Optimal Setup Cost Reduction and Lot Sizing with Imperfect Production Processes and Quantity Discounts

Transcription

1 Proeeings o the Tenth Asia-Paii Conerene on Global Business, onomis, Finane an Soial Sienes (AP7Hong ong Conerene) ISBN: Hong ong-sar 0-, January 07 Paper ID: H735 Optimal Setup Cost Reution an Lot Sizing with Imperet Proution Proesses an uantity Disounts Tien-Yu Lin, Department o Marketing an Supply Chain Management, Overseas Chinese University, Taiwan -mail: amtyl@oueutw Abstrat This paper onentrates on an eonomi proution quantity moel with quantity isounts an imperet quality, where the sreening proess ours at the proution uration Speiially, this paper onsiers that the proution rate is inite, whih is unlike Porteus (985) moel, an the supplier oers the quantity isounts to stimulate the buyer orering more quantities ah item is inspete immeiately ater it is proue Then, the imperet quality items are store at a speii warehouse with a lower holing ost rate ompare to goo items store at another warehouse With respet to the imperet quality items, the manuature sells them or salvage value at a ierent market by the en o proution proess The obetive o this stuy is to etermine the inventory lot size an the setup ost whih is a untion o apital investment maximizing the expete total proit An eiient algorithm is then evelope to in the overall optimal solution or the moel Numerial example is presente to illustrate the propose moel an algorithm Managerial insights are also explore ey Wors: Inventory, Imperet quality, Lot sizing, Capital investment, uantity isounts JL Classiiation: C 6, M

2 Proeeings o the Tenth Asia-Paii Conerene on Global Business, onomis, Finane an Soial Sienes (AP7Hong ong Conerene) ISBN: Hong ong-sar 0-, January 07 Paper ID: H735 Introution Manuaturing the right levels o prout to satisy ustomer nees have beome an important issue or the enterprises The proution proesses are assume to be peret an stationary in the traitional eonomi proution quality (P) moels However, in pratie, this assumption may not be true beause the prout quality usually epens on the state o the proution proess In general, the proution proess initially is uner ontrol an items proue may be peret quality As time goes on, the proess may eteriorate as a result o whih the items proue ontain eetives or items that are o substanar quality (Rosenblatt an Lee, 986) Several exellent researhers have pai their attention to the inventory moels where the quality proue may not be goo ue to an unreliable proution proess One o the pioneer papers in this issue has been stuie by Rosenblatt an Lee (986) in whih they explore the eets o an imperet proution proess on the optimal yle time In the same time, Porteus (986) inorporate the eet o eet items into eonomi orer quantity (O) moel stuying the relationship between quality an lot size Zhang an Gerhak (990) explore a oint lot sizing an inspetion poliy or an O moel onsiering the ranom yiel Cheng (989) propose an P moel with a lexible ranom yiel proess an employe a geometri programming metho to solve the evelope moel Cheng (99) ormulate an O moel with eman-epen unit proution ost an imperet proution proesses He urther transerre this optimization problem as a geometri programming or solving Bose et al (995) propose an O moel or eteriorating items with a linear time-epenent eman rate in whih the shortages an baklogging are allowe Yano an Lee (995) have mae a omprehensive survey on these moels An interesting variant reently has been evelope by Salameh an Jaber (000) who extene the traitional P moel by onsiering that ientiying imperet quality items employs an inspetion proess ver sine Salameh an Jaber s (000) moel was evelope, whih onsiers the quality ontrol an thus is more reasonable than the traitional O/P moels, many exellent researhers have extene their moels into the issue o O/P moels with imperet quality (or example, Chan et al, 003; Huang, 004; roglu an Ozemir, 007; Maah an Jaber, 008; Lin, 00; Lin, 03) In some reent works, Wee an Wiyaana (03) explore a proution system or eteriorating items with stohasti preventive maintenane time an rework Taleizaeh et al (04) evelope an P inventory moel or multi prouts in a single mahine with rework an interruption in proess, whih is ierent traitionally non-interrupt proution proess Wee et al (04) investigate an P moel or imperet quality items with non-synhronize sreening an rework in whih they use time intervals rather than orering size an bakorer size as eision variables An O with imperet items whih onsiers investing in the

