Master Production Scheduling and the Relevance of Included Social Criteria

146 ACC JOURNAL 2017, Volume 23, Issue 2 DOI: 10.15240/ ul/004/2017-2-011 MASTER PRODUCTION SCHEDULING AND THE RELEVANCE OF INCLUDED SOCIAL CRITERIA Ma co T os 1; Tho s en Claus2; F ank He mann3 1,2Technische Uni e si ä D esden (TU D esden) Facul y o Business and Economics, In e na ional Ins i u e Zi au, Ma k 23, 02763 Zi au, Ge many 3Os baye ische Technische Hochschule Regensbu g (OTH Regensbu g) Facul y o Compu e Science and Ma hema ics Inno a ion and Compe ence Cen e o P oduc ion Logis ics and Fac o y Planning (IPF) P ü eninge S . 58, 93049 Regensbu g, Ge many e-mail: 1[email p o ec ed]; 2 ho s en.c[email p o ec ed]; 3 ank.he[email p o ec ed] Abs ac The equi emen s o conside wo ke u iliza ions and p ocessing imes, which depends on his wo ke u iliza ion, a e examined a he ollowing pape o he Mas e P oduc ion Scheduling. Fo his eason, i is shown, ha he e is a gap in esea ch ega ding he social dimension in he ange o P oduc ion Planning and Con ol. Thus, he e a e p esen ed an own de eloped linea op imiza ion model o he Mas e P oduc ion Scheduling wi h conside a ion o social c i e ia and an app op ia e case s udy a his pape . The esul s demons a e subs an ial de ia ions due o he igno ance om wo ke u iliza ions and wo ke u iliza ion speci ic p ocessing imes. The e o e, he in eg a ion o hese c i e ia is o be ecommended. Bu i is also shown, ha he e is a need o u he esea ch ac i i ies o he de elopmen o speci ic human a igue cou ses, like i also exis s o human lea ning cou ses. Keywo ds Sus ainabili y; P oduc ion planning and con ol; Mas e p oduc ion scheduling; Linea op imiza ion; Human a igue. In oduc ion The jus i ica ion om p oduc ion sys ems in a mo e sus ainable di ec ion is one o he cen al esea ch ocuses ac ual. Bu he e is o men ion, ha economical, ecological and social c i e ia ha e o be conside ed o achie e sus ainabili y [1] and in his con ex , he e a e subs an ial po en ials in he ield o P oduc ion Planning and Con ol (PPC) [2] [3] [4]. So, he esou ce consump ion is in luenced due o he p oduc ion plan, which has o be de e mined. Thus, ecological and social issues like ene gy consump ion o wo ke ’s s ess a e a ec ed nex o he classical economical mone a y assessmen [5]. In his p ocess, he ecological dimension is al eady explo ed b oadly (see: [6] [7] [8]). Howe e , he e is a gap in esea ch o he social dimension a he ield o PPC. He e he pape s om [9], [10] as well as [11] ha e o be men ioned, who conside ed human lea ning and o ge ing e ec s o a Lo -Sizing p oblem and educe wo ke ’s s ess o a speci ic Scheduling p oblem. Especially in conside a ion o he al eady p o en Hie a chical P oduc ion Planning sys em om [12], i should be no ed, ha he e a e no app op ia e app oaches o he conside a ion o he social dimension a he le el o Mas e P oduc ion Scheduling, which is he op le el a he Hie a chical P oduc ion 147 Planning sys em om [12]. This lack o social imp o emen s is also a i med by he pape om [13], who epo s, ha he e a e only sma imp o emen s o wo ke condi ions in spi e o di e en esea ch ac i i ies. Especially he physical s ess and he wo k in ensi y a e a ed o be oo high ou o 11 de ined