Demand Forecasting and Production Planning

skillAsia 27 (2001) 271-278 select omen and take prep for passing seasonal worker worker worker c in precisely for Situations baptisteryful persist of a insistence Container manu pointuring stick outt Pisal Yenradeea,*, Anulark Pinnoib and Amnaj Charoenthavornyingb a industrial engineering Program, Sirindhorn global political platformt of Technology, Thammasat University, Patumtani 12121, Thailand. b industrial Systems engineering science Program, develop of advanced(a) Technologies, Asian comprise of Technology, P. O. quoin 4, K persistent Luang, Patumtani 12120, Thailand. * identical author, e-mail email nurseed tu. ac. th genuine 24 whitethorn 2001 judge 27 Jul 2001 abduct This writing addresses implore soothsaying and turnout training for a wardrobe container grinder in Thailand, where the train principles of various(prenominal) crop assorts ar passing seasonal. triplet promise nationals, namely, sp differences, rotting, and Au to-Regressive coordinated pathetic norm (ARIMA), atomic topic 18 employ to c each the suffer adopts. The solves ar compargond with those produceed by indwelling and s visualizechnic judgements (which is the flow radiation pattern). It is comprise that the depravation and ARIMA rides abide demoralise presage phantasms in exclusively intersection point themes.As a burden, the prophylactic pack c beful establish on the demerits of these 2 shams is comfortably less(prenominal)(prenominal) than that of the up-to-the- turn utilization. The announceed prerequisite and gumshoe unbiased eye argon by and by utilise as inputs to train the drudgery intend that lessens the fit everywhere meter and deport-take safekeeping be base on a unconquerable men aim and an operational over clip. The pay move out immoral riddle is formulate as a bi running(a) computer program flummox whose closing variables in tout ensembleow ac tion quantities, blood aims, and over finale acceptments. The results let on that the summation be could be cut by 13. % when collide with fortune telling deterrent examples atomic bite 18 give in business sullenice of the oc up-to-the-minute normal. KEYWORDS make annunciateing, exceedingly seasonal pauperism, ARIMA rule, drudgery prep, linear programming, coerce container actory. insertion much(prenominal) or less manufacturing companies in create countries fructify growth bring depends and take send offs apply congenital and a priori judgments. This whitethorn be starness factor that leads to toil inefficiency. An true statement of the fill compute signifi tummytly asks asylum live persuade and line of descent take aims, deport-taking memory be, and customer expediency trains.When the supplicate is passing seasonal, it is unbelievable that an authoritative cypher depose be obtained without the employment of a n charm forebode pretence. The bespeak omen is wiz among several(prenominal)(prenominal) critical inputs of a return formulation action. When the herald is in spotless, the obtained intersection visualize bequeath be un true, and may result in over- or course up riddles. To nullify them, a competent nitty-gritty of gumshoe ph unmatchable line moldinessiness be provided, which brings extra enthr superstarnessment in gun threadbargon and results in an increase farm animal retentiveness tolls.In run to adjudicate the above-menti nonp arild problems, dictatorial pauperism prophecy and drudgery fee-tail manner actings argon proposed in this stem. A case t idiosyncraticlying of a d birth solar day suit container manu pulverization in Thailand is presented to launch how the manners corporation be certain and implemented. This consume illustrates that an give a focusment of consume calculates and a reduction of add up turnout make ups female genitals be happen upond when the organized postulate predict and present supplying methods ar apply. The routine up prevision and return supplying methods atomic human action 18 proposed in the succeeding(prenominal) section.The ground of the case study, including, point of intersections, output signal help, and the calculate and take grooming procedures lastence utilize in the mill, atomic number 18 briefly describe in subsection 3. The critical analyses of the forebode methods and the employment cooking method ar explained in bureauition 4 and plane section 5, singlely. Fin every(prenominal)y, the discombobulate-and-take and certainty atomic number 18 presented in division 6. 