Logically, one w ould be in tereste d in th e to tal cost of stocking a given line of inventory a s defined in eq u atio n (2.1). However, over a period of tim e th e p u rc h a se cost for a n item will be a c o n s ta n t b ased on dem an d for th e item . T his w ould indicate th e co sts th a t ca n be affected
by an y lot-sizing tech n iq u e are th e fixed cost to order (CR/Q), an d th e variable cost to carry a n item in inventory (QH/2). The revised to tal cost
equation b ase d on th e se term s is
^ CR QH
3.1
At th is point, a m ean s h a d to be devised to estim ate th e total cost as defined by equation (3.1) u n d e r th e p re se n t system . The entire cost
an aly sis w as conducted w ith d a ta ta k e n as of 2 November 1989. Since n eith e r th e o n -h an d q u an tity n o r th e u n it price from th e inventory
control stockage list could be relied upon, it w as decided to u se a ran d o m sam pling te ch n iq u e to estim ate th e p re se n t to tal cost of operating th e inventory. In doing so, th e u n it price, q u an tity on-h an d , an d ac tu a l dem an d h isto ry could be verified a n d corrected for th e lines in th e sam ple.
As sta te d earlier, a high n u m b e r of lines stocked show ed a low or no d em an d history. M any publications on inventory control did n o t a d d ress w hen to stock or drop a n item . One m ethod d iscu ssed by F enske (Fenske
1968, 705) a n d la te r modified by Silver (Silver 1969, 359) required
know ing th e p e rce n t of sales lo st if th e item is n o t stocked. The inability to estim ate th is p a ra m e te r is th e sam e reaso n th e sto ck o u t cost te rm w as om itted from th e to tal cost calculation, equation (2.1). It w as m u tu ally decided w ith th e inventory m a n ag er to u se th e convention of 3 d em an d s in th e m o st rec e n t 52 w eeks to stock or reta in a n item (D.A. 1984, 16). T his is one criterion cu rren tly u se d by th e U.S. Army. Seem ingly
T-3850 27
unscientific, th e criterion w as in ten d ed as a guideline to cau se item s to be reviewed, an d n o t as a h a rd a n d fast rule. A m a n u a l review w as deem ed th e b e s t w ay to m ake th is decision.
Lines appearing on th e stockage list could be th o u g h t of as p a rts or com ponents, a n d th e com pleted p ro d u ct lines. T his th e sis is only
concerned w ith th e stockage of p a rts. There were 1,724 p a rts lines listed on th e 2 November list. T hese lines could be generally classified a s lines to reta in for stockage, lines th a t w ere can d id ates for deletion b ased on th e above criteria, a n d lines n o t stocked. There were also 10 d istin ct p a rt categories w hich are listed in A ppendix C.
It w as desirable to analyze costs b ased on lines th a t w ould sta y in th e stockage, a n d lines th a t were can d id ates to delete. This is b ecau se th e re were so m a n y ca n d id ates for deletion. An initial sam ple w as ta k e n to estim ate th e carrying cost of lines th a t were ca n d id ates to drop from th e stockage. T his sam ple consisted of 22 lines random ly selected from a stockage list r u n on 2 November 1989. Lines were selected utilizing a ran d o m n u m b e r table (CRC 1978, 544). The re su lts of th is sam ple are contained in Table 3.1.