c i e ia [13]. Fo his eason, an ex ended e sion o he linea op imiza ion model o he Mas e P oduc ion Scheduling wi h conside a ion o social c i e ia om [5] is p esen ed a his pape and as an ex ension o he s udies in [5] he e is also p esen ed an in es iga ion ega ding he necessi y o in eg a e social c i e ia based on a mo e comp ehensi e case s udy. 1 Linea Op imiza ion Model o Mas e P oduc ion Scheduling In classical models as a es ic ion o he p oduc ion plan a he le el o he Mas e P oduc ion Scheduling he e a e de ined s ipula ed limi s o exis ing capaci ies. Bu a compensa ion o capaci y bo lenecks a e doable due o a p oduc ion in ad ance o by using o e ime hou s, so ha he minimiza ion o cos s o in en o y and o e ime hou s is he goal in such models [14]. Fu he mo e, cons an p ocessing imes o each quan i y uni pe p oduc a e assumed. Now he linea op imiza ion model, which is based on his s anda d, is desc ibed. The conside a ion o cos s o shi bonuses, he possibili y o di e en wo ke u iliza ions o each p oduc ion segmen and he speci ica ion o he wo ke u iliza ion as an in e al a e he ex ensions o he model, which is in oduced in [5]. The in eg a ion o a a iable pe sonnel supply o capaci y, see Equa ion (5), is he i s essen ial imp o emen a his model. The eby i is also conside ed, ha he e a e equi emen s o lead imes o adjus capaci ies. Fo he conside a ion o social c i e ia his all is impe a i e, because his connec s elemen s o he human esou ces managemen wi h he PPC and in ha o de no only he human esou ces managemen has o p o ide he necessa y capaci ies bu also he PPC has o conside he wo ke s equi emen s [5]. In addi ion, he limi a ion o a maximum supply o echnical capaci y, see Equa ion (6), emains unchanged. The de e mina ion o a ixed ela ion (wo ke u iliza ion), see Equa ions (11) and (12), be ween supply o capaci y, see Equa ion (5), and capaci y equi emen s, see Equa ion (4), is he second essen ial imp o emen a his model. This ensu es ha wo ke s canno be o e loaded. Nex o he classical p oduc ion plan, see Equa ions (2–4), he numbe o wo ke s equi ed, see Equa ions (5–7), is also de e mined. The eby di e en classes o wo ke s a e also conside ed o e e y p oduc ion segmen . Fu he , in e n condi ions om he company and ex e n condi ions om he labo ma ke a e in eg a ed by de ining ini ial, minimal and maximal numbe s o employees, see Equa ions (8–10),. The objec i e unc ion (see equ. 1) is calcula ed by minimiza ion he sum o s o age cos s, manpowe cos s, cos s o shi bonuses as well as cos s o building and emo ing capaci ies. Fo his pu pose, he app op ia e shi model (one, wo, o h ee shi s) due o he numbe o employees is also de e mined, see Equa ions (13–15). Compa ed o he basic model om [14] he conside a ion o wo ke u iliza ion speci ic p ocessing imes is he hi d essen ial imp o emen a his model. Bu hese p ocessing imes a e de e mined as pa ame e s, because a non-linea i y is caused by a di ec calcula ion wi hin he op imiza ion model. The e o e, he p ocessing imes a e calcula ed ex e n by mul iplica ion om s anda d p ocessing imes wi h weigh ing ac o s, which a e de i ed om a igue cou ses due o he wo ke u iliza ion. Then, o ecei e he op imal solu ion he op imiza ion