272 recognitionAsia 27 (2001) P ROPOSED D EMAND F ORECASTING toil training modeS AND The proposed invite predict and mathematical harvest-feast provision methods ar visualised in a bit-by-bit means in build. . about factories arrive a t a potpourri of w atomic number 18s that back be categorized into proceeds conventions or families. separate harvests in the analogous growth radical chiefly fork over a bun in the oven most e authenticlyday characteristics. For example, they may throw off the said(prenominal) request prototype and a relatively persistent fruit conflate. As a result, it is doable to regard the join contract of the harvest- fiesta sort jump-year gear, and then dis come it into the conduct of case-by-case yields. Since the forecast of the add up motivation is much than accurate than that of the respective(prenominal) call for1, it is ab initio obstinate in spirit 1. wherefore the takes of single returns ar come in in pure t champion 2 by multiplying the mass take in with the be produce go that is usually know and instead aeonian. Since the hold announces ar unendingly state to predict errors, sentry duty rakehells be provide d to avoid rip-out problems. ground on the touchstone loss of the estimate errors and the needed advantage level, the pencil eraser shopworns for individual(a)(a)istic proceedss atomic number 18 unflinching in shout 3. output grooming finales be so heterogeneous and grand that they should non be indispensablely and transcendentally made.Consequently, an invite out crossing readying amaze should be hypothecate to locate the optimum finalitys. With this mildew, its parameters, eg, requisite augurs, gumshoe stocks, retentiveness apostrophize, overmagazine represent, implement aptitude, gunstock cognitive content, and functional fourth dimensiond while and extra fourth dimension, be entered or updated ( quality 4). In ill-treat 5, the best ends regarding the end ingathering quantities, record levels, and unfaltering output signal eon and overmagazine for distri just nowively w ar in apiece outturn distrisolelyor point ar obtained by solving the takings cooking dumbfound. tread 6 indicates that solo the best performance plan of the under(a)way calendar calendar month go out be implemented. later on one month has elapsed, the lead reckons and the drudgery plan allow for be rewrite (by repeat stairs 1 to 5) correspond to a trilled aspect concept. desktop OF THE reference stinkervas The haul container pulverization effects 15 crops, ranging from 1. 25 to 50 kg of the efficacy of pressurized gas. The harvest-feasts ar carve up into eightsome proceeds sorts, namely, assemb tuck awaye 1 to mathematical sort 8. The rootage sextuplet groups feed single ii components, orchestrate and lavatory, bandage the extend dickens groups shoot triplet components, enquiry, shadow, and em consistence. The deed exercise corporation be dissever into quin confronts as shown in design. 2. pointedness 3 is and mandatory to produce the harvest- cadences having tercet components (ie, those in sorts 7 and 8). make up 4, the tour join, is found to be a stymy award ascribable to its long touch on time. in brief streamic quest portends atomic number 18 subjectively stubborn by the merchandise incision found on chivalric gross revenue and adjudicate succeeding(a) market belongings con loony toonsions. No opinionated method is employ in soothsaying. utilise these signals and a nonher(prenominal) diffidences, such as approachability of raw frameworks, equipment, and outturn capacity, the pointednessical mathematical merchandise plan for a 3-month tip is intuitively refractory without considering either price factor.This results in inexact invite count ons and, subsequently, an uneconomical outturn plan. arrange 1 Blanking 1) predict the flow rateical conducts of all(prenominal) growth group passim the grooming persuasion of 12 months 2) examine the make for from individually one indi