Table 3.1
Sample of Candidate Lines,jtoLQctete
LINE NUMBER UNIT COST ON-HAND QUANTITY DEMANDS LAST 52 WEEKS $ VALUE OF ON-HAND QTY T183250 $ . 2 0 2 , 5 2 5 158 $ 5 0 5 . 0 0 T150100 $ 6 . 0 0 253 102 $ 1 , 5 1 8 . 0 0 T115230 N / A 0 0 $ 0 . 0 0 T154232 $ . 3 6 638 110 $ 2 2 9 . 6 8 T202120 $ . 0 0 4 1 6 , 8 0 3 200 $ 6 7 . 2 1 *T150730 $ 1 . 7 5 201 2 $ 3 5 1 . 7 5 *T131010 $ 6 . 4 3 63 1 $ 4 0 5 . 0 9 T219120 N / A 0 0 $ 0 . 0 0 *T213101 $ 3 0 . 0 0 73 2 $ 2 , 1 9 0 . 0 0 T150240 $ 1 . 8 0 448 69 $ 8 0 6 . 4 0 T201898 N / A 0 0 $ 0 . 0 0 T240030 $ 2 . 5 0 0 0 $ 0 . 0 0 T219 15 0 $ 8 . 5 0 338 3 , 8 0 0 $ 2 , 8 7 3 . 0 0 T180396 $ 1 . 1 0 1 5 , 2 6 8 5 1 , 0 0 0 $ 1 6 , 7 9 4 . 8 0 T110030 $ 1 2 . 0 0 179 12 $ 2 , 1 4 8 . 0 0 T150090 $ 6 . 0 0 0 80 $ 0 . 0 0 T 202040 $ . 0 0 4 1 5 , 1 5 3 1 8 , 0 0 0 $ 6 0 . 6 1 T 110920 $ 1 . 7 5 0 0 $ 0 . 0 0 T 130060 $ 1 . 7 5 1 , 4 3 5 150 $ 2 , 5 1 1 . 2 5 T 212960 $ 2 0 . 0 0 87 22 $ 1 , 7 4 0 . 0 0 T1 12010 N / A 0 0 $ 0 . 0 0 *T122327 $ 3 . 0 0 46 0 $ 1 3 8 . 0 0
N /A denotes th e u n it price w as n o t applicable since th e line w as n o t stocked.
T-3850 29
The 22 line sam ple contained 4 lines th a t m et th e criterion for deletion. A ssum ing th is ran d o m sam ple w as a tru e rep resen tatio n of th e population, one can estim ate th a t approxim ately 313 lines are
ca n d id ates for deletion. F urth erm o re, th e 4 lines in th e sam ple th a t qualified for deletion h a d a dollar value of $ 3 ,0 8 4 .8 4 or $771.21 p er line. The estim ated to tal dollar value of lines qualifying for deletion becom es
In fact, estim ates resu ltin g from th e a d d /d e le te criteria in J a n u a r y 1990 indicate th a t su b sta n tia lly m ore th a n 313 lines will be deleted. This m e a n s th e u ltim ate cost savings com puted in th e n ex t c h a p ter is probably u n d e rsta te d by som e unk n o w n am o u n t.
None of th e lines qualifying for deletion h a d b een ordered in th e la s t y ear so th e only costs involved were carrying costs. B ased on a n a n n u a l carrying cost of 25%, th e to tal cost to stock th is segm ent of th e inventory w as
The re s u lt of eq u atio n (3.3) re p re se n ts th e carrying cost of th e final o n -h an d b alan ce s a n d does n o t ac co u n t for th e few item s issu ed d u rin g th e previous 52 w eeks. The carrying cost of item s issu ed d u rin g th e y ear a s com puted by eq u atio n (2.5) is negligible.
The n ex t step w as to estim ate th e c u rre n t cost of th o se item s stocked w hich could be expected to rem ain in th e inventory. This w as
($771.21) (313 lines) = $241,388.73 (3.2)
also accom plished u sin g a ran d o m sam ple. T his tim e th e te n p a rts categories in Appendix C were considered. Again, lines were selected u sin g a table of ran d o m n u m b e rs (CRC 1978, 544) w ith a q u o ta of lines for each category preselected. T his w as a 23 line sam ple, w ith each category rep resen ted a t le a st once. The larger categories received larger rep resen tatio n , alth o u g h n o t proportionally to size. The re su lts of th is sam ple are listed in tab le 3.2.
