INTEGRATION OF ECONOMIC PRODUCTION QUANTITY WITH...
32
INTEGRATION OF ECONOMIC PRODUCTION QUANTITY WITH DEFECTIVE ITEMS FOR MULTI-PRODUCT IN MULTI-PERIOD GEETHAMPARI A/P SUBAMANIAM UNIVERSITI TEKNOLOGI MALAYSIA
Transcript of INTEGRATION OF ECONOMIC PRODUCTION QUANTITY WITH...
INTEGRATION OF ECONOMIC PRODUCTION QUANTITY WITH
DEFECTIVE ITEMS FOR MULTI-PRODUCT IN MULTI-PERIOD
GEETHAMPARI A/P SUBAMANIAM
UNIVERSITI TEKNOLOGI MALAYSIA
INTEGRATION OF ECONOMIC PRODUCTION QUANTITY WITH
DEFECTIVE ITEMS FOR MULTI-PRODUCT IN MULTI-PERIOD
GEETHAMPARI A/P SUBAMANIAM
A thesis submitted in fulfilment o f the
requirements for the award o f the degree of
M aster o f Science (Mathematics)
Faculty o f Science
Universiti Teknologi Malaysia
OCTOBER 2017
iv
To m y b e lo v e d fa m ily fo r th e ir n e v e r e rg m ip p o r t ancbare
vi
ABSTRACT
Manufacturers often face material losses during the process o f any specific
production assemblies which are usually unpredictable. However, the attrition
percentage can normally be obtained. In order to make sure that the demand is met
despite attrition, the production needs to be planned wisely. Inefficient production
planning can lead to the consumption o f capital resources that can otherwise be put
into better use elsewhere in the company. In this study, an inventory model that takes
attrition into consideration with no shortage allowed is developed. An Economic
Production Quantity with Attrition (EPQA) model is used to obtain the optimal
production run size and the optimal production cycle. Then, an aggregate planning
model for five periods o f time is developed taking the optimal production run size
obtained as the demand. This model will help the decision making process by
determining the production quantity o f products, use o f overtime labor, number of
workers to be hired or fired and the amount o f inventory to be held in stock each
period so that the demand is met and the annual total cost o f operations is kept to the
minimum. This new production policy can thus scientifically address the attrition
problem, assist in decision making, help in resource planning and optimize the
production process. For future study, the attrition could be included as an inherent
parameter in material or inventory planning to make sure that required materials are
sufficient to satisfy demands even when attritions exist.
vii
ABSTRAK
Pengilang sering menghadapi kekisiran ketara semasa proses mana-mana
pemasangan pengeluaran tertentu dimana kebiasannya adalah tidak dapat
diramalkan. W alau bagaimanapun, peratusan keciciran selalunya boleh diperolehi.
Dalam usaha untuk memastikan bahawa permintaan bahan dipenuhi walaupun
keciciran berlaku, pengeluaran perlu dirancang dengan bijak. Perancangan
pengeluaran yang tidak cekap boleh membawa kepada penggunaan sumber modal
yang sepatutnya lagi baik digunakan oleh bahagian lain dalam syarikat. Dalam kajian
ini, model inventori yang mengambil kira keciciran tanpa membenarkan sebarang
kekurangan telah dibangunkan. Satu model Pengeluaran Kuantiti Ekonomi dengan
keciciran (EPQA) digunakan untuk mendapatkan saiz pengeluaran optimum dan
kitaran pengeluaran yang optimum. Kemudian, satu model perancangan agregat
untuk lima tempoh masa dibangunkan mengambil saiz pengeluaran optimum yang
diperolehi sebagai permintaan. Model ini membantu proses membuat keputusan
dengan menentukan kuantiti pengeluaran produk, penggunaan tenaga buruh lebih
masa, bilangan pekerja yang diambil dan dipecat dan jum lah inventori yang akan
disimpan dalam stok untuk setiap tempoh masa supaya permintaan dipenuhi dan
jum lah kos operasi tahunan ditetapkan pada tahap mininum. Dasar pengeluaran
baharu ini boleh menangani masalah keciciran secara saintifik, membantu dalam
membuat keputusan, membantu dalam perancangan sumber dan mengoptimumkan
proses pengeluaran. Untuk kajian akan datang, keciciran boleh dipertimbangkan
sebagai parameter yang ada dalam perancangan bahan atau inventori untuk
memastikan bahan-bahan yang mencukupi untuk memenuhi permintaan walaupun
keciciran wujud.
viii
TABLE OF CONTENTS
CHAPTER TITLE PAGE
DECLARATION ii
DEDICATION iv
ACKNOWLEDGEMENT v
ABSTRACT vi
ABSTRAK vii
TABLE OF CONTENTS viii
LIST OF TABLES xiii
LIST OF FIGURES xv
LIST OF SYMBOLS xvii
LIST OF APPENDICES xviii
1 INTRODUCTION 1
1.1 Overview 1
1.2 M otivation 3
1.3 Inventory Accuracy 4
1.4 Attirition 5
1.5 Background Research 6
1.6 Problem Statement 10
1.7 Research Question 10
1.8 Research Obejctive 11
1.9 Scope o f the Research 12
1.10 Significance o f the Research 12
1.11 Organization o f Thesis 12
ix
2 LITERATURE REVIEW 14
2.1 Introduction 14
2.2 Optimization in Production Planning 15
2.3 M anufacturing Types 15
2.3.1 Just in Time (JIT) 15
2.3.2 Continous Production 16
2.4 Inventory M anagement 16
2.4.1 EPQ & APP in Inventory M anagement 17
2.5 Birth o f EPQ 17
2.5.1 Tradiotional EPQ 17
2.5.2 Modern EPQ 18
2.5.3 Production Lead Time and Setup Cost in EPQ 18
2.5.4 Imprefect Process in EPQ 19
2.5.5 EPQ Model Formulation 21
2.5.5.1 Example o f EPQ Model Application 24
2.6 Aggregate Production Planning (APP) 26
2.6.1 Chacteristics o f APP 27
2.6.2 APP Strategies 28
2.6.2.1 Level Strategy 28
2.6.2.2 Chase Strategy 29
2.6.3 Related Studies in APP 29
2.6.3.1 Uncertainity in APP 30
2.6.3.2 Integartion o f APP in Real Situation 33
2.6.3.3 Mathematic M ethod in APP 33
2.7 LINGO 15.0 36
2.8 Discussion 39
2.9 Summary 40
x