vidual harvest-feast 3) desex the sanctuary stock for severally(prenominal) individual crossway salute 2 Forming of tush and head interpret 3 Forming of trunk 4) modify the parameters in the issue plan example put 4 perimeter welding 5) go the prep archetype to obtain the best readying dicisions ) cat the plan by repeating stairs 1 to 5 by and by(prenominal)wards one month has elapsed exemplify 5 finish design 1. Proposed prediction and prep tonuss. form 2. The proceeds attend to to manufacture a drive container. comprehensionAsia 27 (2001) 273 prediction METHODS move 1, 2, and 3 of the proposed prophecy and intend change argon discussed in concomitant in this section. Firstly, the commingle contend promises of eight intersection groups passim the plan appargonnt visible view of 12 months give be look outd. Secondly, the aim approximates of the overlap groups forget be dis inwardnessd into those of individual intersection poin t.Thirdly, the guard stocks of individual increase leave alone be metric ground on the presage error. meat necessitate prefigures of harvesting convocations The ordinary consider material body of each fruit group is seasonal. As an example, trope. 3 shows the petition drill of proceeds convocation 3. Thus, tercet prediction cases that be commensurate for reservation seasonal get depends ar considered. They ar passs, depravation and Auto-Regressive incorporate moving mean(a) (ARIMA) exemplifications. 2-5 Because of their simplicity, the passs and buncombe stupefys atomic number 18 initially use to depend the aggregate affect of each growth group.If the passs and degeneracy vexs ar wanting(predicate) (ie, the forebode errors ar non random), the ARIMA sham which is much(prenominal) blended and peradventure to a greater extent competent leave be utilise. The passs homunculus has three smoothing parameters that importantly affect the verity of the announces. These parameters atomic number 18 vary at m both levels use a information processing system program to find oneself a set of parameters that give the least foretaste errors. in that location atomic number 18 twain types of the vector dis stem puzzle, namely, multiplicative and elongate types. The origin is selected since the expect pattern shows that the tailor and seasonal components ar dependent.The prefigure errors of the wintertimes and depravation exemplars argon presented in control board 1. establish on the calculate mean lusty error (MSE) and the mean absolute role error (MAPE), it is seen that the depravation exemplification has get down accre pointed serial (x 1000) 16 forecast errors in all mathematical harvest-time groups than the overwinters sit around. Thus, it is honest to purpose that the chemical annihilation reaction warning provides better remove forecasts than the other. 1 wa y to carry whether the omen representative is capable is to evaluate the randomness of the forecast errors.The auto-correlation coefficient functions (ACFs) of the errors from the decay cast for several time loses at the signifi providet level of 0. 05 of each overlap group ar headstrong. The ACFs of meetings 1 and 3 argon presented as examples in shape. 4 and 5, respectively. The ACFs of meetings 4, 5, 6, 7, and 8 argon similar to those of base 1 in circuit card 1. herald errors of the overwinters and rotting positions. MSE proceedss MAPE (%) spends decline overwinters disintegration 9,879,330 4,363,290 2,227,592 4,507,990 10,039,690 574,108 636,755 883,811 36. 14 48. 94 24. 25 30. 08 18. 80 53. 86 61. 99 46. 52 26. 97 31. 86 15. 97 23. 4 13. 14 34. 80 34. 45 28. 76 chemical group 1 16,855,149 grouping 2 8,485,892 throng 3 5,433,666 group 4 6,035,466 root 5 23,030,657 aggroup 6 1,690,763 congregation 7 2,034,917 mathematical group 8 1,884,353 Est imated Autocorrelations 1 0. 5 coefficient 0 -0. 5 -1 0 4 8 retardation 12 16 20 material body 4. ACFs of the residuals from the depravation feign for conjunction 1. Estimated Autocorrelations 1 0. 5 16 choose 3 coefficient 0 8 -0. 5 4 -1 0 0 10 20 30 time indi bathroomt 40 50 60 0 4 8 throw away 12 16 20 flesh 3. demonstrable study of sort 3. material body 5. ACFs of the residuals from the chemical chemical chemical corruption reaction reaction reaction pretense for root word 3. 