ARTHUR LAKES LIBH/ihi COLORADO SCHOOL oi MINE'
T-3850 31
Table 3.2
Sam ple of Lines to R em ain in Stockage
LINE NUMBER PARTS c a t e g o r y UNIT COST ON-HAND QUANTITY $ VALUE ON-HAND QTY # DEMANDS LAST 52 WEEKS # ORDERS LAST 52 WEEKS T 110210 JAC $ 0 . 2 5 4 , 5 8 9 $ 1 , 1 4 7 . 2 5 146 1 *T115140 JAC $ 2 . 8 0 228 $ 6 3 8 . 4 0 7 2 / 3 0 wks 2 *T221111 CON $ 0 . 2 3 389 $ 8 9 . 4 7 2 7 7 / 3 8 wks 1 T221070 CON $ 0 . 2 5 397 $ 9 9 . 2 5 76 0 T120740 CHA $ 0 . 8 0 11 $ 8 . 8 0 22 0 T122360 CHA $ 3 . 0 0 125 $ 3 7 5 . 0 0 89 2 T120720 CHA $ 2 . 5 0 1 , 1 3 4 $ 2 , 8 3 5 . 0 0 1 , 6 2 6 10 *T230240 MISC PAR $ 0 . 5 4 592 $ 3 1 9 . 6 8 5 2 2 / 2 5 wks 1 T132020 MISC PAR $ 0 . 5 4 1, 983 $ 1 , 0 7 0 . 8 2 113 1 T124490 MISC PAR $ 2 . 5 0 1 , 0 4 2 $ 2 , 6 0 5 . 0 0 1 , 7 5 9 3 *T217000 BDS $ 2 . 8 0 800 $ 2 , 2 4 0 . 0 0 7 0 0 / 2 5 wks 2 T210690 BDS $ 3 8 . 7 9 0 $ 0 . 0 0 165 3 T 210730 BDS $ 1 5 . 8 9 0 $ 0 . 0 0 45 0 T 280040 REM $ 1 1 . 5 0 0 $ 0 . 0 0 8 0 T153140 IC $ 0 . 3 2 499 $ 1 5 9 . 6 8 ' 242 1 * T150105 IC $ 6 . 0 0 2 , 2 9 2 $ 1 3 , 7 5 2 . 0 0 1 4 6 / 1 1 wks 0 * T150135 IC $ 6 . 0 0 1 $ 6 . 0 0 1 5 / 1 0 wks 0 T183020 CAP $ 0 . 2 4 46 $ 1 1 . 0 4 60 0 T180170 CAP $ 0 . 1 0 2 , 1 7 5 $ 2 1 7 . 5 820 1 T184030 CAP $ 0 . 9 3 1 , 3 3 9 $ 1 , 2 4 5 . 2 7 443 0 T200392 RES $ 0 , 7 7 4 195 $ 1 5 0 . 9 3 5 0 *T201642 RES $ 0 , 0 2 5 1 , 3 2 5 $ 3 3 , 1 2 5 2 6 7 5 / 1 3 wks 2 T3 00080 LNB $ 5 5 . 0 0 262 $ 1 4 , 4 1 0 . 0 0 743 5
* D enotes lines w hich did n o t have a full y ear of dem and history. A nnual d em an d w as approxim ated by m ultiplying average weekly
The to tal co st of m ain tain in g th e sam ple lines in th e inventory h ad to be calculated. Since th e original inventory system h a d no lot-sizing algorithm in place, orders w ere placed erratically a n d for varying
am o u n ts. T his m e a n t th a t carrying costs could n o t be calculated w ith th e term (QH)/2 from eq u atio n (2.5) since th ere w as no Q designated. Known factors w hich could be u se d to determ ine carrying a n d order costs were
1. Q u an tity o n -h an d a s of 2 November 1989
2. The w eek in w hich orders were received a n d th e q u an tity received
3. The q u a n tity issu ed by w eek for th e la s t 52 w eeks 4. The correct u n it price could be determ ined
A Lotus 1-2-3 sp re a d sh e e t w as designed to aid in determ ining th e a n n u a l carrying an d ordering co sts b y line. A description of th is sp rea d sh ee t is contained in A ppendix D. In c a ses w here a full y ear of h isto ry w as n o t available, a n average p e r w eek w as calculated from available h isto ry an d m ultiplied by 52. T his m e a n t th a t a n n u a l re su lts w ould always be
com pared w hich is co n siste n t w ith equation (3.1). The re su lts of th is sam ple are listed in Table 3.3.