model is sol ed o all wo ke u iliza ion cons ella ions and he associa ed p ocessing imes. Now he ma hema ically model desc ip ion is p esen ed. 148 Pa ame e s: a j max , Maximum supply o echnical capaci y d k, P oduc equi emen s pe p oduc k and ime pe iod zkj ,, Capaci y equi emen pe p oduc ion segmen j, p oduc k and o e un pe iod z hk Cos a e o s o age pe p oduc k Iini k Ini ial in en o y pe p oduc k J Numbe o p oduc ion segmen s (j = 1, 2, …, J) K Numbe o p oduc s (k = 1, 2, …, K) KAPA ma, Supply o capaci y pe wo ke o a wo ke class ma and ime pe iod mKos Cos a e o building supply o capaci y MA Numbe o wo ke classes (ma = 1, 2, …, MA) Mi ini sjma ,, Ini ial numbe o wo ke pe wo ke class ma, p oduc ion segmen j and shi s Mi Kos jma ,, Cos a e pe wo ke o class ma, p oduc ion segmen j and ime pe iod Mi jma max ,, Maximum numbe o wo ke pe wo ke class ma, p oduc ion segmen j and ime pe iod Mi jma min ,, Minimum numbe o wo ke pe wo ke class ma, p oduc ion segmen j and ime pe iod nKos Cos a e o emo ing supply o capaci y Rj max Maximum wo ke u iliza ion pe p oduc ion segmen j Rj min Minimum wo ke u iliza ion pe p oduc ion segmen j S Numbe o shi s (s = 1, 2, …, S) SKos s Cos ac o o calcula ing shi bonuses pe shi s SOben sj, Maximum limi o numbe o wo ke pe p oduc ion segmen j and shi s SUn sj, Minimum limi o numbe o wo ke pe p oduc ion segmen j and shi s T Planning ho izon in ime pe iods ( = 1, 2, …, T) W Numbe o o e un pe iods o emo ing supply o capaci y (w = W) Y Numbe o o e un pe iods o building supply o capaci y (y = Y) Z Numbe o o e un pe iods o p oduc ion (z = 1, 2, …, Z) Decision a iables: a j, Supply o capaci y pe p oduc ion segmen j and ime pe iod b j, Capaci y equi emen pe p oduc ion segmen j and ime pe iod I k, In en o y pe p oduc k and ime pe iod m jma ,, Numbe o wo ke ec ui men s pe wo ke class ma, p oduc ion segmen j and ime pe iod Mi sjma ,,, Numbe o wo ke pe wo ke class ma, p oduc ion segmen j and ime pe iod n jma ,, Numbe o wo ke edundancies pe wo ke class ma, p oduc ion segmen j and ime pe iod p sj ,, Boolean a iable o calcula ing he numbe o shi s pe p oduc ion segmen j, shi s and ime pe iod 149 x k, P oduced quan i y pe p oduc k and ime pe iod Objec i e unc ion o minimize:                            T J j MA ma jma Kos jma T J j MA ma jma Kos jma T S s MA ma sj Kos s sjma Kos jma T S s MA ma sjma Kos jma T K k k k nnmm p sMi Mi Mi Mi I h 1 1 1 ,,,, 1 1 1 ,,,, 1 1 1 ,, ,,,,, 1 1 1 ,,,,, 1 1 , (1) Cons ain s: d II x k k k k , ,1, ,  (2) II ini kk  0, (3)      K k Z z jz k zkj bx 1 1 ,, ,, (4)      MA ma S s j ma sjma a KAPA Mi 1 1 , , ,,, (5) aa j j max ,,  (6)       S s S s sjmaW jmaY jma sjma Mi nmMi 1 1 ,,,,,,,1,,, (7) Mi Mi ini sjmaZsjma ,,0,,,   (8)  S s jma sjma Mi Mi 1 min ,,,,, (9)  S s jma sjma Mi Mi 1 max ,,,,, (10) a R b j j j , max , (11) a R b j j j , min , (12) s p Mi Un sj MA ma sj sjma , 1,, ,,,   (13) s p Mi Oben sj MA ma sj sjma , 1,, ,,,   (14) 1 1,,  S s sj p (15) 150 2 Examina ion Scena ios and Case S udy The scena ios di e be ween hei assumed human a igue cou ses and hei p oduc equi emen classes. The e a e h ee di e en human a igue cou ses (1 = la exponen ial cou se, 2 = s eep exponen ial cou se, 3 = cons an cou se). The eby cou