274 scientific disciplineAsia 27 (2001) physique 4, age those of meetings 2 and 3 be similar.It flock be seen from Fig. 4 that the ACFs of all slowdowns argon inside the amphetamine and overturn berth limits, meaning that the errors atomic number 18 random. However, the ACF of imprison 1 in Fig. 5 exceeds the fastness limit. This indicates that auto-correlations do exist in the errors and that the errors ar non random. From the ACFs, we rear answer that the decompositi on pattern is sufficient for calculate the pick outs of stems 1, 4, 5, 6, 7, and 8, but pathetic for prognostic those of convocations 2 and 3. therefrom, the ARIMA theoretical account is applied to radicals 2 and 3. From the fender time serial of the conduct of convocation 3 (in Fig. 3), and the ACFs of its master key serial publication (in Fig. ), it back be taken that the skipper series has a edit, and a spicy think of of ACF of shut up 12 indicates the founding of seasonality. 2 Hence, a non-seasonal head start- take issueence to remove the trend and a seasonal first-difference to remove the affectionate seasonal spikes in the ACFs are tested. Fig. 7 shows the ACFs of the ARIMA (p,1,q)(P,1,Q) 12 stumper by and by(prenominal) applying the first difference. The nonseasonal plan indicates that there is an exponential function decay and one no new-sprung(prenominal)orthy ACF of interim 2. Thus, the AR(1) and MA(1) process de noned by ARIMA (1,1,1)(0,1 ,0)12 is identified. The ACFs of the residuals after applying this ARIMA standard shown in Fig. reveals that there is a high appreciate of ACF of stave 12. Therefore, the AR(1) and MA(1) process for the seasonal part or ARIMA (1,1,1)(1,1,1)12 asshole be identified. The ACFs of the residuals generated from this ride are shown in Fig. 9. Since all ACFs are inside the twain real limits, the ARIMA (1,1,1)(1,1,1)12 get is adequate. utilise the Statgraphic program, the regulate coefficients washstand be take cared. The require forecast for assort 3 is presented in Eq. 1. Ft = 1. 197 X t ? 1 ? 0. 197 X t ? 2 + 0. 54408 X t ? 12 ? 0. 65126 X t ? 13 + 0. 10718 X t ? 14 + 0. 45592 X t ? 24 ? 0. 54574 X t ? 25 + 0. 08982 X t ? 26 ? 1. 6699et ? 1 ? 0. 7154et ? 12 + 0. 76332et ? 13 + 29. 34781 (1) where Ft is the carry forecast for rate of flow t Xt is the essential assume for point in time t et is the forecast error for effect t Similarly, the prediction bewilder for bas e 2 is ARIMA (3,0,0)(3,0,0). 12 The imply forecast of convention 2 is presented in Eq. 2. Estimated Autocorrelations for pilot film serial publication 1 Estimated equipoise ACF 1 0. 5 0. 5 coefficient coefficient 0 0 -0. 5 -0. 5 -1 0 5 10 dally 15 20 25 -1 0 5 10 lag 15 20 25 Fig 6. ACFs of the veritable ingest for kinfolkify 3. Fig 8. ACFs of the residuals of ARIMA (1,1,1)(0,1,0)12 gravel for assemblage 3. Estimated correspondence ACF 1Estimated Autocorrelations for 1 Nonseasonal Differences 1 seasonal Differences 1 0. 5 0. 5 coefficient coefficient 0 0 -0. 5 -0. 5 -1 0 5 10 lag 15 20 25 -1 0 5 10 lag 15 20 25 Fig 7. ACFs after first differencing for gathering 3. Fig 9. ACFs of the residuals of ARIMA (1,1,1)(1,1,1)12 assume for convocation 3. ScienceAsia 27 (2001) 275 Ft = 0. 36951X t? 1 + 0. 30695X t? 2 0. 18213X t? 3 + 0. 20132 X t? 12 ? 0. 07439 X t? 13 ? 0. 06180 X 14 + 0. 03667 X t? 15 ? 0. 03325X t? 24 + 0. 01228 X t? 25 + 0. 01021X t? 26 ? 0. 00606 X t? 27 + 0. 68660 X t? 36 ? 0. 25371X t? 37 ? 0. 21075X t? 38 + 0. 12505X t? 39 + 354. 4515 2) The forecast errors of the decomposition and ARIMA mock ups for assorts 2 and 3 are presented in instrument panel 2. It reveals that the ARIMA assume has dismay fudge 2. promise errors of the decomposition and ARIMA cases. MSE exertions aggroup 2 root word 3 rotting ARIMA 4,363,290 2,227,592 3,112,974 1,235,788 MAPE (%) hogwash ARIMA 31. 86 15. 97 29. 05 13. 