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Table 3.3
C osts For Sam ple of R etained Lines
LINE # PARTS CATEGORY ANNUAL CARRY COST ANNUAL ORDER COST TOTAL ANNUAL COST T1 10210 JAC $ 2 9 1 . 0 8 $ 7 5 . 0 0 $ 3 6 6 . 0 8 T115140 JAC $ 8 7 . 6 9 $ 2 6 0 . 0 0 $ 3 4 7 . 6 9 T2 21111 CON $ 3 0 . 5 0 $ 1 0 2 . 6 3 $ 1 3 3 . 1 3 T221070 CON $ 2 6 . 3 0 $ 0 . 0 0 $ 2 6 . 3 0 T120740 CHA $ 3 . 2 8 $ 0 . 0 0 $ 3 . 2 8 T122360 CHA $ 1 0 1 . 6 8 $ 1 5 0 . 0 0 $ 2 5 1 . 6 8 T120720 CHA $ 8 4 4 . 0 1 $ 7 5 0 . 0 0 $ 1 , 5 9 4 . 0 1 T230240 MISC PAR $ 8 3 . 7 1 $ 1 5 6 . 0 0 $ 2 3 9 . 7 1 T1 32020 MISC PAR $ 1 9 3 . 9 9 $ 7 5 . 0 0 $ 2 6 8 . 9 9 . T1 24 49 0 MISC PAR $ 4 3 0 . 4 4 $ 2 2 5 . 0 0 $ 6 5 5 . 4 4 T217000 BDS $ 2 1 6 . 1 8 $ 2 2 9 . 4 1 $ 4 4 5 . 5 9 T2 10 69 0 BDS $ 2 6 0 . 0 6 $ 2 2 5 . 0 0 $ 4 8 5 . 0 6 T2 10 73 0 BDS $ 7 9 . 2 6 $ 0 . 0 0 $ 7 9 . 2 6 T280040 REM $ 4 . 5 3 $ 0 . 0 0 $ 4 . 5 3 T153140 IC $ 2 0 . 0 2 $ 7 5 . 0 0 $ 9 5 . 0 2 T 15 0105 IC $ 3 , 5 4 1 . 2 3 $ 0 . 0 0 * $ 3 , 5 4 1 . 2 3 T1 50135 IC $ 1 3 . 5 8 $ 0 . 0 0 $ 1 3 . 5 8 T1 83020 CAP $ 4 . 8 5 $ 0 . 0 0 $ 4 . 8 5 T180170 CAP $ 3 0 . 0 8 $ 7 5 . 0 0 $ 1 0 5 . 0 8 T184030 CAP $ 3 5 0 . 6 6 $ 0 . 0 0 $ 3 5 0 . 6 6 T200392 RES $ 3 5 . 2 5 $ 0 . 0 0 $ 3 5 . 2 5 T 201642 RES $ 8 . 6 0 $ 5 5 7 . 1 4 $ 5 6 5 . 7 4 T 300080 LNB $ 3 , 7 6 9 . 6 2 $ 3 7 5 . 0 0 $ 4 , 1 4 4 . 6 2 TOTAL: $ 1 0 , 4 2 6 . 6 0 $ 3 , 3 3 0 . 1 8 $ 1 3 , 7 5 6 . 7 8
A n u m b e r of th e lines sam pled h a d n o t been ordered in th e m o st recen t 52 weeks. A lthough th ere logically should have b een som e average order cost assigned to th e se lines, th e benefit of th e d o u b t w as given to th e p re se n t system to com pute a conservative estim ate of th e original costs. Therefore, a n u m b e r of lines have order costs of $0.00.
