roceedng of e 00 nernonl onference on ndusrl ngneerng nd Operons Mngeen k, Bngldes, Jnur 9 0, 00 A Tbu Serc Algor for eernng e conoc esgn reers of n negred roducon lnnng, Qul onrol nd revenve Mnennce olc Abdur R cul of Busness Adnsron Unvers of Ne Brunsck, redercon, NB, nd Mud Skl epren of Sses ngneerng Kng d Unvers of eroleu nd Mnerls, rn 36, Sud Arb Absrc n s ork, n negred odel of econoc producon qun, econoc desgn of n -conrol cr, nd prevenve nennce re nvesged under non-unfor qul conrol preers. Te effec on e expeced ol cos nd qul conrol cos s nvesged ree dfferen ssupons of e qul conrol preers. Usng bu sec lgor, e opl vlues of qul conrol preers, for dfferen M levels, re found. A non-unfor scee for splng frequenc, sple sze nd conrol l co-effcen provdes loer cos s copred o scees ere onl splng frequenc s ken s non-unfor. Keords Tbu serc lgor, econoc desgn preers, producon plnnng, qul conrol, prevenve nennce. nroducon Qul conrol, producon plnnng nd nennce polc re porn fcors n n nufcurng process. ffecve negron of ese fcors ll gve copn copeve edge of dvnge n e globl rke. Te cusoers ssfcon g led o n ncresed cos of producon process. Te opzon of producon cos s n porn re of reserc. conoc producon qun, econoc desgn of n -conrol cr, nd prevenve nennce re e ree n eleens n producon ngeen. n e ps, ese specs ve been consdered seprel nd dfferen odfcons ere de n e ndvdul odels o ceve opl producon coss. n s ork, n negred odel of econoc producon qun, qul conrol, nd prevenve nennce polc s suded. Opl vlues of desgn preers of e odel re obned usng bu-serc lgor.. Sse Operons nd Assupons Te se process s ssued s n R nd Ben- []. s ssued e process s producng sngle e. Te process s ne.e., ge s zero e sr nd s n n n-conrol se. Te process sf o n ouof-conrol se s e sse ges. Te e e process sfs o n ou-of-conrol se s rndo vrble. follos generl dsrbuon ncresng zrd re. Te produc qul s nspeced usng n -conrol cr. Te process s nspeced e nervls,,,, 3 K. s e nuber of qul nspecon nervls n producon ccle. revenve nennce cves re sceduled l neger ulples of qul nspecon nervls, us prevenve nennce cves re crred ou l, l, 3l, K. f l, ens e prevenve nennce cves re crred ou ec nspecon nervl. f l, ens e prevenve nennce cves re sceduled ec lernve nspecon nervl. Te process producon ccle ends qul nervls or rue lr, ndcng e process s ou-of-conrol. Te process s resored o n s good s ne se roug nennce. end s consn nd ll dends us be e. lsscl econoc producon qun Q odel ssupons ppl ere.
R nd Skl 3. Noons gure : nvenor levels, M s e es e - M 3. ecson Vrbles ecson vrbles reled o -conrol cr. Nuber of nspecon nervls n Sple sze - nspecon nervl k Splng frequenc - nspecon nervl onrol l co-effcen - nspecon nervl Oer noons for e -conrol cr re s follos. x xpeced e o resore sse o s good s ne se b xpeced e o perfor one M con xpeced e o repr sse en flure s deeced xed cos for splng Vrble cos of splng os of deecng flse lr Qul cos le producng n n n-conrol se Qul cos le producng n n ou-of-conrol se Mgnude of e sf n process en robbl, exceedng conrol ls; process n-conrol: - nspecon nervl robbl, no exceedng conrol ls; process ou-of-conrol: - nspecon nervl uulve e o sf dsrbuon qul o f M s crred ou - nspecon Te e end of - M nspecon nervl nd ere xpeced ol leng of producon ccle ncludng M e xpeced ol cos xpeced qul cos per producon ccle ncludng repr cos; M cos no ncluded Noon used for Q odel L Slvge vlue e end re uns per un e
R nd Skl roducon run roducon re uns per un e nvenor level e, nvenor oldng cos per un, per un e S 0 Seup cos per producon ccle T xpeced leng of producon ccle T xpeced leng of nvenor ccle H xpeced nvenor oldng cos per producon ccle Noon used for prevenve nennce 0 p p Mxu sse ge reducon os of cul M cves M xpeced prevenve nennce cos per producon ccle 3. negred Model Assupons Te process ssupons re kep e se s ose de n R nd Ben- []. uron of n n-conrol perod s ssued o follo n rbrr probbl dsrbuon f, vng n ncresng zrd re r, nd cuulve dsrbuon funcon. Te prevenve nennce cons reduce e ge of e sse proporonl o e cos of e nennce. f ere s no M, en ens e e o serc for n ssgnble cuse s neglgble. o x urng e M cv, s ssued producon ceses for e. p / p Te producon ends eer rue lr or e, cever occurs frs. f ere s no rue lr up o e en e ccle s lloed o connue for ddonl e. Tere s no cos of splng nd crng durng nervl. A e necessr nennce or equpen replceen s done. urng e nspecon, f n ou-of-conrol se s observed en producon ceses unl ccuuled on nd nvenor s depleed o zero. Oerse, producon connues. A slvge vlue s eploed n e odel, snce e resdul lfe beond cern ge for e sses nvolvng ncresng zrd re ll be rer sor. lure re, r of e sse s decresed fer ec M. Te ge reducon of e sse s funcon of e cos of e nennce. Le p denoe e effecve ge of e equpen rg before rg fer e γ quon gves e lner relonsp beeen M cos nd ge reducon of e sse, o ere γ η / p p ere η 0 < η or, s e perfecness fcor for e equpen. nd for,3, K,,. 4. Non-unfor Splng requenc, Sple Sze nd onrol L o-effcen n s ork, e -conrol cr preers re lso ssued o be nonunfor. As e process ges, e sple sze nd conrol l coeffcens cnge, re seleced fro O nd R [].