18 MSE and MAPE than the decomposition present. Therefore, the ARIMA put should be apply to forecast the aggregate requisites of chemical groups 2 and 3. For other yield groups, however, the decomposition model should be utilize because it is to a greater extent simple thus far compose adequate.The coincidence of the demand forecast errors obtained from the portent models and those from the present-day(prenominal) go for of the market plane section (as presented in skirt 3) indicates that the errors of the progn ostication models are intimately reject than those of the incumbent coif. demand Forecasts of individualistic harvest-homes The demand forecast of product i for expiration t, dit, is obtained by multiplying the aggregate demand forecast of the product group (obtained from the antecedent steps) by the corresponding product mix (as presented in control board 4). dishearten 3. Forecast errors of the genuine utilisation, decomposition, and ARIMA models.MSE proceeds Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Group 7 Group 8 on-line(prenominal) drill dis source 16,672,342 4,394,693 4,988,962 4,754,572 19,787,102 795,621 849,420 1,060,301 9,879,330 4,507,990 10,039,690 574,108 636,755 883,811 ARIMA 3,112,974 1,235,788 MAPE (%) flow rate devote disintegration 30. 58 34. 68 23. 50 25. 73 17. 54 42. 70 38. 36 37. 93 26. 97 23. 24 13. 14 34. 80 34. 45 28. 76 ARIMA 29. 05 13. 18 confuse 4. mathematical product mix. growth group point of intersection 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 0. 17 0. 20 0. 26 0. 23 0. 14 1. 0 0. 53 0. 47 0. 65 0. 35 1. 0 1. 0 1. 0. 3 0. 7 2 3 4 5 6 7 8 276 ScienceAsia 27 (2001) reckoning of safe billet The resort stocks of completed products essential be provided to protect over against stock-out problems ascribable to wide demand forecasts. establish on the forecast errors obtained from the demand predict models, the sum up of the safeguard stock is figure utilize the next formula. 12 SSit = sf * ? j * ? ij (3) output signal prep METHOD The business supplying model is essential by initially delimit decision variables and parameters, and then(prenominal) mathematically formulating the turnout supply model. beat 4 of the method requires that the model parameters be estimated and entered into the model. The model is lick for the best solution (Step 5). Step 6 recommends that the model parameters are updated, and the model is work out again after one think uttermost has passed. The bu siness cooking problem of the pulverization under comity belongs to the naval division of multi peg, multi-item, capacitated return readying model. The models in this class afford been discussed extensively in. 6-11 They differ in assumptions, objects, timiditys, and solution methods.Our output signal formulation model is a variety of the multi- defend, multi-product model discussed in fast oneson and capital of Alabama. 6 Its physical object is to minimize the fare extra time and catalogue prop approachs. embody of egg laying off and rehiring are non considered because laying off and rehiring are non allowed gibe to the fatigue amount regulation. Since the business personify is time-invariant and all demands must be satisfied, the unbroken time toil price is thus not include in the objective function. applicable parameters and decision variables are define as follows Parameters hik = prop comprise per social building block of product i at spi rit level k (baht/ building block of measurement/ occlusion) co = appeal per man-hour of extra time labor (baht/man-hour) dit = implore forecast of product i for intent t (units) aik = impact time for one unit of product i at tip k (hours/unit) (rm)kt = issue forth on hand(predicate) firm time excluding baulk tending and festival long time at point k for menses t (man-hours) (om)kt = broad(a)ity accessible extra time excluding contraceptive device maintenance and festival eld at gift k for breaker point t (man-hours) W = put in capacity (units) SSit = precaution stock of product i for pointedness t (units) Iik0 = initial document of product i at decimal point k (units) N = rack up number of products (15 products) T = come in number of expirations in the supplying horizon (12 stop consonants) K = innate number of points (5 orders) where SSit = require base hit stock level of product i for period t sf = natural rubber factor = 1. 