The average order a n d carrying cost for each p a rts category w as th e n com puted by
I Q
(3.4)
Hi
w here
C,. = average order or carrying cost for p a rts in category i Q = order or carrying co st for line j in category i
rii = to tal lines from th e sam ple in category i
T he average order a n d carrying co sts now h a d to be d istrib u ted over th e entire inventory. T his w as first done w ithin each p a rts category w ith th e form ula
TCC = K f i , (3.5)
w here
TCC = Total category carrying or holding cost
Ki = Total n u m b e r of lines in category i
The to tal carrying or holding cost could th e n be found by sum m ing all th e TCC’s. The re su lts of th is are contained in Table 3.4.
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Table 3.4
C ost bv Category for R etained Lines
PARTS CAT'Y TOTAL LINES AVG CARRY COST AVG ORDER COST TOTAL CARRY COST TOTAL ORDER COST TOTAL COST JAC 96 $ 1 8 9 . 3 9 $ 1 6 7 . 5 0 $ 1 8 , 1 8 1 . 4 4 $ 1 6 , 0 8 0 . 0 0 $ 3 4 , 2 6 1 . 4 4 CON 89 $ 2 8 . 4 0 $ 5 1 . 3 2 $ 2 , 5 2 7 . 6 0 $ 4 , 5 6 7 . 4 8 $ 7 , 0 9 5 . 0 8 CHA 127 $ 3 1 6 . 3 2 $ 3 0 0 . 0 0 $ 4 0 , 1 7 2 . 6 4 $ 3 8 , 1 0 0 . 0 0 $ 7 8 , 2 7 2 . 6 4 MISC PAR 205 $ 2 3 6 . 0 5 $ 1 5 2 . 0 0 $ 4 8 , 3 9 0 . 2 5 $ 3 1 , 1 6 0 . 0 0 $ 7 9 , 5 5 0 . 2 5 BDS 109 $ 1 8 5 . 1 7 $ 1 5 1 . 4 7 $ 2 0 , 1 8 3 . 5 3 $ 1 6 , 5 1 0 . 2 3 $ 3 6 , 6 9 3 . 7 6 REM 29 $ 4 . 5 3 $ 0 . 0 0 $ 1 3 1 . 3 7 $ 0 . 0 0 $ 1 3 1 . 3 7 IC 151 $ 1 , 1 9 1 . 6 1 $ 2 5 . 0 0 $ 1 7 9 , 9 3 3 . 1 1 $ 3 , 7 7 5 . 0 0 $ 1 8 3 , 7 0 8 . 1 1 CAP 115 $ 1 2 8 . 5 3 $ 2 5 . 0 0 $ 1 4 , 7 8 0 . 9 5 $ 2 , 8 7 5 . 0 0 $ 1 7 , 6 5 5 . 9 5 RES 148 $ 2 1 . 9 3 $ 2 7 8 . 5 7 $ 3 , 2 4 5 . 6 4 $ 4 1 , 2 2 8 . 3 6 $ 4 4 , 4 7 4 . 0 0 LNB 9 $ 3 , 7 6 9 . 6 2 $ 3 7 5 . 0 0 $ 3 3 , 9 2 6 . 5 8 $ 3 , 3 7 5 . 0 0 $ 3 7 , 3 0 1 . 5 8 TOTAL: $ 3 6 1 , 4 7 3 . 1 1 $ 1 5 7 , 6 7 1 . 0 7 $ 5 1 9 , 1 4 4 . 1 8
B ased on th e se resu lts, th e to tal cost of stocking th e inventory u n d e r th e original system w as th e su m m ed to tal for those lines w hich could be expected to be deleted from table 3.3 an d those lines w hich w ould rem ain a s depicted in table 3.4. The to tal cost estim ate for m ain tain in g th e
inventory u n d e r th e old system w as
$519,144.18 + $60,347.18 = $579,491.36 (3.6)
At th is point, th e sam pling tech n iq u es u se d in th is th e sis should be d iscu ssed . T here is probably a correlation betw een th e p a rts category a n item falls in a n d th e u n it price. T h a t is to say, th e average price of circuit b o a rd s is certainly higher th a n th e average cost of resisto rs. It w ould have b een desirable to sam ple by p a rts category. The 22 line sam ple described in th is c h a p ter w as ta k e n w ith no consideration given to p a rts categories. T his decision w as m ade b ecau se of th e tim e required to
sam ple from each category a n d th e re se arch required to determ ine tru e d em an d history. It sh o u ld be k ep t in m ind th a t all estim ates b ase d on th e deletion ca n d id ates w ere m ade u n d e r th is condition. The 23 line sam ple u se d to analyze item s to rem ain in th e stockage w as m ade w ith p a rts categories in m ind. E ach category w as sam pled to select a
p redeterm ined n u m b e r of lines for th e analysis. C ost estim ates were th e n m ade u sin g eq u atio n s (3.4) a n d (3.5).
