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).
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F ank He mann
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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.