3 Proeeings o the Tenth Asia-Paii Conerene on Global Business, onomis, Finane an Soial Sienes (AP7Hong ong Conerene) ISBN: Hong ong-sar 0-, January 07 Paper ID: H735 spee o the quality ontrol hek is presente in Hauk an Voros (05) an Lin et al (06) The authors in Moussawi-Haiar et al (06) integrate the inspetion time into the eonomi proution moel with rework, an emonstrate the signiiant eet that the inspetion time has on the results They urther onsiere a manuaturing proess with ranom supply an a sreening proess onute uring an at the en o proution Al- Salamah (06) evelope an eonomi proution quantity (P) moel or the ase where the proution proess an inspetion are both not peret in whih two settings or the sampling stage have been onsiere: estrutive an non estrutive testing o the sample items A omprehensive survey o the moiie O moel extensions or imperet quality items was explore by han et al (0b) Note that the above-mentione moels base on Salameh an Jaber s (000) work mostly ealt with O moels an selom stuie P moes However, in pratie, the proution apaity is inite an thus P moels play an important role or the inventory issue We also note that imperet quality O moels base on Salameh an Jaber s (000) moel assume the retailer perorms the sreening proesses or items ater an orer reeive This assumption may not math P ases beause eah item is immeiately sreene ater it is proue The eetive items are then usually store in a ierent warehouse rom the goo items to separate the traking o osts an quantities or the eetive items (Paknea et al, 005; Wahab an Jaber, 00; Lin et al, 06) Many semionutor inustries provie goo examples With this onsieration, the holing ost or a unit o goo items per perio is larger than or a unit o eetive items per perio Thus, an P moel, where the sreening proess ours at the proution uration, with ierent holing ost is worth stuy Reently, the issue o setup ost reution in proution systems reeive a onsierable attention (eg Porteus, 985; Hong an Hayya, 993; Sarkar an Coates, 997; Moon et al, 00; Hou, 007) in whih the researhers have reognize setup ost an be ontrolle an reue through various eorts suh as speialize equipment aquisition, proeural hanges an learning eets Porteus (985) is the irst pioneer to evelop a ramework enompassing not only altering the setup ost but the eman rate or investing in reuing setup ost in the O moel Porteus (986) urther introue the investing options into the O moel to explore the eets o proess quality improvement an setup ost reution on the lot size ver sine Porteus (985, 986) showe his ieas, several extensions were built For example, Billington (987) evelope an P moel with the setup ost parameter replae by a untion o apital investment The eonomi beneits o reuing setup ost an improving proess quality by simultaneously investing in new tehnology was stuie by eller an Noori (988), Hong et al (99), an Hong an Hayya (995) Several relationships between the setup ost level an the expeniture o apital investment have been isusse by Paknea et al (990), im et al (99), an Hou (007) Unlike previously 3

