155
ACC JOURNAL 2017, Volume 23, Issue 2 DOI: 10.15240/ ul/004/2017-2-012
CAN AGGREGATE PRODUCTION PLANNING (APP) BE MODIFIED TO BE AS
GOOD AS MASTER PRODUCTION SCHEDULING (MPS)?
Tho s en Vi z hum1; 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[email p o ec ed];
3 ank.he[email p o ec ed]
Abs ac
In his pape , he signi icance o mas e p oduc ion scheduling (MPS) o hie a chical
p oduc ion planning should be b ough ou . The e o e, se e al modi ica ions o agg ega e
p oduc ion planning (APP) a e made and ealiza ion o he planning esul s o APP and MPS
a e compa ed. The goal is o imp o e he ealiza ion o APP in such a way ha he ealiza ion
is as good as he ealiza ion o MPS. Imp o emen s o indi idual planning si ua ions could
be achie ed, bu no gene al solu ion could be ound. Especially he use o a sui able capaci y
educ ion ac o (CRF) combined wi h he conside a ion o lead ime leads o an imp o emen
o he solu ion. Howe e , inding a sui able CRF o mo e han one p oduc is di icul . This
usually depends on he unde lying demand p o ile and mus be e-de e mined o each
cons ella ion.
Keywo ds
Hie a chical p oduc ion planning; Agg ega e p oduc ion planning (APP); Mas e p oduc ion
scheduling (MPS); Ma e ial equi emen planning; Resou ce p o iles.
In oduc ion
P oduc ion planning is a e y complex. A high numbe o pa ame e s and hei mul iple
dependencies a e simul aneously o be aken in o accoun . This esul ing planning p oblem
can’ be sol ed in an app op ia e ime e en wi h mos powe ul compu e s and sophis ica ed
so wa e [1].
In he mos comme cial p oduc ion planning and con ol sys ems, he complex planning o
p oduc ion planning is eplaced by he hie a chical p oduc ion planning app oach [6]. In his
case he complex singula p oblem is decomposed in se e al manageable p oblems. These
p oblems a e sol ed successi ely and he indi idual solu ions a e combined in o one o e all
solu ion a he end. The hie a chical p oduc ion planning app oach is a ibu ed o Hax and
Meal in he yea 1975 [5]. D exl, Fleischmann, Gün he and S adle sugges ed in 1994 o
expand his concep by limi ed capaci ies o esou ces [2]. On his planning concep , he pape
is based. Typical hie a chical p oduc ion planning is shown in Figu e 1.
156
Scheduling
P ojec shop
Job shop
FMS
Flow shop
JIT
p oduc ion
...
Linked p oduc ion segmen s
Capaci y-o ien ed PPC-Sys em
Agg ega e Mas e Planning
P oduc ion segmen (Loca ion 1)
Linked p oduc ion segmen s
Capaci y-o ien ed PPC-Sys em
Agg ega e Mas e Planning
P oduc ion segmen (Loca ion N)
Loca ion-in eg a ed P oduc ion- P ocu emen - and T anspo a ion planning
(Supply Ne wo k Planning, Mas e Planning, En e p ise Planning) agg ega ed
de ailed
De e minis ic View
S ochas ic View
P ocu emen
Dis ibu ion
Shipmen s Shipmen sSupply Ne wo k
Demand o ecas ing, Demand ul illmen (A ailable- o-p omise), Wa ning-Moni o ing
Suppo i e modules
Bu e ing, Sa e y S ocks, Sa e y Times
...
Mas e
P oduc ion
Planning
Ma e ial
Requi emen s
Planning
P ojec shop
Job shop
FMS
Flow shop
JIT
p oduc ion
...
Cus ome
Supplie
Sou ce: [4]
Fig. 1: Typical hie a chical p oduc ion planning
Agg ega ion plays an impo an ole in his planning app oach. The e a e h ee di e en ypes
o agg ega ion. The agg ega ion o ime especially he pe iod size, decision a iables like
g ouping o p oduc s o cons ain s like g ouping o machines o wo k cen e s o p oduc ion
si es [3][7]. This planning concep consis s o he ollowing s eps: Agg ega e p oduc ion
planning (APP), mas e p oduc ion scheduling (MPS), ma e ial equi emen s planning and
scheduling.
APP p edic s he planned independen equi emen s o one p oduc ion si e on a p oduc
g oup le el based on demand o ecas s. MPS p edic s he planned independen equi emen s
o inal p oduc s o a p oduc ion si e. The e o e, p oduc g oups a e disagg ega ed in o inal
p oduc s. Th ough he use o esou ce p o iles p oduc ion lead ime and he capaci y
equi emen s o each wo k cen e is conside ed [9].