3 RESEARCH METHODOLOGY 41
3.1 Introduction 41
3.2 Overall Research Plan 41
3.3 Research Design & Procedure 45
3.3.1 Step1: Framing the Questions 46
3.3.2 Step2: Finding Research Gap 46
3.3.3 Step3: Data Collection 47
3.3.4 Step4: Data Analysis 48
3.3.5 Step5: Build EPQA and APP model 48
3.3.6 Step6: Running & Testing Model 49
3.3.7 Step7: Interpreting the Results 49
3.3.8 Step 8: Sensitivity Analysis 49
3.4 Theoretical Framework 49
3.5 Summary 52
4 EPQA MODEL DEVELOPMENT AND SOLUTION 53
ANALYSIS
4.1 Introduction 53
4.2 Problem Description 53
4.3 Mathematical Model Formulation 55
4.3.1 Notation 55
4.3.2 Assumption 56
4.3.3 Modelling with Attirition and Shortage N ot 56
Allowed
4.4 Model Implementation and Numerical Analysis 60
4.5 Conclusion 70
xii
6 CONCLUSION AND RECOMMENDATION 108
6.0 Overview 108
6.1 Summary 108
6.2 Conclusion 110
6.3 Recommendation for Future Research 111
REFERENCES
Appendices A - L
112
119
xv
LIST OF FIGURES
FIGURE NO. TITLE PAGE
1.1 Flowchart o f Problem Formulation 9
2.1 Operation Planning Hierarchy (Chinguwa, 2013) 31
2.2 Example o f LINGO 15.0 Interface 37
2.3 Example o f LINGO 15.0 Solver Status Box 38
2.4 Example o f LINGO 15.0 Solution Report 39
3.1 Operational Framework o f Research 50
3.2 Theoretical Framework o f Research 51
4.1 Behaviour O f Inventory Level Over Time 57
5.1 Solver Status W indow: Scenario 1 83
5.2 Solver Status W indow: Scenario 2 87
5.3 Solver Status W indow: Scenario 3 90
5.4 Solver Status W indow: Scenario 4 94
5.5 Solver Status W indow: Scenario 5 98
5.6 Solver Status W indow: Scenario 6 102
xvi
LIST OF SYMBOLS
p t - D aily rep len ishm ent or p roduction rate at p roduct i /; - D aily dem and rate at p roduct iI t - A nnual dem and in un its
m - N um ber o f annual orders or p roduction runst - T ransit tim e in years for rep len ishm en t order
P - P roduction cost
C - Setup cost/ / - H old ing cost pe r un it for p roduct iT C ( m ) - T otal annual cost for m p roduction runs pe r year
Q - L o t size for p roduct iN - N um ber o f annual opera ting days
ik - P roduction rate
x - inven to ry level
- w o
xvii
LIST OF APPENDICES
APPENDIX TITLE PAGE
A LINGO Model : Scenario 1 119
B LINGO Solution Report : Scenario 1 123
C LINGO Model : Scenario 2 128
D LINGO Solution Report : Scenario 2 132
E LINGO Model : Scenario 3 137
F LINGO Solution Report : Scenario 3 141
G LINGO Model : Scenario 4 146
H LINGO Solution Report : Scenario 4 150
I LINGO Model : Scenario 5 157
J LINGO Solution Report: Scenario 5 161
K LINGO M odel: Scenario 6 167
L LINGO Solution Report: Scenario 6 172
CHAPTER 1
INTRODUCTION
1.1 Overview
P roduction p lannin gin m anufacturing is the p lanning for sm ooth an d
optim um production an the com pany .It utilizes m anufactuain g r e tu u r c e s , lei^lerial
avallabliity and pir(^(^^ctiancap^i^cityto s^^^^ecu^oc^n^^rsPi^^n^v^ct^finpla^nn^g S a
p lan for Utture prroUuc^^^^n Quantit^y o f m anu fac tu n n g sot^a^^cene^c^^d are
de tem tn idd an d ^anan^nd. A n fo d k rtio n p ia n n S n g ls m a d rp c r io d ira l ly fo r if specific
time cabled horizon To d ev ek )p an efficien iproS^t^ct^c^n planinn, the producCirn
p lanner is reqtta^^d to w urk c k )se ly w tlh i^ le s depgrtm ed l. A criiifalU adaor
proS^t^ct^c^n planning it thaccuraee ertimaCiok oflh^i^c^cs<C^i^^la^f^^^i^>'r ofvnallab le
resouccs.s A pronuction )p^^;anr also con idaersm ateria i ^^f^ila^ii:^ty , re ro u rc es
avallabliity and f;tCuae ngm and .
Economic P toUu ^ ^ nQucrLti(y (EP fa^^^^^it^^y fwinely ^^^(^^^ron^t^ct^c^n
plannmgpractice b c f f u f u f its simplicity. Basic EPQ applis swhendem and o fhe
produce ss r rn s ia n C o u e a th e yenarn there is fixed cosf ^tar^a^e0 ena ca cfuoduct
producey regardass o f the n g m n ero fu n it fro n u ced (H su , 2014.) There se ak o a
holding c o t t rar acch unstoredin s torage.Recenttyreseasah f k b r t s h a v a e ee n
m a^^ to extend f te b a c i c E P Q by a^e^a^iit^e assumpCirns so it^a.tt^llg model
conforms maaeslosety to real worCdpronlgms. ehere are twa maj(Sf gfcirnrlftafn
2
the c la s r i f a lE P Q m n d eThese a ie l) the quality o fou tpu iis o f perfect; qual^y and
2) the pronuction rc te iip re d e tg m tm n i a n d dxa d iv a a v a nee .
A ggregate production plannoig AEE) m odel is a production p lannin g
activity. An A PP for the p ro d u c rin n p ro c r sis no rn ianydone in ad v an ceo f 2 to 18
m onths to cVne a n idea tthe m a n a g g m e n i ns to w h a C q u c y tity s f a ra ir ric i s t o be
o rdered an d w h e n A ro n u c ish o u k i be runucecHo o rd er to mnimize t hie Coil \ coet
o f the p ro n u c tio n o v erth a t priod.
The conepptof APP is to tranplctethe fo recas ted n em a n d an n producCion
c a p a c ity to fattne m aunC ccC eaingpkfor a family ofp ro u u s e ^ E P greatiy redcon d
the a m o e d to e ita iu os e (t c iu a iu g p la n n iru sp sf an d r i e o th e au q u e n c d t) f re v if in g
the plan(B aykasopCu , 2001 i The com m on AE objective! aae mtgsnilomg coet,
m toim titog inventoeylevel, m intm iiinn c h a f e s m fo rce ivvy 1, m tgim tem f o se
o f overtim e i m inmtizind ua e os Quontracting , m icgniiog ch an g e s in p ro d u u t in n
rat^^i m oim t^rag nnm O er n g m a ch in e ^ s u p s an d m axim iiuro s r°fiti i Thn ch sea rch
neve io p m en tin A P P involves the conriOeraCio n ngmu4kQjective uinction , m ulti
p ro n u ctim u lt4period im u itinem and an d m ultiaeety sCark.