4 Proeeings o the Tenth Asia-Paii Conerene on Global Business, onomis, Finane an Soial Sienes (AP7Hong ong Conerene) ISBN: Hong ong-sar 0-, January 07 Paper ID: H735 stuies, some researhers (Aniani, 998; Wu, 00, Goyal an Gunasekarn, 990) urther explore setup ost reution in multi-stage proution inventory systems Other relate stuies on setup ost reution inlue Huang et al (00), Voigt an Inerurth (0), Sarkar an Maumer (03); Sarkar an Moon (04) an reerenes therein We note that the above literatures iniate the setup ost an be reue at an ae investment an thus has signiiantly inluene or eision making Thus, onsiering the relationships between the amount o apital investment an setup ost level is very important when apital investment strategies are employe Base on the above arguments this paper stuies an P moel with quantity isounts an imperet quality, where the sreening proess ours at the proution uration Speiially, this paper onsiers that the proution rate is inite, whih is unlike Porteus (985) moel, an the supplier oers the quantity isounts to stimulate the buyer orering more quantities ah item is inspete immeiately ater it is proue Then, the imperet quality items are store at a speii warehouse with holing ost rate (a unit o eet item per perio, expresse as a ration o ollar value) ompare to goo items store at another warehouse with holing ost g (a unit o goo item per perio, expresse as a ration o ollar value), in whih g > With respet to the imperet quality items, the manuature sells them or salvage value at a ierent market by the en o proution proess The obetive o this stuy is to etermine the inventory lot size an the setup ost whih is a untion o apital investment maximizing the expete total proit Notations an Assumptions moel The ollowing notations are use throughout this paper to evelop the mathematial Notations D eman rate setup ost or eah proution run M proution rate, M > D, 0 g p lot sizes or eah proution run, a eision variable original setup ost or eah proution run prior to investment nominal setup ost, a eision variable unit purhase (proution) ost o th level orresponing to the ost isount struture holing ost rate or a unit o goo item per perio, expresse as a ration o ollar value an g > holing ost rate or a unit o eet item per perio, expresse as a ration o ollar value an < g perentage rate o eetive items in 4

5 s v x t φ k α T Proeeings o the Tenth Asia-Paii Conerene on Global Business, onomis, Finane an Soial Sienes (AP7Hong ong Conerene) ISBN: Hong ong-sar 0-, January 07 Paper ID: H735 unit selling prie o peret items unit salvage value o srap items, v<s unit sreening ost proution run, t =/M apital investment require to reue setup ost rom 0 to ration o reution in per ollar inrease in φ k,, α<i yle length Assumptions The assumptions in this paper are esribe as ollows: () The eman rate or items is known an onstant () The holing ost or goo items in a speii warehouse is higher than that o eetive items in another warehouse (3) ah item is sreene at the time o items as it is output rom the proution run, an all eetive items are etete an then sol with a salvage value when the proution yle is over (4) Shortages are not allowe (5) The relationship between setup ost reution an apital investment or eah yle time an be esribe by the logarithmi investment ost untion That is, setup ost,, an the apital investment in setup ost reution, φ k, or eah yle time is esribe as ollows: k ln 0 (6) The supplier provies all-unit quantity isounts to the buyer The ost sheme is liste in Table an is the unit prourement ost or the th level (ie, i the unit prourement ost is ) 3 r 3 Mathematial Moel Table : Prourement ost struture r r, then In this setion we evelop a mathematial moel with the total proit maximization obetive or the investment ost o hanging an the inventory relate osts assoiate with 5

6 Proeeings o the Tenth Asia-Paii Conerene on Global Business, onomis, Finane an Soial Sienes (AP7Hong ong Conerene) ISBN: Hong ong-sar 0-, January 07 Paper ID: H735 quantity isounts, by optimizing over both an This moel onsiers that items have imperet quality an thus eah item is inspete immeiately ater it is proue Then, the imperet quality items are store at a speii warehouse with holing ost rate ompare to goo items store at another warehouse with holing ost g, in whih g > With respet to the imperet quality items, the manuature sells them or salvage value at a ierent market by the en o proution proess uantity isounts are oere by the supplier to stimulate the buyer to orer a larger amount Beause this paper eals with unisounte osts, an opportunity ost per unit time is thereore harge Thus, the proution system with imperet proesses an ierent holing osts is illustrate in Fig in whih T is the yle time or eah proution lot an t is a proution run (t =/M) Unlike Salameh an Jaber s (000) work, this paper assumes eah item is sreene as it is output rom the proution run (ie [0, t ]) The eetive items are sol at a ierent market or salvage value when the proution run is over Thereore, the yle time T oul be expresse as T p D () Inventory (-p) (-D/M) (-D/M-p) M-D e p D b g y t t Time T=(-p)/D Figure The behavior o the inventory level per yle From Figure, we know the maximum inventory level at the en o t is (-D/M) As the proution run is inishe, the eetive items, p, are then sol at ierent market an thereore the inventory level immeiately rops to (-D/M-p) Other explanations or Figure will be introue when they are neee Let TR () an TC (,) be the total revenue an the total ost per yle orresponing to the quantity isounts sheule, respetively TR () inlues the revenues rom goo an eetive items an is given by 6