R nd Skl 4. Non-unfor splng frequenc Unfor splng provdes consn negred zrd re r for Mrkovn sock odel. Beneree nd R [3] exended s fc o non-mrkovn sock odels b coosng e leng of splng nervls, suc e negred zrd re over ec nervl s e se s for ll nervls, f e e process rens n n n-conrol se nd follos Webull dsrbuon. ere λ nd v re spe preers for e Webull dsrbuon. Snce flure re s reduced. quon becoes for 6 4. Non-unfor sple sze Non-unfor sple sze s seleced suc e relve proporon of sple sze o correspondng splng nervl s consn. T s,. ens sple sze drn per un e n ec splng nervl s consn. Usng fro quon 6, n expresson for non-unfor sple sze s obned, 3 4 5 7 4.3 Non-unfor conrol l co-effcen s seleced suc poer of e conrol cr rens se n ec nervl. 8 5. xpeced Tol os xpeced ol cos per un of e s obned b, 9 Were T s gven b, 0 5. xpeced leng of producon ccle T 5. xpeced prevenve nennce cos M p, ere, ere 0 p f l,l,3l,... Oerse 0 p f l,l,3l,... Oerse 3
R nd Skl B U B B U A s clculed usng 4 5.3 xpeced qul conrol cos 5 5.4 xpeced nvenor oldng cos Le be e nvenor e. H s gven b, 6 A s e re under nd cn be clculed s follos; Le nd be e nvenor e nd nspecon nervls respecvel. ere B nd U re gven b, 7 > 0 0.5 0.5 0 0.5 0.5 for for U,,,3, K U 0.5 6. Opl reer A proble s foruled n e for of quon 9 connng fve decson vrbles, k, n, nd l. l s ken explcl nd dfferen Ts re found usng dfferen vlues of l. A bu serc lgor n Glover nd Tllrd [4] s used ere o fnd opl soluons. 7. scussons Selecon nd non-unfor scee for, n nd k s gl dependen on process pe nd operon. s possble selecon of non-unfor n nd k does no ve uc effec on expeced qul nd ol cos for cern processes. onsder e follong cses: 7. se onsder process nufcurng sngle e; e process follos e se ssupons s de n secon. Te e n producon s expensve nd requres desrucve esng. So, e cos ssoced kng sple sze b s lrge. So selecng non-unfor scee for n nd k poer of es ll ren consn for suc processes ll effec e bn er. xpeced ol cos ll be gl dependen on non-unfor sple sze snce, n ll be reduced n ec qul nspecon nervl. 7. se f ou n ou n ou n L d f bn bn bn Q α 0 A d H T f,...,,3
R nd Skl onsder process producng uooble pr on uoed N cne. Sze nd densons of suc prs re conrolled nd cecked roug n uoed process nd requres uc less e. n suc cses, e cos ssoced kng sple s ver sll. So, selecng non-unfor ll ve ver sll effec on qul conrol coss, unless e pr s exned n sepre qul depren. 8. oncluson n s ork e negred odel of producon, qul nd prevenve nennce s presened, ere nonunfor splng frequenc, sple sze, nd conrol l co-effcen ere seleced. xpeced ol nd qul conrol cos s nvesged for dfferen prevenve nennce polces. Tbu serc lgor s used o fnd opl vlues of sse vrbles. s found non-unfor scee for splng frequenc, sple sze nd conrol l co-effcen provded loer cos s copred o scees ere onl splng frequenc s ken s non-unfor. s lso dscussed selecon of non-unfor splng frequenc nd conrol l co-effcen no effec cern processes. Selecon for suc scees s dependen on e process nd operon under consderon. Acknoledgeen nncl sssnce of e Nonl Scences nd ngneerng Reserc ouncl of nd nd grns fro e cul of Busness Adnsron, UNB, s grefull cknoledged. Te uors ould lso lke o cknoledge Kng d Unvers of eroleu nd Mnerls for fclng s proec. Te sssnce of K Wlson, Rlp O llgn nd eb Ter, for png, proof redng nd edng e nuscrp, s grel ppreced. References. R, M.A, nd Ben-, M., 998, A Generlzed conoc Model for Jon eernon of roducon Run, nspecon Scedule, nd onrol r esgn, nernonl Journl of roducon Reserc, 36, 77-89.. O, H., nd R, M.A., 997, A nc Model for n -onrol r esgn, Trnscons, 96, 48-486. 3. Beneree,.K., nd R, M.A., 988, conoc esgn of -onrol rs Under Webull Sock Models, Tecnoercs, 304, 407-44. 4. Glover,., nd Tllrd,., 993, A User's Gude o Tbu Serc, Annls of Operons Reserc, 4, 3-8.