In he pape E idence o he ele ance o mas e p oduc ion Scheduling o hie a chical
P oduc ion Planning [8] he ele ance o MPS was demons a ed h ough a case s udy. MPS
can a oid sho ages h ough a close examina ion o he capaci y. I was sugges ed o
in oduce a capaci y es ic ion and o conside he exac o se pe iods on APP le el o
possibly a oid sho ages. This will be ca ied ou . Capaci y on APP le el will be educed by a
capaci y educ ion ac o (CRF).
The poin o his pape is bes illus a ed by ollowing a clea example om a case s udy. A
he beginning o he case s udy solu ion and ealiza ion o APP and MPS a e compa ed. In he
nex s ep, a CRF o APP is in oduced and he exac o se pe iods a e conside ed. In he end,
i is examined wha happens i o al demand o all p oduc s is he same, bu he demand o
each p oduc is di e en .
157
1 Case S udy
One p oduc ion si e wi h wo wo k cen e s is conside ed. The capaci y o each wo k cen e is
500 hou s pe pe iod. So, he p oduc ion si e has a capaci y o 1000 hou s pe pe iod. Human
capaci y is equal echnical capaci y and he e is no addi ional capaci y. In o de o be able o
compa e esul s which each o he , he pe iod size o agg ega e p oduc ion planning (APP) and
mas e p oduc ion scheduling (MPS) is he same and i is assumed ha he p edic ed planned
independen equi emen s a e iden ical o he eal cus ome equi emen s. The de i ed
equi emen s o all componen s a e p oduced jus in ime. The model o a closed p oduc ion is
used. Closed p oduc ion is cha ac e ized by he ac ha each planned o de mus be inished
and s o ed, be o e i can be u he p ocessed o shipped [6].
Two p oduc g oups which a e p oduced in one p oduc ion si e a e conside ed. Each p oduc
g oup consis s o one inal p oduc . The inal p oduc (E) needs 3 hou s o capaci y pe uni in
wo k cen e (A) and he componen (V) needs 7 hou s o capaci y pe uni in wo k cen e (B).
I ollows ha p oduc g oup (P) needs 10 hou s o capaci y pe uni in p oduc ion si e. The
inal p oduc (F) needs 5 hou s o capaci y pe uni in wo k cen e (A) and he componen (V)
needs 5 hou s o capaci y pe uni in wo k cen e (B). I ollows ha p oduc g oup (Q) needs
also 10 hou s o capaci y pe uni in p oduc ion si e. The es ima ed lead ime o all p oduc s
and componen s is 1 pe iod. Se -up imes and cos s a e no conside ed.
The planning ho izon o he case s udy s a s in pe iod 1 and ends wi h he las cus ome
demand in pe iod 10. The demands o p oduc g oup (P) espec i ely p oduc (E) and p oduc
g oup (Q) espec i ely p oduc (F) a e shown in Table 1.
Tab. 1: Demand o he case s udy
Pe iod ( )
1
2
3
4
5
6
7
8
9
10
∑
Demand (𝑑𝐸,𝑡
𝐴)[uni s]
0
0
0
0
40
50
60
50
40
60
300
Demand (𝑑𝐹,𝑡
𝐴)[uni s]
0
0
0
0
40
50
60
50
40
60
300
Sou ce: Own
As shown in [8] due o he agg ega ed conside a ion o capaci y equi emen o p oduc
g oups, APP o e es ima es he numbe o p oduc s which can be p oduced in o one pe iod.
This was shown o one p oduc g oup which is ela ed o one inal p oduc . To a oid his
CRF o 0.83 is in oduced in combina ion wi h he conside a ion o he lead ime o 2 pe iods.
The solu ion and he ealiza ion o his APP is as good as he one o MPS.
The Solu ion o APP wi h a CRF o 0.83 and MPS is shown in Table 2. The objec i e is
€872.
Tab. 2: Solu ion o APP wi h capaci y educ ion ac o 0.83 and MPS
Pe iod ( )
1
2
3
4
5
6
7
8
9
10
∑
𝑑𝐸,𝑡
𝐴 [uni s]
0
0
0
0
80
100
120
100
80
120
600
𝑥𝐸,𝑡
𝐴 [uni s]
0
19
83
83
83
83
83
83
83
0
600
𝑦𝐸,𝑡
𝐸 [uni s]
0
0
19
102
105
88
51
34
37
0
436
Sou ce: Own
The solu ion can be ealized wi hou exceeding he pe iod capaci y and no sho age occu s in
he indi idual pe iods.