7 TR Proeeings o the Tenth Asia-Paii Conerene on Global Business, onomis, Finane an Soial Sienes (AP7Hong ong Conerene) ISBN: Hong ong-sar 0-, January 07 Paper ID: H735 =s -p vp TC (,) onsists o set up ost per yle, sreening ost per yle, prourement ost, amortize apital ost, an holing ost These osts are esribe as ollows We know the yle time T or eah proution lot is ompose o two parts (t : proution run; t : non-proution run) an the eetive items are sol at the terminal time o t Thus, the inventory quantities in the t uration o are ompose o goo an imperet quality items; the inventory quantities in the uration o t are all goo quality items Thereore, the inventory holing ost oul be obtaine shown as below: () The holing ost ours in the uration o t In the proution run, t, the items proue an be lassiie as peret quality items an imperet quality items ater the sreening proesses an then store them at ierent warehouse The imperet quality items with p proportion o eah proution lot are sol when the proution is over Let HC () be the holing ost or imperet quality items in the uration o t Thus, HC () oul be ompute base on the triangular area o (beg) with proportion p in Figure an an be easily obtain by employing a geometri argument through the ollowing: HC p, where π - D M an,,, r M Alternatively, let HC g() be the holing ost or peret quality items in the uration o t We have () HC g p g,,,, r M (3) () The holing ost ours in the uration o t We note that the sreening proesses or all items are inishe at the en o t an then the imperet quality items are sol at that time This implies all the items in the non-proution run, t, are in the goo quality onition Let HC g() be the holing ost or peret quality items in the uration o t Thus, HC g() oul be ompute base on the triangular area o (gy) in Figure an an be easily obtain by employing a geometri argument through the ollowing: p HC g g,,,, r D Other osts in eah yle oul be esribe as ollows: (a) Setup osts: The setup ost in a proution yle is Setup ost = (5) (4) 7

8 Proeeings o the Tenth Asia-Paii Conerene on Global Business, onomis, Finane an Soial Sienes (AP7Hong ong Conerene) ISBN: Hong ong-sar 0-, January 07 Paper ID: H735 8 (b) Prourement (proution) ost: We assume the supplier oers the all-units quantity isounts to enourage the manuature into orering more quantities This implies the prourement (proution) prie is some untion o the quantity purhase Thus, the prourement ost orresponing to the unit invoie ost or eah proution yle is Prourement ost= (6) () Amortize apital ost: The relationship between the reution in setup ost an apital investment an be esribe as logarithmi investment untion whih has been aopte by Poteus (985, 986), Sarker an Coates (997), Sarker an Moon (04), Hou et al (06) That is, the setup ost,, an the apital investment in setup ost reution, φ k, an be shown as or, ln α k Thereore, the amortize total apital ost or eah proution yle an be presente as D p ln α st Amortize apital o 0 (7) () Sreening ost: The manuature perorms 00% inspetion when the items are proue rom the proution line Thus, the sreening ost is given by Sreening ost= x (8) Synthesizing the osts esribe in the above, we have the total ost per yle shown as ollows:,,r,, D p ln x M p D p M p ) (, TC g 0 The total proit, TP (,), per yle is the total revenue less the total ost an is given as 0 r,,,, D p ln x M p D p M p vp p s, TC ( ) TR, TP g Taking the expete value o the total proit per yle TP, with respet to p, we have