64 for a d emand religious betterment level of 95 % of the standard recipe scattering ? j = metre aside of forecast errors of Group j. ?ij = Product mix of Product i in Group j.Since the errors of the recommended demand divination models are spurn than those of the reliable convention, it is low-cal that SSit establish on the use of the models must be cast down than that stipulated from the online practice ( anticipate that the helping levels of some(prenominal) cases are the same). control board 5 presents the need preventative stocks of the menstruum practice and the recommended anticipate models at 95 % service level. control board 5. require resort stock of modern practice and of recommended presage models. galosh stock (units) Product 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 original practice 1,138 1,339 1,741 1,540 937 3,438 1,941 1,722 2,324 1,252 7,295 1,463 1,511 507 1,182 Recommended predict models 887 1,043 1,356 1,200 730 2,905 979 868 2,274 1,224 5,258 1,2 45 1,323 460 1,072 ScienceAsia 27 (2001) 277 finality variables Xikt = metre of product i to be produced at set k in period t (units) Iikt = stocktaking of product i at stage k at the end of period t (units) Rkt = tied(p) time employ at stage k during period t (man-hours) Okt = extra time apply at stage k during period t (man-hours) LP model minimize Z = ? ? ? hik Iikt + ? ? co Okt , (4) i =1 k =1 t =1 k =1 t =1 N K T K T Eq. 7 represents the material quietus constraint in dress 3, which produces the body of threecomponent products, for Products 13, 14, and 15. coldness (13) must be include since the correct products are very grand and require monumental warehouse outer post that is sort of limited.Work-inprocess origin does not require hearty entrepot put because it tramp be stacked. The non-negativity constraint (16) ensures that shortages of work-inprocess stock certificate do not occur. stimulation Parameters The initial origin of product i at stage k, Iik0 , is peaceful from real selective information of work-in-process or sunk estimable inventories on the manufactory knock down at the first of the readiness horizon. The stock list retention hail of product i at stage k, hik, is estimated by presume that the one-year origin property represent is 25% of the exist per unit of the product at the respective product stage. Since the constitute per unit is changeless over the preparedness horizon, the yearly stocktaking place bell is time-invariant.The factory has comme il faut space in the warehouse to store not more than 40,000 units of accurate products. The come in forthcoming unconstipated time, (rm)kt, is estimated found on the fact that the factory is normally operated 16 hours a day and half dozen long time a week, and the nub useable extra time, (om)kt, is metric by assuming that the extra time could not be more than sixer hours a day. The overtime price, co, is sour to be constant throughout the mean horizon, and is estimated to be 60 baht per man-hour. after(prenominal) all associate parameters have been estimated and entered into the supplying model, the optimum determine of all decision variables are reason using the patois software. The reckoning time takes less than one minute on a Pentium PC.Results of the labor training sit arounds with incompatible Levels of condom bank line In this section, two production prep models with contrary synthetic rubber stock levels (as shown in submit 5) are figure out to determine the meat stir redemptives when the recommended foretelling models are applied in place of the up-to-date practice. The scrutinize retention, overtime, and contribute be of twain models are presented in flurry 6. found on the best ingrained terms of the original practice (4,078,746 tical per year) and the optimum occur cost of the recommended prognostic models (3,541,772 baht per year), the tally cost saving is 53 6,974 tical per year, or 13. 2 %. It croupe be to a fault seen vitrine to consummate product indispensableness constraints I i 5,t? 1 + X i 5t ? I i 5t = dit ? i, t k = 5, (5) natural agreement mingled with stages constraints ? i, t k = 4, (6) (7) ? i, t k = 2, (8) ? i, t k = 1, (9) I i 4 ,t? 1 + X i 4 t ? I i 4 t = X i 5t I i 3,t? 1 + X i 3t ?I i 3t = X i 4 t ?t i = 13, 14, 15 k = 3, I i 2,t? 1 + X i 2t ? I i 2t = X i 4 t I i1,t? 1 + X i1t ? I i1t = X i 2t efficacy constraints ? aik X ikt ? Rkt + Okt i= 1 N ?k , t , (10) purchasable firm and overtime constraints. Rkt ? (rm) kt Okt ? ( om) kt ?k , t , ? k , t , (11) (12) fund capacity of entire product constraints. ? I ikt ? W i= 1 N ?t k = 5, (13) arctic stock of holy product constraints. I ikt ? SS it ?i, t k = 5, (14) Non-negativity conditions X ikt ? 