2 Resul s o he Resea ch
In his case s udy, he planning esul s o wo p oduc g oups as desc ibed in he case s udy
a e compa ed. Fi s he Solu ion o APP which is p o ided by ILOG is p esen ed. Nex , an
158
op imal solu ion o APP wi hou sho ages and delay is sea ched and p esen ed. A he end
he esul s a e compa ed wi h he esul s o MPS.
Tab. 3: Solu ion o APP wi h CRF 0.83 (ILOG)
Pe iod ( )
1
2
3
4
5
6
7
8
9
10
∑
𝑑𝑃,𝑡
𝐴 [uni s]
0
0
0
0
40
50
60
50
40
60
300
𝑥𝑃,𝑡
𝐴 [uni s]
0
19
0
21
83
27
50
77
23
0
300
𝑦𝑃,𝑡
𝐸 [uni s]
0
0
19
19
0
33
0
0
37
0
108
𝑑𝑄,𝑡
𝐴 [uni s]
0
0
0
0
40
50
60
50
40
60
300
𝑥𝑄,𝑡
𝐴 [uni s]
0
0
83
62
0
56
33
6
60
0
300
𝑦𝑄,𝑡
𝐸 [uni s]
0
0
0
83
105
55
51
34
0
0
328
Sum 𝑥𝑃,𝑡
𝐴+ 𝑥𝑄,𝑡
𝐴
0
19
83
83
83
83
83
83
83
0
600
Sou ce: Own
dE,5=40
dE,6=50
dE,7=60
dE,8=50
dE,9=40
dE,10=60
dF,5=40
dF,6=50
Pe iod ( )41 2 3 5 6 107 8 9 11 12
WCB
WCA
V_1
E_1
W_1W_1
V_2 V_4 V_6V_5 V_7V_3V_3
W_2 W_5W_4W_3 W_6
E_2 E_3 E_5
F_1F_1 F_2 F_3
E_7E_7
F_4
E_6E_6
F_5 F_6F_6
E_4
dF,7=60
dF,8=50
dF,9=40
dF,10=60
Delay
Sou ce: Own
Fig. 2: Realiza ion o APP wi h CRF 0.83 (ILOG)
In Figu e 2 he ealiza ion o Table 3 is illus a ed as Gan cha . The lead ime is aken in o
accoun du ing he ealiza ion. Figu e 2 shows ha he demand o p oduc (E) o pe iod 6 is
ul illed wi h 1 pe iod delay. The same beha io can be seen o he demand o p oduc (F) o
he pe iods 7, 9 and 10. The o al delay in pe iods is 4. Besides he o al sho age o 510 uni s
he in en o y holding cos s inc ease om €872 o €1266. ILOG inds an op imal solu ion.
This may no be he only solu ion, he e may be o he solu ions. Ano he solu ion is shown in
Table 4 and he ealiza ion is illus a ed in Figu e 3. This solu ion can be ealized wi hou
sho age and delay. The in en o y holding cos s co espond o he objec i e o €872. Bo h
solu ions ha e in common ha a maximum o 83 uni s o bo h p oduc s can be p oduced pe
pe iod. The exac p oduc ion quan i ies can be ound in ables unde “Sum 𝑥𝑃,𝑡
𝐴+ 𝑥𝑄,𝑡
𝐴”.
Fu he mo e, he esul s a e compa ed wi h he solu ion and ealiza ion o he case s udy wi h
one p oduc g oup shown in he pape o Vi z hum & He mann [8]. We see ha in his case
s udy we ha e he same p oduc ion quan i ies and he same in en o y holding cos s o €872.