Both E PQ a d AEP m ot® ! tovolve different tm plem eniatiod to
m anufacCuriae .Firstly, E PQ prov(de tofoemation on 1o t rio e th a tn e e d toQe run
b a s e i o n O sm ay productron rc te se ttip r s s a an d V ie c n to c y c o fin the ohae r i a n d,
S e c o n d ^ , dEPP d e te ^ e e lf cm ourfi oUnfaCuo^ti toventoey an d worirforcp veveC to
m e e i dgm an U aequnem entv e n e r a r l a n n in g UoriBomandSf a n g u p o a ia n i i f d u i in
Qoth APP an d E PQ
Attrition is throw o u ip ro ceseo f raw m atealp luua ig g m au n C cc te iin g p ro ee ss .
The throw o u io f raw m aterip 1 fo r m anuccured p ro tu c ts o ru unpacdia1tadSs. The
am oun i of raw 1X1111111 which hae Oea n ss ss i n s t suffieienl for n iu fp ro d e e tio n
Qatch thu s t o e f la n a aa afuu(fed to o e d e a th s a e m a c e r ia lo r s to e k m o a e to h n s ^ e there
is no stopoe r fo ip a o d u c tio n .H ow eych i feisiiC oa lieade tohiah iaL veuto eQ^a^^isae
the attrition q u an tity ise n o rc d lcaa b le.
3
1.2 Motivation
D em andp lann ing an d esoentory control a re ilm osi im portan i operafio n
activities m m anufacturm g an d afuu irs m a n g o em e n t a l fts b h i t t ^ g ^ d e ^ n n d d a ta ,
inventory aging s ^^^,inoentorn anelysir Or ee c h lo ia tfun u s e d to cusiify tn e o r d e r
quantity and raCeis f irc ir iu p ro d u c t i in p ta n n iEuonom ic p roductionq loaity is
im portan iQ ecaur e h u id n i g to s u c u c d e lv fn to rn ii po stly aul( i n kUugl(Ow stock
can a lc u fs to rk c ts , io si aalee, an d som e c a se s p ronuctionp1anshyC dow n.
E PQ ss d e s id n ed to h e id in v fn to ry m a n eg o rm a0 l1 aec th e lt i S1i am cu n C o f
Coventory. EPQ) m o d e i h as Oeen e x ten d ed U u cy n s td e riu g t f e efffcS pa feccierfect
p roduction p rc e s s^ P o r te u s , 1886 )Praciically, imp^^^^ci qnaiity itsm scan be
so m e tm te sro w o rk e n e n O repairA E P can be avaluaO ln aid m p la n n iu g n c a d k e tio n
andw orkforce levese fp r a fsm p e n y b e c a u sn rU v in e s e m a ^ u o feU so rn iy o m an d
U uctuationsbysm oatha ldn w orkforce an d p ru d u c tio levels.
Inventory d^^icfurae y m a p c c u r due Co sh o rtag e o f m ateclas, Cmpenoect
production p r c e ^ ^ da la e ipu t/cu ipu t arrsrsn ira n s fe tio n e r ra e s ,c u fC e f t)u u t errors
and u n rfu o rte d sfra.p I t addition i attrition w here m cteria l are s^ian^^^ded during
production p rocess ,a lso affecte ivoenfory a f e u r e f ^ h is will c a u se gnm ediaie
phe^^^c^a i th o r n o eio com plete the pryduct^m perfeci proC ucC ionproee susually
happens Q ecaur e ofm achdie en-tst: This situation ss often uravoiUaQle w hen
m a c h in s tun a t hiuh ppee dThus, the p lanne d quantitys n o t i^^l^ivoe d and
production te u s to u se m are materiaChatshouCdQe c o n tn m e d anthis a lso tends
to to c re a re production se tu p cfTt. sfhntuation fu s ts e s t im dianncr- p u rc h a re r
difficulty to bring m m aterlisl on time cte to extra m aterlas neeO e cOrl:^^r than
eepectecCo m ake u d f a r ie s ip r o d u f t ie dm som e c u fg m a ia n e e i(P c o d u e tio n p la m le r
tends to p r jrc t for buffer s to ck , Qut this resultto higher inventory on production
floor. An invenfoey moO el Co de tsrm lne ogliPndot size which takee info
consCderafioiattritions ra tfn e lp s th u la n n e c to OcciO fo n t io u m Q e f o iworkers and
inventory lev e to ex ec u te tO p f ta if-
1
The influence o f d s m a n d iAEP is significart. B asically d em an d ss a
guideline foe e planneto m eeing cusfom e r requO•emenC.uynenmaCer1a i s 0s ; 1 aoe
for the d em an d t n e Ccfttipition will have impacC on the ag g reg c te pruducCron
planndig don aaariierand th e re is uonCinousneed to rvvia ih e p lan a g c m n a s e o on
cu rrenC m cteria lv va1labiliey.TU ilw lll e-niually f cu^ ^ ^ ^ cr se rv iee lev e l.
1.3 Inventory Accuracy
Som e m aqufactnrm p pdcnts h a to n a eorm aipoiicy e i r r e d n r tin g a n d reducing
inventory u r e d in tu b e a sa m b lic s Chet muaC bw rrw orP ed o f aeradped i ids detailed
investigation in require d t u deCenmnontpCQution o f the scraniatttru io n ra te ta Che
inventory a l a c f P l • a e ie s .T h e m n r e e o m p i f x o f (ha su b e se e m b ly to 0 e re w u rk e d , the
m ore difficult 1; is Co i ^cCs i^ the noire e tm a le r ie Is f f r s p p e d o r u e e d aa rep tacem en t.
Som e CQnaasemO1ics are o o fo m p ie d tCietUifficult to detem cine w ine co m p o n en t
is sc rap p ed . W h e n t h e e i m p o n e n t g e irw rrw o rU e d ie veey dem otex, routine stock
ar^j^^^e^^^in^edo to b o d o n e o r th e w h o ic parC noede in p f ae ra p p e U o ffin t i e sy stem
with an y sevcanable ^em donen^ii p lacad b o ek on Osceee. Tlae accn ro eo o f
reportd ig secf] ,i^ i i ]^^^^n^a a i^^cfl^r^l^;t a r r a o e c o n fo m fo r in n e n to rp control.