9 TP Proeeings o the Tenth Asia-Paii Conerene on Global Business, onomis, Finane an Soial Sienes (AP7Hong ong Conerene) ISBN: Hong ong-sar 0-, January 07 Paper ID: H735, s p vp p M g x D M p p p p D 0 ln,,,, r have Reerring to q () an taking the expete uration o yle time T with respet to p, we T D p Using the renewal-rewar theorem (Ross, 996), the expete proit per unit time an be expresse as ollows: TP lim t t t, Dv Ds TPU p D D x D M p, g TP T, D M ln 0 p p p,,, r, where p (9) To maximize the expete total proit per unit time, we nee to show that the Hessian Matrix o q (9) is negatively einite However, it is not easy to etermine the onavity o the Hessian Matrix in q (9) We thereore employ an alternative proeure to obtain the proit untion properties 4 Methoology an algorithm To in the unique solution or the expete proit property Property : For ixe, TPU, is onave in TPU,, we nee the ollowing mploying Property, we obtain the possible optimal value o by letting, 0 TPU, we have ~ D,,,, r Substituting q (0) into q (9), one has (0) 9

10 Proeeings o the Tenth Asia-Paii Conerene on Global Business, onomis, Finane an Soial Sienes (AP7Hong ong Conerene) ISBN: Hong ong-sar 0-, January 07 Paper ID: H735 p D x Dv D 0 TPU Ds ln g D p p p Dp, M M,,, r () Taking the irst an seon partial erivatives o q () with respet to, we have TPU TPU g D p p D M M p,,,, r () 0,,, r (3) qs () an (3) reveal that the aniate optimal lot size * orresponing to eah prourement ost exists an is unique Letting 0 TPU, we obtain the possible optimal value o as ollows: ~ g D M p p Dp M,,, r (4) We note that ~ ~ orresponing to the unit-purhasing ost is vali o However, ~ may not exist at, an thus two ases may our: ~ Case I:, where ~ is the maximum lot size orresponing to In this ase, the buyer aopts the lower unit-prourement ost (say b an b < ) to obtain ~ ~ TPU TPU This implies the easible the lot size From q (), we have aniate ~ orresponing to woul not be the global optimization ~ Case II:, where is the minimum lot size orresponing to b In this ase, we an ix an respetively uner given an then two senarios our: Senario I: the perspetive o the breakpoint orresponing to In this senario, the aniate optimal lot size may our at the break point with its orresponing aniate optimal setup ost This is beause the unit-prourement ost 0

11 Proeeings o the Tenth Asia-Paii Conerene on Global Business, onomis, Finane an Soial Sienes (AP7Hong ong Conerene) ISBN: Hong ong-sar 0-, January 07 Paper ID: H735 epene on the lot size an thus has a ierent ost Thus, or given orresponing to, the setup ost, similar to q (0), oul be etermine as ollows: ˆ,,,, r (5) D Senario II: the perspetive o ixe In this senario, the aniate optimal solution may our at, satisying TPU Thus, given q (9) or ixe, we have, D g D p p TPU, Letting TPU g D M p, M,,, r (6) D 0 3, D M 0, we have Plugging q (8) into D D p p p M (7),,, r (8), we have the ollowing results D D p p p g M D,,, r (9) Until now, the aniate optimal lot size an setup ost orresponing to unit-prourement ost has been obtaine To in the global optimal solution, an algorithm is evelope as ollows: Algorithm: ~ Step Obtaine Step For = to r ~ I, Next lse { rom q (0) an M ~ rom q (4) or all =,,, r