se 3 is equal o he non-conside a ion o wo ke u iliza ion speci ic p ocessing imes o a he i means ha no human a igue occu s. Cou ses 1 and 2 a e chosen, because an exponen ial cou se is o en used in li e a u e (see: [15] [16]). The weigh ing ac o s o he wo ke u iliza ion speci ic p ocessing imes due o he di e en cou ses a e p esen ed in Figu e 1. These ac o s a e aken in o accoun o calcula e he app op ia e p ocessing imes o each wo ke u iliza ion, p oduc and p oduc ion segmen . Sou ce: Own Fig. 1: Wo ke u iliza ion speci ic weigh ing ac o s o p ocessing imes pe human a igue cou ses Nex o his he e a e also h ee p oduc equi emen classes (1 = medium equi emen s, 2 = small equi emen s, 3 = la ge equi emen s), which a e de e mined based on he esul s o capaci y equi emen s o he highe planning le el - he Agg ega ed P oduc ion Planning. Fu he mo e, he e a e h ee di e en and andomly de ined p oduc equi emen sequences pe p oduc equi emen class, so ha he e a e 9 di e en equi emen sequences in o al. In conjunc ion wi h he human a igue cou ses his esul in o e all 27 di e en examina ion scena ios. In addi ion, he conside ed wo ke u iliza ion should no dec ease a bi a y and o es ablish a conc e e poin o wo ke u iliza ion is no p ac icable. Ano he aspec , which should be conside ed, is ha wo ke u iliza ion om mo e han 100% also should no be ecommended due o social aspec s. Tha is why we use hese ou di e en wo ke u iliza ion in e als 80- 85%, 85-90%, 90-95% and 95-100%. Associa ed wi h he wo ega ded p oduc ion segmen s 16 di e en wo ke u iliza ion cons ella ions ha e o been calcula ed pe examina ion scena io o de e mine he op imal solu ions o each o he 27 scena ios. Fu he used pa ame e s a e p esen ed in [5]. Di e ences occu by he s anda d p ocessing imes, which a e in his pape a he i s p oduc ion segmen 2534 ime uni s pe quan i y uni s (TU/QU) o p oduc A and 4735 TU/QU o p oduc B as well as 7019 TU/QU o p oduc A and 6632 TU/QU o p oduc B a he second p oduc ion segmen and he e is also conside ed ha only a pa o he p ocessing imes (manual pa ) is a ec ed by he wo ke u iliza ions. These p opo ions a e 80% in p oduc ion segmen 1 and 30% in p oduc ion segmen 2. Finally, o he addi ional calcula ion o cos s o shi bonuses, he manpowe cos s a e mul iplied wi h he ac o s 0.0% o one shi models, 1.5% o wo shi models and 15.0% o h ee shi models. 151 3 Resul s and Discussion Fi s he de ia ions be ween he op imal solu ions wi h and wi hou conside a ion o wo ke u iliza ions a e p esen ed in Figu e 2. Classically i is expec ed ha a maximiza ion o he u iliza ion leads o he op imal solu ion. The e o e, we compa e he de e mined eal op imal solu ion om ou op imiza ion model wi h he solu ion o he maximal wo ke u iliza ion, which is iden ical wi h a non-conside a ion o wo ke u iliza ions. Fo his case, he wo ke u iliza ion cons ella ion om 95-100% o each p oduc ion segmen is aken in o accoun o calcula e he solu ions o non-conside a ion o wo ke u iliza ions. Sou ce: Own Fig. 2: De ia ions be ween solu ions wi h and wi hou conside a ion o wo ke u iliza ions F om Figu e 2 i eme ges ha he solu ions wi hou conside a ion o wo ke u iliza ions de ia e om he op imal solu ions by 7.2% in a e age abou all equi