O pera tion ! o o o d le m a Q tie relucfao t to a s s is t m fm drovcng se^ ;s» reoorting
since tu s h a p p ro v em cn tt ultim atelg m a y o ie re ase CPc lcrcp/aCtrillqn vatUo in
sy stem reoorting. With tUis ci1uoiions tdere is q •equfh t p n y s ic a lv a c ia n e e and
production will have P>reakdown/ oe m a lp r ic i iu d p iy to iPuqroU uction> M aterial
p lanndig s en p n rtan t an d crilicai if attrition ia d si the n o a r to octual
p lannm glo riod .
A nother is tn e in iv d e o to ru eonlcoi cs Clif IcoU o fp ro e o s c o n fro io n sc rap s .
P o o r ctc v o e n ^ n reposting e f i f c a p c a v h e n e m ujor effects o n th e in v c n to ry occuracy .
O ne w a y ie fo ioo lr n 1 w h e re th c i f r e p i r geing p la e e d o o d Ccea ii^^ l t f r ru o ro c e sse d .
The question is “W hat is the efficient way to do this?” The way it was done may be
5
conscdered f te ic ie n C o n th e p la n tlB n t wi w as o^^cda^^sept twere w ere s u m e o 1 h f r scrap
lots which w ere o o C d e f r a r e d a n d w ereh id U o n for c (^^^i^^tn(^(^r^o^. t e e n the b e s t
sy stem will n o t Qe able Co gioe a fe u ra te iu v o n to ry da ta w han Chers e Siuman
toter^ier^^i^^^.
Inventory a c fu ra e y is im p o r ic u f fo rA P P as it will calculcte tSe m a teria l
n e e d e d n a s e o on O m a n t^s a r a b o v e foceooai to n s u r e cro d u n l in ran w ithout an y
m ateria l brcrUcwwiuuppiy; A good iy a te m /fo u ld iue1u<:ls thc aftrilrupOp rcte
with d em an d io aU e id sy s te m fo to m u p to C o lm a te r ia lu e e Of d fo r th e p ro /d . :tion
1.4 Attrition
Attrition refers to the stoic Ci n s u W e n ^ a l^ r ia iH e w t ort C n r i s la t t (during
production p reen s s.suhloss o f th e a^ul^ii^al tu s u a l ln h u d n m s w hen aO em asn tne h as
pIcO up errors iO r whe n tU eiu^^en tnea a ro d n w n .P ru n n p rw ff ld o drnQf^iuy Ceased on
sy stem O a ta o n m a tc r ia lq u a y tiIy . sitU e agstem s h o e s A e quan ivn la evcslable the
m o n e lw lllp ro c e e d to p ro d u k W , and pruqucC ionw illp frP orm m atcrio lkaring a t r u b
s to re r Co a llecuC em ateriais e n m m a to a to r f ( to corn e f r ta m p (a n u e q peoductr. O nce
production in fomp1eCedsCnose m ateriols will O e re tu m e d le s ir irb s au d ruounC
p ro cese on^liem ^^tfi^i^^ ’ Ql lnnr•fotmed. T n e q u a n tltu during-Dotm! m a u o o a d e
the same with the required quantity in the system. This situation creates “attrition” .
Iu this study, a ttr iC io n n a p p n n sm o s jly ft^asmr^lOCif^ii ( a r ts such as re ris to rs
and c a p e s i i to n w r r ic e f a u r fU tcUpliis^s^^i"^^^ on nexf o^oditftioauid p roduct
p ro d u ced e s y e e c v tiy E la n n e rs fa c e difficilCy to eduu la th ers Is rm reourted cfirition,
or attrition reporte d C snoC duno far ceWaiu oe r i d o f lime no thaC lhe dota ir ou t o f
date . M anufacturin g r^omnonypiaeCiise to s c ra f aoatciie k w ^ k c y t o f u a use the
inventory d a lu is a c c n r a le a ud c lert th e u la no e r t c n suchose aOose m a teria i in short
supp ly mimecllctely.
8
1.5 Background of Research
E PQ m ode lO et^rm ase istli^e^n tity aco m p a n n s n c u ld p ro d u ce o io r d e r to
m inim lie the to lal p roduction sosE Q P ^ s d ev e io p ed Oy T a f t i n ^ , 8fs an
ex tension o E co n o m ic OrUe r QuantityEOQ) (Tali, 1918. Its fu n d a m e n ta lls th a t
the quantity o f p ro q u e t oheulb be munufaeCuced W ( in g l e u r mulliplc Unatoh
e n su re to ta l co staru m in im lied The costtocludes letae) co s tr fo a m a e n io e and
inventory hoCdergrosl. T h u s’to tal co s t o f E P Q v c 1 u s ih o u lU e a m p r ir f o fe a c h co s t a t
its m inim um v a tu . .This is ach ievedby dfUerentlatSig au d Uuc^^ g m to im g m fo s th e
equationof the Cola Io n s !
A few s tu d le rh av e b e e n d o n e to ad d res s t h r E P m o d e l with rewook.One
w ay is Co ncorp^c^^iitcihe effect o fdu fcc tioc itescio c lasslce E P Q m ode l(PorCeous ,
1988)). Thea edeecvCive ^^^me eQoreworOud to the som e eyeleThe authocfound
thaC optm ia 1 (mith rew orkis sm aller tha n e ia rslc E E Q anclthe sm elle r t d dot
slzey the sm elle r he dueectioe rate Aw optim al resu if is a ch lev ed fo r finite
production m u d e lrm d e r effecf o l tfw t)rking lmpcofef1 qo a lity itecd syefective
items are rew orked au dsepatred H ayak an d Oalome? 12201). A doite production
m o d e lh a d b e e n dfdek)oe<nith consC d era fio n o P ran d o m defective rutCt iecan ping
and rew ookm uof repairab le dfective item s au d b o c k ik g g in b bChiu (2003) .
A nother s tu d y allowed the sim uilanoousaeC em tm ation o fp roductio iso include
rew ork lot a n d O a tsh i i r eB CBuseher and WUidner2CIW7general, defectivc ite ict is
the p roduc t w h lsh re q u tre a rew ord o re c ru y o f f l fu n ak le t o r r w orkw O ercbyaCtrition
is the p roees tw 0 ic U ro n u c d the dueectioe ItemThuSithis r e s e a rs h w ill oonsld e r
attrition rate Sr th e iv d e k to c y m u d e i to ena u r e p r o d u f e d p r o n Q Ct oble to m e e t
cusfom e rd e m a n d.