12 (9)} Proeeings o the Tenth Asia-Paii Conerene on Global Business, onomis, Finane an Soial Sienes (AP7Hong ong Conerene) ISBN: Hong ong-sar 0-, January 07 Paper ID: H735 I ~ then Do { } } lse { ~ I, then Do { {obtain {obtain ~ ~ {ompute TPU, {Next } rom q (9) an reor it} ˆ rom q (5) an ompute TPU ˆ rom q (9) an ompute I { Compute lse { } } TPU, } TPU, rom q (9), rom q rom q (8) ~ ~ {ompare TPU,, TPU, ˆ, TPU, an then reor the maximum one} {Next } } } Step3 The maximum expete proit obtaine in Step provies the optimal proution lot size, setup ost, an the unit-prourement ost Note that i we ignore the apital investment in setup ost reution, an quantity isounts an then onsier all items are peret quality (ie p=0 an h= g= ), the optimal lot size in q (8) reues to * D, (0) h D M whih is equivalent to the result in the lassial eonomi proution quantity moel This helps or valiating our moel 5 Numerial example To illustrate the optimal lot size an setup ost ( *, * ) behavior, let us onsier the ollowing example Deman rate, D=400 units/year, Proution rate, M=900 units/year, Original setup ost, 0=$400/yle,

13 Proeeings o the Tenth Asia-Paii Conerene on Global Business, onomis, Finane an Soial Sienes (AP7Hong ong Conerene) ISBN: Hong ong-sar 0-, January 07 Paper ID: H735 Sreening ost, =$/unit Holing ost rate or a unit o goo item (a ration o ollar value) g = $005/$/year Holing ost rate or a unit o eet item (a ration o ollar value) = $005/$/year Selling prie o goo quality items, s=$50/unit Salvage value o srap items, v=$5/unit In aition, the perentage srap p is uniormly istribute over the range [0, 004], then the probability ensity untion (p) is p 5, 0 p 0 04, 0, otherwise Furthermore, the supplier oers a prie isount sheule as shown in Table Table : Prourement Cost Struture or the Manuature ~ Consiering the type o ost struture an using the algorithm evelope in setion 4, we obtain the optimal lot size, setup ost, an maximum expete total proit as ollows: Step : From q (0) an q (4), we have ~ 93, ~ 93 7, ~ 933, ~ 933 6, ~ ~ 5, ~ 5 3, ~ 5 4, ~ 5 5, ~ Step : () Beause ~ 00, ~ 500, ~ 900, This implies the optimal solution may 3 4 not our at these results We thereore o not urther ompute them ~ () Beause , we substitute ~ an ~ 5 5 into q (9) 4 4 an thus obtain TPU 9336, (3) Beause ~ 400, rom q (5), we then have 5 5 ˆ 56 an TPU 400, (4) Obtaining 5 5 rom q (9) an an rom q (8), we have Substituting them into q (9), one has TPU 400,

14 Proeeings o the Tenth Asia-Paii Conerene on Global Business, onomis, Finane an Soial Sienes (AP7Hong ong Conerene) ISBN: Hong ong-sar 0-, January 07 Paper ID: H735 Step 3: Compare the results obtaine in Step, we know TPU 9336, gives the maximum expete total proit This implies the optimal lot size is 9336 units an the optimal setup ost is $55, whih orresponing to the prourement ost 4=00 The optimal solution or the given parameter set is * =9336 units an * =$55, an the expete annual proit is $70099, whih meets the results obtaine in our evelope Algorithm 6 Conlusions In this paper, we evelope a new P moel with imperet proution proesses an quantity isounts, where the sreening proess ours at the proution stage An optimal set up ost reution an lot sizing are the eision variables employing to onstrut an P moel There were several ierent onsierations inlue in this new moel: () the ierent holing ost or goo items an eetive items () the quantity isounts (3) the apital investment (4) imperet proution proesses The expete total proit untion was erive an a proeure assoiate with an algorithm was establishe to in the optimal solution The work o the traitional P moel is a speial ase use in our moel assoiate = g=h an p=0 when we ignore the apital investment in set up ost reution an quantity isounts Numerial results in general showe that: () the lowest unit purhasing ost in the ost isount sheule may not guarantee that the retailer oul obtain maximum expete total proit beause the extra quantity purhase may a aitional holing ost an thus reue the expete total proit; () the lower the holing ost rate or a unit o goo item, the lower the optimal orer quantity, set up ost an the expete annual total proit However, i the optimal orer quantity ours at the orering quantity break point orresponing to the least unit purhasing ost o the ost isount sheule, the optimal orer quantity then remains unhange with the holing ost rate or a unit o goo items, while the set up ost inreases an the expete total proit ereases; an (3) the higher the eetive rate, the higher the orer quantities an set up ost, an the less expete total proit I the optimal orer lot size ours at the orering quantity break point orresponing to the lowest ost in the ost isount sheule, the optimal lot size remains unhange with the eetive rate, while the set up ost inreases an the expete total proit ereases Aknowlegements The author sinerely thanks the anonymous reerees or their very helpul omments an or the improvement o the paper This researh was partially supporte by the Ministry o Siene an Tehnology o ROC uner Grant MOST H