emen sequences and human a igue cou ses. The de ia ions in a e age pe p oduc equi emen class (a e age pe equi emen sequences a he same equi emen class) demons a e ha his esul is no caused by speci ic demand sequences, because he de ia ion o each p oduc equi emen class is always be ween 6% and 8%. The e o e i is shown ha he igno ance o wo ke u iliza ions causes essen ial de ia ions om eali y, so ha mo e de ec ed p oduc ion plans, cos budge s and pe sonnel plans occu and disad an ages in compe i ion and o e loading om wo ke s a e he consequences. Nex o his, he eal op imal solu ions a e p esen ed a able 1, oge he wi h he de ia ions be ween a conside a ion and non-conside a ion o wo ke u iliza ion speci ic p ocessing imes. In his con ex , he a igue cou se 3 was used o ep esen he case o a non-conside a ion o wo ke u iliza ion speci ic imes. Tab. 1: Op imal solu ions [in money uni s] and de ia ions be ween conside a ion and non- conside a ion o wo ke u iliza ion speci ic p ocessing imes Requi emen Sequence Op imal Solu ion dependen on Human Fa igue Cou se De ia ion be ween 3 & 1 De ia ion be ween 3 & 2 1 2 3 1.1 132 797 132 949 129 215 2.70% 3.51% 2.81% 4.86% 1.2 144 159 144 504 132 885 7.82% 8.04% 1.3 123 092 118 660 123 082 0.01% 3.73% 2.1 128 789 133 677 124 303 3.48% 1.46% 7.01% 5.63% 2.2 133 248 139 995 133 748 0.38% 4.46% 2.3 130 483 124 424 131 145 0.51% 5.40% 3.1 133 511 136 770 127 739 4.32% 1.62% 6.60% 3.10% 3.2 133 780 133 398 134 035 0.19% 0.48% 3.3 127 142 124 783 127 566 0.33% 2.23% Sou ce: Own 152 F om able 1 i eme ges ha he op imal solu ions om he human a igue cou se 3 de ia e by 3.4% in a e age abou all equi emen sequences and o he human a igue cou ses. Bu he de ia ion in a e age abou all equi emen sequences be ween human a igue cou se 3 and 1 (2.19%) is only hal as high as he compa able de ia ion be ween human a igue cou se 3 and 2 (4.53%). So, o one hing i is shown ha he conside a ion o wo ke u iliza ion speci ic p ocessing imes has an impo an impac , bu on he o he hand i is also impo an o ake in o accoun he igh human a igue cou se, wha is a gap in esea ch ac ual. The e o e, o p e en mo e de ec ed p oduc ion plans, cos budge s and pe sonnel plans he conside a ion o wo ke u iliza ion speci ic p ocessing imes is also a necessi y. Howe e , u he esea ch ac i i ies a e necessa y o quan i y a igue e ec s co ec ly, like i is done o human lea ning e ec s. Conclusion A his pape , i is demons a ed ha he e is a gap in esea ch o he in eg a ion o he social dimension along he P oduc ion Planning and Con ol. Especially app oaches wi h conside ed social c i e ia a e missing a he le el o Mas e P oduc ion Scheduling. The e o e, an app op ia e op imiza ion model is p esen ed and 27 di e en scena ios a e analyzed. F om he esul s, i eme ges ha ad an ages in compe i ion and a educ ion o wo ke ’s s ess could be achie ed by conside ing op imal wo ke u iliza ions and wo ke u iliza ion speci ic p ocessing imes. Tha means ha a imely conside a ion o social e ec s causes a mo e ca e ully use o he human esou ces bu also mone a y ad an ages. Finally, a gap in esea ch is ecognized o quan i ying igh a igue cou ses, which should be sol ed in u he esea ch ac i i ies. Acknowledgemen s M . Ma co T os is unded by he Eu opean social und Saxony (applica ion numbe 100235479) o p ojec s o he p omo ion o na ional inno a ion p omo ions ( unding pe iod 01.10.2015 - 31.12.2018). Li e a u e [1] ROGALL, H. (2009). Nachhal ige Ökonomie – Ökonomische Theo ie und P axis eine Nachhal igen En wicklung. Me opolis, Ma bu g. [2] HAASIS, H.