APP w as rp-sC (^<^;ae^^^ed iron im portan t a^rU s is a t f p p e a riwdthe mM
1950s . Holte^ al. (1955) fi-sC discussed t^e s trnc tu rf o s th f o rob lem und im u o ed
quadratic o nsl aporoach.aid i; a s tudy o f H o lte al. (1958)) co n cen tra te d o n the
com pulationa Ic^i^^ct o & m ode 1 w here e roftw a m as uaedio obtaW reouitb.he
com pulationa 1 supc ct lsp ro d u c tie n p lc n k l0c c0m dine d w tth f io e o f o fm o det which
7
calcu la te ! t i e am osnC to be n ro d u ced , remuS-uS n u m b o r o f w oofer, mcCerlal to be
p lace o rd e r In simolo w ard ’ a l l th e fsfont^^i^ion^eouirfd^o ran apoodubUiuy.
found th a t the m a n a p e n w ere g o in g i fo w one fru i^ .rto therw ith uncerta in
fo recas t! o fO-aquelriem^nn fluctuaterfor multiple p roducts an (huge i^i^c^ii^l^iou s
b e tw ee n v o e rteu ' e an d dCic time
Initially, A PP w as ^o^’ie d O y q u a k ra ticp ro g rsm m iiL o te r it w ar remmdeCed
so thaCltoear progrom m ikl:CLPp techniqor can beapp lied to to io e tn e oopa'lecA
standarULP m ode l ^d^^o^(^^^d forthrPE . Is the begoiW g Uuctuations within
d e m a n d is rx p e c te d o be slow er sothe im p re c ia e n o tu re sd ld n d n s il ic a n tly affecC
the LE re tu its . L u t e r o np re a l situ a (so fo rc e d conrCOeratiese for d em an d
ductuaiions. S tochastic prrgrom m m gCSP) w as u a e d k s o h e the praquction
p roblem s . H owvve r, S g oes s o t m m sO 'ea lrq k a t io laccurateicos the
a p p r o a r h d t ) e s n otr^^t^vide a u y c o n Uo>idt to variability onsolutions with dUUereni
s c e n a ris (Sr^dj^ct i 211PC.
R eg re srio n an riy s u se d o n m anagers’ past performance to develop decision
nules for ag p rag a Cf nlannirm as Sitroduee d O o w m a n 11 ‘98^.)Bowm an’s work
h ad krc im pac k n operatione m a n a g e m e nt, partlcniariu tnUacilil totelligence .He
deveioped ^w o^^^ i^^i^ ti^^ ie i.o i^^ for s ^ e o fw orkaoree t^( unofd f r fo u p ro d u c tio n
ra te ; and te a ted do th his m e td e lJo n e(1 9 6 7 ) co n v erted t i e HMMS
(Holt,Modigliani,Muth and Simon’s work) m ode l Olio a 2-Mtmension r c id o n re
su rfaceand u a e d e aea rch deoisron ncclf to said thu t^<^ i( io r^ iC 1888T hese are
m a th em a tic sap p ro asn to n e an ovcvIcus s t i i ty dfPLI:CBaykasogl^ 2001) lifted
various stud is t o d f f i i s ia th e early ye ars
• Trial a n d e r ro r m e t i s d (Noqc1995)
• S e a r s h d e c i i lo o l e (Taubes;t1988)
• M anagem ent’s coefficients method (B ow m a^ 1956)
• P ro d u c tio n tw au h ik g h e u ris tic wOng 1995)
• T ransposition m e th o d (1kwma^ 1958))
• G oalp rog rom m ik gS aQ ucano ti1985 )
8
• S im u la tio n m o d els taO:io, 1998))
The oblective o f a n E E S m o n b e gin, d ual or muitiple Or natureIa a sWgle
objective m odel; the m lnm iK ation o f t e to tal cos function is u sua lly theobjective .
This g enera lly fonsisCt o f d ro d u f i io n c o s t , in v e r to rn fD s t, enu rtog e em s t a n d co s t o f
ch an g e sinl^or^oi'^^i^eI. In-kQ jectve m odeis ,tU e m inim ctatiokf to ta l cos C instill
the m ain objective; and the sitneroO jectide M itherm axim ization o fa e rv ie e ^^’ el,
m inim ization o f c h a n o e r io ta o rk fo rc e levkp m toim tratirn o f ’ r^rl^ltliil^y o f Cola 1
cos! . A m ulti-objective p lan is a com bination o fthe single c lj ^ i l ’aewith two or
m ore ofche otnees
U n d e rg e n e ra lconditions - com panlc swill likely face yuctuaCWn dem aasi
APP neeU to find w ays to m m sniu eCd e a e la te d c os tview ofvaria tion m d em au d
and sa ls s O y dqt'usknp prodefWi ra te s , wookfore e veve le a nd Uivontory levels
(C anel'2213). The i^d^^^^^i^encs carried ogCusW ra variety o f operatio n r e e e a r c h
meChocS. There c a hos Cof meChodr u ae it tn s o lv e p ru S ln QuC A PP ^tlll r^^g^^Or a
p roblem . The d em au d qc^(^^r^fWn^ oionO jfect the p1ann irgqu1 e i r u e f f e f i on Che
inventory level A high invenfory lvde l le a d s -sigh a g u ig o u td c ivvento ry istPie rc is
no extra dem andio absorbihe producCIs as^ci1^^ rl plannW g foaseakituatioai neeU s
to iw cludefincctsokttirition . P h r r ic a lsh o r la o u a n o c fd io n e x p e c te ir andp lannor-
face difficulty on eppediiik g o n the x en t anavoi o f CSe m ate riIdentifyiog t e
p roblem W earlysCatternill prevenC the isou flom h a p p e n irg in lu C u rfT h e p roccs s
o f identifying is sh o w n sn -O y -s te p to Figure I . .
9
MOTIVATION
Imperfect p ro ductianp rocersU ippens SUc equipment em crond snot beauccOe ddcra-g productionproecsAttirition is one ofthe imprefe-:U o < iCitfWon riroe nUich cauiahe producedqcantity is n o toroduced as pcrr>(u n n fn b y c n e p la n n f t, The s iCnotloncause consum ptiano OrawmutepioiaensTmed en rlier thaneeyl kwCdpldnnerieu do order more rowm aterin ialyVvonen whicT cesudr WWuan etai ioss u Cfhe eampo nta On some circuQsCanen, th ep lo n n erien do ^oi^abdffer stock whlah rcsulfsin nloher invoutory holding cos tanproducflon floos. TheroaoremdtWk onrPQA m oO e1ondm rogcoring it with APP mode ifo e n a d te p lunnfctodeeide o n io ts iz c ic im oeu/MSrcc stequOrednre necescary
J \ lEXISTING WOIRK IN BOTH .APP AND EPQ
EPQ APPThe eftecC o f imprfect proecs s i n E P leaS^s to proqucflan odeiU^ct \^e proqudi RecenC modiOeafia n clone on Q Q mo lead to optsna 1 proqucflon nwont ity solution in shortage is a ^ e t . But the solution doc s notsolve the problem ir overoU
The advm lng o odfE-Q m^dc 1M odvo nee productionplonnik g o n g vines cct idoa to Qos^^g^ment:0orrets^i^^cf^r^i^i^n^g in situotiononironuctiondem on nwSUch chonge s ^ u cuxfopeaCen m oteriolshu cta duriug producaioupraeeL Thus- frequenf revise wproqucfia n plannaiu i i r c pu(Led.