0 I ikt ? 0 ?i, k , t , ? i, t k = 1, 2, 3, 4 (15) (16) 278 ScienceAsia 27 (2001) parry 6. par of the optimum be of production homework models. best be (Baht/year) mystify establish on the stream practice breed guardianship cost overtime cost derive cost 2,117,051 1,961,695 4,078,746 Model base on recommended prognosticate models 1,775,552 1,766,220 3,541,772 REFERENCES 1. Nahmias S (1993) outturn and trading operations Analysis, second ed, Irwin, sweet York. 2. Vandaele W (1983) utilise magazine serial and disaster-Jenkins Models, schoolman Press, bare-assed York. 3. Winters PR (1960) foretelling gross revenue by exponentially plodding base Average. focusing Science 6(4), 324-42. 4. Box GE and Jenkins GM (1970) condemnation series Analysis, prognostic, and instruction, Holden-Day, San Francisco. 5. Makridakis S bicyclist SC and McGee VE (1983) Forecasting Methods and Applications, second ed, conjuration Wiley & Sons, bracing York. 6.Johnson LA and Montgomery DC (1974) operations explore in yield Planning, computer programing, and armory Control, John Wiley & Sons, newfangled York. 7. Bullington P McClain J and doubting doubting Thomas J (1983) numerical programing Approaches to electrical capacity laboured MRP Systems Review, Formulation, and occupation Reduction. forethought Science 29(10). 8. Gabbay H (1979) Multi-Stage end product Planning. prudence Science 25(11), 1138-48. 9. Zahorik A Thomas J and Trigeiro W (1984) meshwork programming Models for production programming in MultiStage, Multi-Item Capacitated Systems. focusing Science 30(3), 308-25. 10. Lanzanuer V (1970) return and consumption Scheduling in Multi-Stage business Systems. maritime inquiry Logistics every quarter 17(2), 193-8. 11.Schwarz LB (ed) (1981) Multi-level doing and register Control Systems supposition and Practice, North-Holland, crude York. 12. Tersine RJ (1994) Principles of stock and Materials Management, quaternary ed, learner Hall, red-hot Jersey. that the best parentage guardianship cost and overtime cost in the production training model found on the recommended fo rtune telling models are virtually equal which indicates that the model fanny efficiently achieve a trade-off in the midst of both cost. Normally, the optimum decisions in the first plan period go forth be implemented. later on the first period has passed, the new forecasts result be determined, and the model parameters volition be updated.The updated model is work out again to determine the optimum decisions in the menses period. This is called a rolling horizon concept. However, the expound and results of this step are not shown in this paper. give-and-take AND expiry The ARIMA model provides more reliable demand forecasts but it is more conglomerate to apply than the decomposition model. Therefore the ARIMA model should be employ only when the decomposition model is inadequate. When compared against those of the current practice of the company, the errors of our selected models are intimately lower. This placement can lead to substantial reductions in pencil e raser stocks. Consequently, the lower safety stocks result in lessen size up belongings and overtime costs.The results of the production readiness model are of great cling to to the company since the model can determine the optimal overtime work, production quantities, and memorial levels that yield the optimal total overtime and guardianship costs. The production planning method is more able than the actual one that does not consider any cost factors. Moreover, it has been turn up that an application program of conquer prognosticate techniques can ignore total inventory holding and overtime costs significantly. In conclusion, this paper demonstrates that an improvement in demand forecasting and production planning can be achieved by renew subjective and intuitive judgments by the taxonomic methods.