T his ch a p te r h a s served to p re se n t th e costs of stocking inventory u n d e r th e original system a t HTS. While th e final dollar figure m ay seem high, one m u s t rem em ber th e se co sts are som ew hat hidden. No p ay m en t is m ade by th e com pany each m o n th or y e a r. However, th ey are a real
T-3850 37
cost an d financial b u rd e n to th e com pany. In th e following chapter, th e cost of m ain tain in g th e inventory u n d e r th e revised system will be presen ted .
C hapter 4
THE REVISED SYSTEM FOR HTS
4 .1 O verview
The revised inventory control system for HTS w as a variation of econom ic order quantity. The inventory m an ag er w as very concerned a b o u t th e perception th a t th e cu sto m er service level w as too low. This m ade th e u se of a n effective safety level p aram o u n t. The m o st effective safety level com putation d iscu sse d is contained in equation (2.8), w hich is b ased on th e service level desired an d s ta n d a rd deviation of dem and. The inventory m a n ag er indicated th a t he felt a 97.5% cu sto m er service level w as a m u st. While th is m ay seem high, th e cost savings com pared to th e original system is still significant. The final p rese n tatio n to
m an ag em en t in November 1989 revealed th a t th is level of service a n d th e asso ciated co st were acceptable. The MIS program m er h a s b ee n provided a range of z-statistics in order to a d ju s t th is value. Obviously, lowering th e cu sto m er service level m e an s a lower carrying cost for safety stock, w hile th e reverse is tru e for raisin g th e service level. T his concept is explored la ter in th e chapter.
R eorder p o in ts also h a d to be determ ined, a s no system w as in place to m ake th is com putation. U sing th e 23 line sam ple from c h a p te r 3 for item s rem aining in th e inventory, it w as found th a t th e re w ere lines th a t w ould require th e altern ate m ethod of reorder p o in t calculation a s
described a t th e end of section 2.2. Therefore, b o th th is m ethod an d eq u atio n (2.4) h a d to be applied.
T-3850 39
In th e case of HTS, d em an d s frequently were for m ultiples of a given item . It w ould be possible u n d e r th ese conditions for th e o n -h an d
q u an tity to fall well below th e established reo rd er p oint w ith th e arrival of one dem and. Therefore, a n (s,S) policy of reordering w as adopted
(Nahm ias 1989, 209). U nder th is policy, s is defined a s th e calculated reorder p oint p lu s th e safety level. S equals th e safety level p lu s Q from equation (2.2). The m ethod req u ires th a t w hen th e o n -h an d b alan ce is less th a n or equal to s, a rep le n ish m e n t order is placed for th e difference betw een S an d th e o n -h an d balance. While th e (s,S) policy is u su a lly associated w ith a periodic review system , its u se allows th e o n -h an d balan ce to reac h th e m axim al quantity, or S, even in a perpetually
u p d a ted system . It is incorporated in th e EOQ system cu rren tly u se d by th e U.S. Army (D.A. 1984, 17), w hich is a p erp etu ally u p d a te d system .