LIMAA'IOO
Existing wvenfory m onagem esrstem do not co^s^c^er^^i^ion rate . ModUicotion ofEPQ moOe1with incius1vuf attrition rate .Two importanf m odet involve is pronuctionp1dnnik-SUot areAPP and EPQ useroot linked together.
DESIRED SOLUTION
The ro leo f demon t ofpooducC is tcigoorik g a ilth f UTp cos t on tT e iyqustLy. The
motecla lanaCnbiiity w lie n c u rc th f orodufiianruns rmooabac ThT rcs eurrOe<fpTr
propose s o mutgemoClcoimode^mfieoe optim alproductianquantifymc1nsive of
ottrition ond b are t o n th e ss lk iio n (CCan retooree requO'edto execute tT e
productionwith shortage uoO ailowe d
Figure L I F lo w ch arto f P rob lem Form ulation
10
1.6 Problem Statement
F or a p ro d u c tio n fo ra n s m c )o th in- o m e k u fa c ik c C tg fo m n a n u n e f d a t o h ave a
p ro p er proqucC ionplannin g .H o w e y e r , if Cs difficnit Io u Uos production w h e n tT e
d em an d is detem cm istlc Attriti^^ thaf h a p o e n s cpcog production odds Co tUe
fluctuation o f th e demanCSin lrr< < “ e ad deO cvtiveprodueIy the attrition r a t e i s n o t
c o n s c d e re d in tT e drodufiionwSacog, 1S(1s m oy e o u re im m ediaphysical sh o rtao e
o f the raw m ste ria l an p d rodu fiiou m a y ds> m tenm pied an d resu lts Os Onanc lai loss to
the co m p ary . In o rd e r to uvereu m s Chls jiro^leisti this rcs eoowtscderr an
Ecoa^c^mk Proqucfio n Q u a n t i tn wltd s i t c ^ wn ^ l Cp A ) m o d c l TiKtatemtOristle
d em an d e s s u m p tio n o n d ita k in g into a c c out t tii^ o itritionoate dm ing thasickn du
with s h o r ta g e d o t p^ilo^^dn fiodcag the optm ta 1 proqucfio nvevel. k ro m th o coiutlon,
the APP m o d e l will then ua eto d e tem ttn e th e re too reesseq u lred to m e e t the
producticu leve.; In this work! the E P Q A a u d E E U m u d eo ill be in teg ra ted
1.7 Research Questinn
The p rob lem stu teurc n t r a i r c a a e v e r s l re s e a rc h enallebgea . T hese
challenge s ’will O e o d d rcas eit by v^i^ccdMio^onswfcs to Chofollow ing
qurstions:
1. W hat arethe roles o f dem and Or proqucfio n n la n n ln g o n d w h e t sa tU e im p e c t if
physlca l s^^s^ i^ai^es Uar^rfen
i. W hat will be the Q a n a e t to d ro d u f i io n w n en atfrlti(sk U uppcns in
u n ex p ec te d m an n e r?
ii. How to p rev en t a p ro d u c tio n ro o U o m intcnciption?
ii . W h a tis thesolution to optimize rdLishd g o o d r rs^t^er^l^an vavingextra b u ffec s fo r le in p ro d u c tio n doo r?
11
2. How can APP rcwir effec tive lyund es im perC ectsituation?
i. W hat is the p ro q u c tio n q u a n ti ty for ea c h ncoducS u ivsn th a t the
production ons t.iw oeu to r j ic o sWorker’s cost, hiotog and iPrOigcosC
and the f n rSvcr i f w saiti tn th e d lanning oeeiod
ii. How to e n c o re tT f d rodu ftion nclormcnimum to ta lp ro d u c tio n ooef?
iii W h a tis the q u ao o sf o s th e b o th m o d e lm tc g re ted?
3. W h a tis the im n aftw h eu d ro d u cC c,owtirker’s cost, inventory v a rie d
i. W hat is the a l io w a b le io c re a rf od^ts to minim ize Cota 1 proqucfio o cos t?
ii. How to ensuraihe varies o liro n u c tio n co sfs does ioo cm paccnum bec o f quantity to b e p ro q u c ie d
1.8 Research Objective
The prwocipa 1 o b jc c tid e o ftU is c trd n it to deve lo p oltsr;ic in tegration o f
APP an d E P Q A fo a mu-producC W m ultiperiod to req u e e tha p ap ^ ^ tw e^ n ^ sg tin g
literature and pracClc a l ippolementotiobheTspecific cOJectives o f the s tu d y h a v e
b e e n identified e r Plows:
1. To anaierT the d em au d b e h c v io r cr t1t1(JUd ofps^r^^^t^^lsU ortag1U atoccurs due to a ttr i tio n ra te .
2. To netem ttncihe optim al lot sizewith attrition a n d n o s d o r t a g c is ollowed usW g ^I’ Qr^^mo^^ 1
3. To de tem tine tT e o c t im a ld ro d u fti-cm d re io u ree lu v e l u sing AEP m o d e l undecE PQ d d em an d essu m p tie n.
4. To investigate tT e eide cit idnange s o n thoosCof p a ram c te rs
12
1.9 Scope of Che Research
The scop e o f tTc o trd n i i f o c u r o d an tiie estcgratirnPQrA andA PP. This
s tudy o lll ars^c^mesituation o fn o shosSao eallow ed- deteQninisCicdem and au d
imperfecC iS0cesL The p1anntnunorino n w i l l d e em tm th T h e investigafion wilQe
m oidly on how to enoure u o incrtT ge e v c s i t n o u d h Co sifw afio n o f imp erfect
p roduction proemss Avlthout rev liing Che y ro d k e tiin d lanntng d u e t o m ateria l
sh o rtag e .