15 Reerenes Proeeings o the Tenth Asia-Paii Conerene on Global Business, onomis, Finane an Soial Sienes (AP7Hong ong Conerene) ISBN: Hong ong-sar 0-, January 07 Paper ID: H735 Al-Salamah, M, 06, onomi proution quantity in bath manuaturing with imperet quality, imperet inspetion, an estrutive an non-estrutive aeptane sampling in a two-tier market Computers & Inustrial ngineering 93, Aniani, A, 998, Setup ost reution in a multi-stage orer quantity moel Proution Planning an Control 9,-6 Billington, PJ, 987, The lassi eonomi proution quantity moel with setup ost as a untion o apital expeniture Deision sienes 8, 5-40 Bose, S, A Goswami, an S Chauhuri, 995, An O Moel or Deteriorating Items with Linear Time-epenent Deman Rate an Shortages uner Inlation an Time Disounting Journal o the Operational Researh Soiety 46, Chan, WM, RN Ibrahim, an PB Lohert, 003, A new P moel: Integrating lower priing, rework an reet situations Proution Planning an Control 4, Cheng, TC, 989, An eonomi proution quantity moel with lexibility an reliability onsierations uropean Journal o Operational Researh 39, Cheng, TC, 99, An eonomi orer quantity with eman-epenent unit proution ost an imperet proution proesses II Transations 3, 3-8 roglu, A, an A Ozemir, 007, An eonomi orer quantity moel with eetive items an shortages International Journal o Proution onomis 06, Goyal, S, an A Gunasekaran, 990, Multi-stage proution-inventory systems uropean Journal o Operational Researh 46, -0 Hauk, Z, an J Voros, 05, Lot sizing in ase o eetive items with investments to inrease the spee o quality ontrol Omega 5, Hong, Y, CR Glassey, an D Seong, 99, The analysis o a proution line with unreliable mahine an ranom proessing times II Transations 4, Hong, JD, an JC Hayya, 993, Dynami lot sizing with setup reution Computers & Inustrial ngineering 4, 09-8 Hong, JD, an JC Hayya, 995, Joint investment in quality improvement an setup reution Computers & Operations Researh, Hou, L, 007, An P moel with setup ost an proess quality as untions o apital expeniture Applie Mathematial Moelling 3, 0-7 Huang, C, 004, An optimal poliy or a single-venor single buyer integrate proution-inventory problem with proess unreliability onsieration International Journal o Proution onomis 9, 9-98 Huang, C, 004, DM Tsai, JC Wu, an J Chung, 00, An integrate venor buyer inventory moel with orer-proessing ost reution an permissible elay in payments uropean Journal o Operational Researh 0, eller, G, an H Noori, 988, Justiying new tehnology aquisition through its impat on the ost o running an inventory poliy II Transitions 0, 84-9 han, M, MY Jaber, AL Guiria, an S Zolaghari, 0b, A review o the extensions o a moiie O moel or imperet quality items International Journal o Proution onomis 3, - im, L, JC Hayya, an JD Hong, 99, Setup reution in eonomi proution quantity moel Deision Siene 3, Lin, TY, 00, An eonomi orer quantity with imperet quality an quantity isounts Applie Mathematial Moelling 34, Lin, TY, 03, Coorination poliy or a two-stage supply hain onsiering quantity isounts an overlappe elivery with imperet quality Computers & Inustrial ngineering 66,