4 .2 R evised C osts
At th is point, th e cost of operating u n d e r th e new system h a d to be estim ated. Since it m ak es se n se to only estim ate costs for lines expected to rem ain in th e inventory, th e previous 23 line sam ple w as u se d for th is pu rp o se. E stim ated costs for th e sam ple w ere com puted u sin g th e
softw are program s STORM II an d QSOM in conjunction. A d iscu ssio n of th is m ethod a n d a sam ple calculation a p p e a r in A ppendix E. E stim ated co sts for th e sam ple u n d e r th e revised system are show n in Table 4.1.
Table 4.1
Revised C osts For 23 fRetalned) Line S am ple
LINE # PARTS CATEGORY ANNUAL CARRY COST ANNUAL ORDER COST SAFETY LEVEL CARRY COST TOTAL ANNUAL COST T110210 JAC $ 1 8 . 5 0 $ 1 8 . 5 0 $ 3 . 5 8 $ 4 0 . 5 8 T115140 JAC $ 5 7 . 4 0 $ 5 7 . 0 7 $ 1 1 . 8 8 $ 1 2 6 . 3 5 T 221111 CON $ 2 8 . 7 5 $ 2 8 . 5 0 $ 3 . 7 6 $ 6 1 . 0 1 T221070 CON $ 1 5 . 6 3 $ 1 1 . 4 0 $ 1 . 2 2 $ 2 8 . 2 5 T120740 CHA $ 1 2 . 8 0 $ 1 2 . 8 9 $ 3 . 4 1 $ 2 9 . 1 0 T122360 CHA $ 4 9 . 8 8 $ 5 0 . 1 9 $ 4 1 . 9 7 $ 1 4 2 . 0 4 T120720 CHA $ 1 9 5 . 3 1 $ 1 9 5 . 0 0 $ 1 6 8 . 4 4 $ 5 5 8 . 7 5 T230240 MISC PAR $ 7 4 . 1 2 $ 7 4 . 1 6 $ 9 . 1 6 $ 1 5 7 . 4 4 T132020 MISC PAR $ 3 3 . 7 5 $ 1 6 . 9 5 $ 1 . 5 0 $ 5 2 . 2 0 T124490 MISC PAR $ 2 0 3 . 1 3 $ 2 0 2 . 9 6 $ 3 1 6 . 0 9 $ 7 2 2 . 1 8 T217000 BDS $ 1 9 5 . 6 5 $ 1 9 5 . 3 5 $ 1 7 2 . 8 2 $ 5 6 3 . 8 2 T210690 BDS $ 2 4 7 . 2 9 $ 2 4 2 . 6 5 $ 6 2 9 . 6 6 $ 1 , 1 1 9 . 6 0 T210730 BDS $ 8 1 . 4 4 $ 8 2 . 3 2 $ 6 8 . 9 9 $ 2 3 2 . 7 5 T2 80 040 REM $ 2 8 . 7 5 $ 2 9 . 9 9 $ 1 9 . 8 7 $ 7 8 . 6 1 T1 53140 IC $ 2 6 . 9 6 $ 2 6 . 9 3 $ 3 . 3 6 $ 5 7 . 2 5 T150105 IC $ 1 9 7 . 2 5 $ 1 9 6 . 8 2 $ 7 5 . 6 0 $ 4 6 9 . 6 7 T1 50 13 5 IC $ 6 6 . 0 0 $ 6 6 . 4 8 $ 5 . 2 8 $ 1 3 7 . 7 6 T1 83 02 0 CAP $ 1 5 . 0 0 $ 9 . 0 0 $ 0 , 5 7 9 $ 2 4 . 5 8 T1 80 17 0 CAP $ 2 7 . 7 3 $ 2 7 . 7 3 $ 2 . 2 0 $ 5 7 . 6 6 T1 84 03 0 CAP $ 6 2 . 1 9 $ 6 2 . 1 0 $ 1 5 . 8 4 $ 1 4 0 . 1 3 T2 00392 RES $ 6 . 0 0 $ 6 . 0 5 $ 0 , 2 6 3 $ 1 2 . 3 1 T 201642 RES $ 5 0 . 0 8 $ 5 0 . 0 8 $ 3 . 8 3 $ 1 0 3 . 9 9 T3 00080 LNB $ 6 1 8 . 7 5 $ 6 1 9 . 1 7 $ 2 , 3 6 4 . 5 4 $ 3 , 6 0 2 . 4 6 TOTAL: $ 2 , 3 1 2 . 3 6 $ 2 , 2 8 2 . 2 9 $ 3 , 9 2 3 . 8 4 $ 8 , 5 1 8 . 4 9
T -3850 41
A com parison of Table 4.1 w ith Table 3.4 show s th e difference in costs betw een th e old a n d revised system s for th e sam ple. The old system h a d a to tal cost of $ 1 3 ,756.78, com pared to $ 8 ,518.49 for th e revised system . T hese are p re se n t w orth, before ta x dollars, n o t corrected for inflation. In light of th e first p a rag rap h of th is chapter, one could a s k how high th e service level could be p u sh ed , while preserving a cost advantage. The difference betw een th e revised order p lu s carrying costs a n d th e original co st of stockage is