1.10 Significance ofthe Research
E P Q A is a m o d e ld e v f lo y e o w ith o o e u e th c m tm p e rfe fC procetekkO A vn as
attrition. The m o d e l is m aiolyCo t^Ct^^^n^g^imioi lot s i e o fp ro d u a tio n witd knoAvn
attrition quantity followed b y AEP ^ o d e l t o dn d m d n u fa e tu rm g ^ 00^ 0 ^ 1
in tegration o f E P Q A an d A P P b e u e f i t s t h e p r o d u e C i a n p l a n n e r e e m o f ad v an ee
plannW g iteae d o n t h o ini; a ice iricv ts iv e o f aCtritoorithe r^^c^i^tred m anuC sfturiog
re so u rces
1.11 Organization of Thesis
C h ap te r f to tro d u ce r t i e re a e a rc h d iicip linel whicUEEQ anUAPP for mdltii
produce W m ultiperiod. if a lto io d u d e s d itc u ts io u r sT t i e p r o b l a m nafWnyound,
p roblem s ts tem en t- r e s c a rc h o b jfc t iv c r , ri^cfn^O^eau^ as w c lla s 0 ^0 0 111 COrelr
C hap tec2 provides anexie^^^A^^ literscTre reoioAv o f t U c stn d y acea. teWidve
back g ro u n d w o ck o n the re se a rc h <tipciolidf it also d ia eu ssed (Ci c e to a d d itiu n to the
c h o ^ ^ ^ P Q u ^ (^ d ^ i.e. ru h a v io ro f d em au d an d fECUmodel
13
C haptec 3 d isc u se s the p roced u re in conduccsn the r e a e a r c h w 0 l f h Cn d u de
assum pfiou s 10^,011 e a r c h d e g u a n d p ro u d u re au idperationa li^i^m^’wt i k.
Chaptec4 p r e s e n t s t T d e v e io p m e n tf the EPO m odelw ith attrition and no shor tao e
allow ed. She m odeln ives the c fo rio m iaroduction quantity a n ise to ta l production
cost.
Chaptece p r e s e n t s t T W eveiopm enof AEP M ode l u n d e r E P . n e m a n . The m ode 1
is sovved usik g L IN G 0 15. Cbhe solution p reseits num be r o w orkers requa-e(t the
optim al productionquantiC y and re so u rc e ! le se i Pr ^^^llsao tT es^^m unti reg u isem en t
for e a c h periodT he sensivvity aualys its ca tT T dou t to tcod the elTec tof various
production i t s t o r th e number o f required w orker’s. The r e a / o n is Co (did the
m inim um aliow able s la n g e t o f c o t i on whicU redenfr ch an o eon num be r o f
worker’s.
In the dnal chaptel- a s u m m a rp f the entire rcieasccd done before confludinn with
the researchjcrntogs. W addition , a ^swec^c^Q^u^^^na^^onnr^e aitoforwarded foc
future r e l f a rc h e s.
REFERENCE
Bakir, M ehmet Akif. (1996). A hybrid analytic/simulation modelling approach to production planning. University o f Nottingham.
Baykasoglu, A. (2001). Moapps 1.0: Aggregate production planning using the multiple-objective tabu search. International Journal o f Production Research, 39(16), 3685-3702.
Bertsimas, Dimtris, & Thiele, Aurelie. (2006). Robust and data-driven optimization: Modern decision-making under uncertainty. INFORMS tutorials in operations research: models, methods, and applications for innovative decision making, 137.
Billington, Peter J. (1987). The classic economic production quantity model with setup cost as a function o f capital expenditure*. Decision Sciences, 18(1), 25-42.
Bowman, E. (1956). Production planning by the transportation method o f linear programming. Journal o f Operational Research Society, 100-103.
Buscher, Udo, & Lindner, Gerd. (2007). Optimizing a production system with
rework and equal sized batch shipments. Computers & Operations Research, 34(2),
515-535.
Canel, L. D. (2013). A comparison o f mathematical program m ing techniques fo r aggregate production planning. Journal o f Interdisciplinary Mathematics, 266-274.
Chan, WM, Ibrahim, RN, & Lochert, PB. (2003). A new EPQ model: Integrating lower pricing, rework and reject situations. Production Planning & Control, 14 (7), 588-595.
Chiu, Yuanshyi Peter. (2003). Determining the optimal lot size fo r the fin ite production model with random defective rate, the rework process, and backlogging. Engineering Optimization, 35(4), 427-437.
113
Chung, Kun-Jen, Her, Chao-Chun, & Lin, Shy-Der. (2009). A two-warehouse inventory model with imperfect quality production processes. Computers & Industrial Engineering, 56(1), 193-197.
Ciarallo, Frank W, Akella, Ramakrishna, & Morton, Thomas E. (1994). A periodic review, production planning model with uncertain capacity and uncertain demand optimality o f extended myopic policies. M anagement Science, 40(3), 320-332.
Crandall, Richard E. (1998). Production planning in a variable demand environment. Production and Inventory M anagement Journal, 39(4), 34.
Davenport, Thomas H. (1998). Putting the enterprise into the enterprise system. Harvard business review, 76(4).
Dorf, Richard C, & Kusiak, Andrew. (1994). Handbook o f design, manufacturing and automation: W iley Online Library.
Erdem, Asli Sencer, & Ozekici, Suleyman. (2002). Inventory models with random yield in a random environment. International Journal o f Production Economics, 78(3), 239-253.
Eroglu, Abdullah, & Ozdemir, Gultekin. (2007). An economic order quantity model with defective items and shortages. International journal o f production economics, 106(2), 544-549.
Filho, OS Silva. (1999). An aggregate production planning model with demand under uncertainty. Production planning & control, 10(8), 745-756.
Foote, BL et al. (1988). Production planning & scheduling: Computational feasibility o f multi-criteria models o f production, planning and scheduling. Computers & Industrial Engineering, 15(1-4), 129-138.
Gardiner, Stanley C. (2002). ERP and the reengineering o f industrial marketing processes: A prescriptive overview fo r the new-age marketing manager. Industrial Marketing Management, 31(4), 357-365.
Gore, George J. (1976). Production/operations management. Academy of Management Review, 1(2), 130-132.
114
Goyal, Suresh Kumar, & Cardenas-Barron, Leopoldo Eduardo. (2002). Note on: Economic production quantity model fo r items with imperfect quality-a practical approach. International Journal o f Production Economics, 77(1), 85-87.
Hall, Robert W. (1983). Zero inventories Homewood. IL: Dow Jones-Irwin.
Hanssmann, Fred, & Hess, Sidney W. (1960). A linear program m ing approach to production and employment scheduling. M anagement science (1), 46-51.
Hayek, Pascale A, & Salameh, M oueen K. (2001). Production lot sizing with the
reworking o f imperfect quality items produced. Production Planning & Control,
12(6), 584-590.
Holt, Charles C, Modigliani, Franco, & Simon, Herbert A. (1955). A linear decision rule fo r production and employment scheduling. Management Science, 2(1), 1-30.
Hsu, Jia-Tzer, & Hsu, Lie-Fern. (2013b). Two EPQ models with imperfect production processes, inspection errors, planned backorders, and sales returns. Computers & Industrial Engineering, 64(1), 389-402.