16 Proeeings o the Tenth Asia-Paii Conerene on Global Business, onomis, Finane an Soial Sienes (AP7Hong ong Conerene) ISBN: Hong ong-sar 0-, January 07 Paper ID: H735 Lin, TY, MT Chen, an L Hou, 06, An inventory moel or items with imperet quality an quantity isounts uner auste sreening rate an earne interest Journal o Inustrial an Management Optimization, Maah, B, an MY Jaber, 008, onomi orer quantity or items with imperet quality: Revisite International Journal o Proution onomis, Moon, I, BC Giri, an Choi, 00, onomi lot sheuling problem with imperet proution proesses an setup times Journal o the Operational Researh Soiety 53, Moussawi-Haiar, L, M Salameh, an W Nasr, 06, Proution lot sizing with quality sreening an rework Applie Mathematial Moelling 40, Nasri, F, JF Aiso, an MJ Paknea, 990, Setup ost reution in an inventory moel with initerange stohasti lea times International Journal o Proution Researh 8, 99- Paknea, J, F Nasri, an JF Aiso, 005, uality improvement in an inventory moel with initerange stohasti lea times Journal o Applie Mathematis an Deision Sienes 3, Porteus, L, 985, Investing in reue setups in the O moel Management Sienes 3, Porteus, L, 986, Optimal lot sizing, proess quality improvement an setup ost reution Operations Researh 34, Rosenblatt, MJ, an HL Lee, 986, onomi proution yle with imperet proution proesses II Transitions 8, Salameh, M, an MY Jaber, 000, onomi proution quantity moel or items with imperet quality International Journal o Proution onomis 64, Sarkar, B, an A Maumer, 03, Integrate venor buyer supply hain moel with venor s setup ost reution Applie Mathematis an Computation 4, Sarkar, B, an R Coates, 997, Manuaturing setup ost reution uner variable lea times an inite opportunities or investment International Journal o Proution onomis 49, Sarkar, B, an I Moon, 04, Improve quality, setup ost reution, an variable bakorer osts in an imperet proution proess International Journal o Proution onomis 55, 04-3 Taleizaeh, AA, L Carenas-Barron, an B Mohammai, 04, A eterministi multi prout single mahine P moel with bakorering, srape prouts, rework an interruption in manuaturing proess International Journal o Proution onomis 50, 9-7 Voigt, G, an Inerurth, 0, Supply hain oorination an setup ost reution in ase o asymmetri inormation OR Spetrum 33, 99- Wahab, MIM, an MY Jaber, 00, onomi orer quantity moel or items with imperet quality, ierent holing osts, an learning eets: A note Computers & Inustrial ngineering 58, Wee, HM, an GA Wiyaana, 03, A proution moel or eteriorating items with stohasti preventive maintenane time an rework proess with FIFO rule Omega 44, Wee, HM, WT Wang, TC uo, YL Cheng, an YD Huang, 04, An eonomi proution quantity moel with non-synhronize sreening an rework Applie Mathematis an Computation 33, 7-38 Wu, SY, 00, Optimal poliy or set-up time reution in a multistage proution-inventory system International Journal o Systems Siene 33, Yano, CA, an HL Lee, 995, Lot sizing with ranom yiels: a review Operations Researh 43, Zhang, X, an G Yigal, 990, Joint Lot Sizing an Inspetion Poliy in an O Moel with Ranom Yiel II Transations,