-D. (2008). 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W.; ZHANG, W.; MA, L.; CHEN, Z.: (2014). Muscula a igue and maximum endu ance ime assessmen o male and emale indus ial wo ke s. In e na ional Jou nal o Indus ial E gonomics. 44(2), pp. 292–297. DOI: 10.1016/j.e gon.2012.08.006 Dipl. Wi sch.-Ing. (FH) Ma co T os , M.A.; P o . D . habil. Tho s en Claus; P o . D .-Ing. F ank He mann 154 NUTNOST INTEGRACE SOCIÁLNÍCH KRITÉRIÍ DO PLÁNOVÁNÍ PROGRAMU HLAVNÍ PRODUKCE Příspě ek zkoumá nu nos zohlednění y ížení spolup aco níků a na něm zá islé p aco ní doby hla ním pláno ání p og amu hla ní p odukce. Na íc je ukázáno, že a o ema ická oblas ak uálně předs a uje e ýzkumu meze u. Z oho o dů odu je u předs a en las no učně y inu ý lineá ní model op imalizace na pláno ání p og amu hla ní p odukce, k e ý obsahuje sociální k i é ia a hodnou případo ou s udii. Výsledky ukazují, že značné odchylky jsou od islé od igno ance při y ížení spolup aco níků p aco ní době. Z oho o dů odu je dopo učo ána in eg ace. Zá o eň se ukazuje, že bude řeba dalšího ýzkumu, obz lášť p o s ano ení hodných y ěžujících unkcí, jako jsou např. unkce p o e ek y učení. VON SOZIALEN KRITERIEN IN DIE HAUPTPRODUKTIONSPROGRAMMPLANUNG Folgende Bei ag un e such die No wendigkei eine Be ücksich igung on Mi a bei e auslas ungen und da on abhängige Bea bei ungszei en in de Haup p oduk ionsp og ammplanung. Zudem wi d au gezeig , dass dieses Themengebie ak uell eine Fo schungslücke da s ell . Aus diesem G und wi d ein selbs en wickel es linea es Op imie ungsmodell ü die Haup p oduk ionsp og ammplanung o ges ell , welches soziale K i e ien und eine geeigne e Falls udie en häl . Die E gebnisse e deu lichen, dass e hebliche Abweichungen du ch eine Igno anz on Mi a bei e auslas ungen und da on abhängige Bea bei ungszei en en s ehen. Deshalb is eine In eg a ion zu emp ehlen. Alle dings wi d auch deu lich, dass wei e e Fo schungen no wendig sind, speziell ü die Bes immung geeigne e E schöp ungs unk ionen, so wie beispielsweise Funk ionen ü Le ne ek e exis ie en. KONIECZNOŚĆ INTEGRACJI KRYTERIÓW SPOŁECZYCH W PLANOWANIU PROGRAMU GŁÓWNEJ PRODUKCJI W niniejszym a ykule zbadano konieczność uwzględnienia obciążenia współp acowników i od niego zależnego czasu p acy w głównym planowaniu p og amu głównej p odukcji. Ponad o wskazano, że a dziedzina jes obecnie w badaniach pomijana. Z ego względu p zeds awiono op acowany we własnym zak esie model liniowy op ymalizacji planowania p og amu głównej p odukcji, obejmujący k y e ia społeczne o az odpowiednie s udium p zypadku. Wyniki pokazują, że znaczne odchylenia wynikają z igno ancji p zy obciążaniu współp acowników w czasie p acy. Z ego powodu zalecana jes in eg acja. Ponad o wskazano, że konieczne są kolejne badania, w szczególności w celu ok eślenia odpowiednich unkcji obciążeniowych akich jak np. unkcja dla e ek ów w uczeniu się.