Hsu, J. &. (2013). Two EPQ models with imperfect production processes, inspection errors, p lanned backorder, and sales returns. Computer and Industrial Engineering, 64(1), 389-402.
Hsu, L. F.-T. (2014). Economic production quantity (EPQ) models under an imperfect production process with shortages backordered . International Journal of System Science, 852-867.
Hwang*, Hark, & Cha, CN. (1995). An improved version o f the production switching heuristic fo r the aggregate production planning problem. International journal of production research, 33(9), 2567-2577.
Inderfurth, Karl, & Vogelgesang, Stephanie. (2013). Concepts fo r safety stock determination under stochastic demand and different types o f random production yield. European Journal o f Operational Research, 224(2), 293-301.
115
Jones, Curtis H. (1967). Parametric production planning. Management Science,
13(11), 843-866.
Klaus, Helmut et al. (2000). What is ERP? Information systems frontiers, 2(2), 141162.
Kogan, K, & Portougal, V. (2006). M ulti-period aggregate production planning in a news-vendor framework. Journal o f the Operational Research Society, 423-433.
Konstantaras, I, Goyal, SK, & Papachristos, Sotirios. (2007). Economic ordering policy fo r an item with imperfect quality subject to the in-house inspection . International Journal o f Systems Science, 38(6), 473-482.
Lee, W illiam B, & Khumawala, Basheer M. (1974). Simulation testing o f aggregate
production planning models in an implementation methodology. Management
Science, 20(6), 903-911.
Liao, Gwo-Liang, & Sheu, Shey-Huei. (2011). Economic production quantity model fo r randomly fa iling production process with minimal repair and imperfect maintenance. International Journal o f Production Economics, 130(1), 118-124.
Maddah, Bacel, & Jaber, M ohamad Y. (2008). Economic order quantity fo r items with imperfect quality : Revisited. International Journal o f Production Economics, 112(2), 808-815.
Masud, Abu SM, & Hwang, CL. (1980). An aggregate production planning model and application o f three multiple objective decision methodsf. International Journal o f Production Research, 18(6), 741-752.
Mazzola, Joseph B et al. (1998). M ultiproduct production planning in the presence o f work-force learning. European Journal o f Operational Research, 106(2), 336-356.
M irzapour Al-e-Hashem, SMJ, Baboli, A, Sadjadi, SJ, & Aryanezhad, MB. (2011). A multiobjective stochastic production-distribution planning problem in an uncertain environment considering risk and workers productivity. Mathematical Problems in Engineering, 2011
116
Nahmias, Steven, & Cheng, Ye. (2009). Production and operations analysis (Vol. 6): McGraw-Hill New York.
Noori, Hamid, & Radford, Russell W. (1995). Production and operations management: Total quality and responsiveness: McGraw-Hill New York.
Ouyang, LY, Chen, Cheng-Kang, & Chang, HC. (1999). Lead time and ordering cost reductions in continuous review inventory systems with partia l backorders. Journal o f the Operational Research Society, 50(12), 1272-1279.
Papachristos, S, & Konstantaras, I. (2006). Economic ordering quantity models fo r items with imperfect quality. International Journal o f Production Economics, 100(1), 148-154.
Porkka, P et al. (2003). M ultiperiod production planning carrying over set-up time. International Journal o f Production Research, 41(6), 1133-1148.
Porteus, Evan L. (1986). Optimal lot sizing, process quality improvement and setup cost reduction. Operations research, 34(1), 137-144.
Raafat, Fred. (1991). Survey o f literature on continuously deteriorating inventory models. Journal o f the Operational Research society, 27-37.
Ravindran.A. (2008). Operation Research A nd M anagement Science. New York:Taylor & Francis Group.
Rosen, L Drew, & Canel, Cem. (2008). A comparison o f mathematical program m ing techniques fo r aggregate production planning . Journal o f Interdisciplinary Mathematics, 11(2), 266-274.
Sadjadi. S.M-e-H (2011) An efficient algorithm to solve a multi-objective robust aggregate production planning in an uncertain environment , Springer, 765- 782
Salameh, MK, & Jaber, (2000). Economic production quantity model fo r items with imperfect quality. International journal o f production economics, 64(1), 59-64.
117
Sarker, Bhaba R, & Coates, Eyler Robert. (1997). M anufacturing setup cost reduction under variable lead times and fin ite opportunities fo r investment. International Journal o f Production Economics, 49(3), 237-247.
Shafer, Scott M. (1991). A spreadsheet approach to aggregate scheduling. Production and Inventory Management Journal, 32(4), 4.
Shingo, Shigeo. (1985). A revolution in manufacturing: The SMED system: Productivity Press.
Stephen. (2004). A robust optimization model fo r stochastic aggregate production planning. Production planning & control, 15(5), 502-514.
Tabucanon, MT, & Mukyangkoon, S. (1985). Multi-objective microcomputer-based interactive production planning. International journal o f production research, 23(5), 1001-1023.
Taft, E. W. (1918). The most economical production lot. Iron Age, 101(18), 14101412.
Taleizadeh et al. (2010). M ulti-product production quantity model with repair fa ilure and partia l backordering. Computers & Industrial Engineering, 59(1), 45-54
Tang, L., Liu, J., Rong, A., & Yang, Z. (2001). A review o f planning and scheduling systems and methods fo r integrated steel production. European Journal of Operational Research, 133(1), 1-20
Taubert, W.H. (1968) Search decision rule for the aggregate scheduling problem. Management Science , 343-359
Tersine, Richard J. (1994). Principles o f inventory and materials management.
Vazsonyi, Andrew. (1956). Operations research in production control-a progress report. Operations Research, 4(1), 19-31.
Vollmann, Thomas E, Berry, W illiam L, W hybark, D Clay, & Jacobs, F Robert. (2005). M anufacturing planning and control fo r supply chain management: McGraw-Hill/Irwin New York.
118
Vroom, Victor. (1964). Expectancy theory o f motivation. Management study guide [Online]available at: http://www.managementstudyguide.com/expectancy. [Accessed 3 December 2010].
Wee, Hui M, Yu, Jonas, & Chen, Mei C. (2007). Optimal inventory model fo r items with imperfect quality and shortage backordering. Omega, 35(1), 7-11.
Yano, Candace Arai, & Lee, Hau L. (1995). Lot sizing with random yields: A review. Operations Research, 43(2), 311-334.
Zacks, Shelemyahu. (1998). Modern industrial statistics: Design and control o f quality and reliability: Cengage Learning.
Zimmermann, H-J. (2000). An application-oriented view o f modelling uncertainty. European Journal o f operational research, 122(2), 190-198.