$13,756.78 -$4,594.65 = $9,162.13 (4.1)
This figure re p re se n ts th e breakeven p oint for th e safety stock carrying cost. A sensitivity an aly sis of th is carrying cost u sin g STORM II follows:
Table 4.2
Safety Stock C arrying Cost an d Service Level
CUSTOMER SERVICE LEVEL SAFETY STOCK CARRYING COST 90.00% $2,565.66 92.00% $2,812.93 94.00% $3,112.64 96.00% $3,504.84 97.50% $3,923.84 98.00% $4,111.59 99.00% $4,657.30 99.99% $7,445.33
A b e tte r rep rese n tatio n of th is relationship is portrayed graphically in figure 4.1.
Figure 4.1
Safety Stock C arrying Cost Vs. Service Level
CO 8 0 2 _
1
c 1 § O g Cu £ > w UJ(n
8 7 6 5 4 3 2 90 92 94 96CUSTOMER SERVICE LEVEL (%)
98 99.99
T he g rap h su g g ests th a t a s th e service level is p u sh e d higher, th e carrying co st in creases exponentially. There is, in fact, a dim inishing r e tu rn for every additional dollar invested in th e safety level. From th e cost stan d p o in t, it is desirable to hold th e service level to a reaso n ab le
T-3850 43
n u m b e r. B ecause costs were so high u n d e r th e old system , th e service level could be p u sh e d to 99.99% an d still m ake th e new system
econom ically feasible. It is doubtful th a t sh elf space is available to su p p o rt th is kind of service level, a n d it w ould seriously c u t th e cost savings. Therefore, 97.5% is probably a good sta rtin g point given th e realities involved.
The final te s t is to com pare projected costs for th e entire inventory a n d form ulate th e final cost savings. U sing equations (3.4) an d (3.5), costs were projected for th e revised system by p a rt category a n d ap p e ar in table 4.3.
Table 4.3
C ost Projections - Revised System
PARTS CAT'Y TOTAL LINES TOTAL CARRY COST TOTAL ORDER COST SAFETY LEVEL CARRY COST TOTAL COST JAC 96 $3,643.20 $3,627.84 $742.08 $8,013.12 CON 89 $1,974.91 $1,775.55 $221.61 $3,972.07 CHA 127 $10,922.00 $10,925.81 $9,051.29 $30,899.10 MISC PAR 205 $21,252.35 $20,094.10 $22,328.60 $63,675.05 BDS 109 $19,052.11 $18,904.96 $31,663.41 $69,620.48 REM 29 $833.75 $869.71 $576.23 $2279.69 IC 151 $14,607.74 $14,607.74 $4,240.08 $33,455.56 CAP 115 $4,021.55 $3,788.10 $714.15 $8,523.80 RES 148 $4,149.92 $4,154.36 $303.40 $8,607.68 LNB 9 $5,568.75 $5,572.53 $21,280.86 $32,422.14 TOTAL: $86,026.28 $84,320.70 $91,121.71 $261,468.69