159
Tab. 4: Solu ion o APP wi h CRF 0.83 (al e na i e)
Pe iod ( )
1
2
3
4
5
6
7
8
9
10
∑
𝑑𝑃,𝑡
𝐴 [uni s]
0
0
0
0
40
50
60
50
40
60
300
𝑥𝑃,𝑡
𝐴 [uni s]
0
6
42
42
42
42
42
42
42
0
300
𝑦𝑃,𝑡
𝐸 [uni s]
0
0
6
48
50
42
24
16
18
0
204
𝑑𝑄,𝑡
𝐴 [uni s]
0
0
0
0
40
50
60
50
40
60
300
𝑥𝑄,𝑡
𝐴 [uni s]
0
13
41
41
41
41
41
41
41
0
300
𝑦𝑄,𝑡
𝐸 [uni s]
0
0
13
43
55
46
27
18
19
0
232
Sum 𝑥𝑃,𝑡
𝐴+ 𝑥𝑄,𝑡
𝐴
0
19
83
83
83
83
83
83
83
0
600
Sou ce: Own
dE,5=40
dE,6=50
dE,7=60
dE,8=50
dE,9=40
dE,10=60
dF,5=40
dF,6=50
dF,7=60
dF,8=50
dF,9=40
dF,10=60
dE,5=40
dE,6=50
dE,7=60
dE,8=50
dE,9=40
dE,10=60
dF,5=40
dF,6=50
dF,7=60
dF,8=50
dF,9=40
dF,10=60
Pe iod ( )41 2 3 5 6 107 8 9 11 12
WCB
WCA
V_1 V_2 V_3 V_4 V_6V_5 V_7 V_8
E_1 E_2 E_3 E_4 E_6E_5 E_7E_7 E_8
W_1 W_2 W_4W_3 W_5 W_6W_5 W_6 W_7 W_8
F_1 F_2 F_4F_3 F_5 F_6F_5 F_6 F_5 F_6F_5 F_6
Sou ce: Own
Fig. 3: Realiza ion o APP wi h CRF 0.83 (al e na i e)
Finally, he esul s o he APP a e compa ed wi h he esul s o he MPS. The esul s o he
MPS a e shown in Table 5 and illus a ed in Figu e 4.
Tab. 5: Solu ion o MPS
Pe iod ( )
1
2
3
4
5
6
7
8
9
10
∑
𝑑𝐸,𝑡
𝐴 [uni s]
0
0
0
0
40
50
60
50
40
60
300
𝑥𝐸,𝑡
𝐴 [uni s]
0
15
71
42
35
30
35
42
30
0
300
𝑦𝐸,𝑡
𝐸 [uni s]
0
0
15
86
88
73
43
28
30
0
363
𝑑𝐹,𝑡
𝐴 [uni s]
0
0
0
0
40
50
60
50
40
60
300
𝑥𝐹,𝑡
𝐴 [uni s]
0
0
0
41
51
58
51
41
58
0
300
𝑦𝐹,𝑡
𝐸 [uni s]
0
0
0
0
1
2
0
1
2
0
6
Sum 𝑥𝐸,𝑡
𝐴+ 𝑥𝐹,𝑡
𝐴
0
15
71
83
86
88
86
83
88
0
600
Sou ce: Own

160
dE,5=40
dE,6=50
dE,7=60
dE,8=50
dE,9=40
dE,10=60
dF,5=40
dF,6=50
dF,7=60
dF,8=50
dF,9=40
dF,10=60
dE,5=40
dE,6=50
dE,7=60
dE,8=50
dE,9=40
dE,10=60
dF,5=40
dF,6=50
dF,7=60
dF,8=50
dF,9=40
dF,10=60
Pe iod ( )41 2 3 5 6 107 8 9 11 12
WCB
WCA
V_1 V_2 V_3 V_4 V_6V_5
W_1 W_2 W_5 W_6W_4W_3
V_7 V_8
E_1 E_2 E_3 E_4 E_6E_5 E_7E_7 E_8E_1 E_2 E_3 E_4 E_6E_5 E_7 E_8
F_1 F_2 F_5 F_6F_4F_3F_1 F_2 F_5 F_6F_4F_3
Sou ce: Own
Fig. 4: Realiza ion o MPS
The ealiza ion can be done wi hou sho age and delay. The in en o y holding cos s a e €738.
Compa ed o he APP, he s o age cos s ha e dec eased by €134. This means a sa ing o
15.37%. In o de o unde s and he di e ences, he planed independen equi emen s o APP
and MPS ha e o be compa ed. APP has a maximum o 83 uni s which can be p oduced
independen ly o he p oduc which is p oduced. MPS has a maximum o 88 uni s, bu i
depends on he p oduc mix, which is p oduced.
3 Discussion
One ad an age o MPS is he conside a ion o lead ime. Bu e en i APP akes lead ime in o
accoun , we do no ge any plans ha can be ealized wi hou sho ages and delay. APP
es ima es he a ailable capaci y o he wo k cen e w ongly, because o he agg ega ed
planning o he p oduc ion si e. No mally APP o e es ima es he a ailable capaci y. One way
o co ec his is CRF. A good chosen CRF will p o ide easible plans. Due o he gene al
educ ion, a ough es ima e is made. The e is no di e en ia ion o capaci y equi emen s by
p oduc s. The main ad an age o he MPS is he use o esou ce p o iles. A esou ce p o ile
gi es in o ma ion abou he capaci y equi emen s o inal p oduc s in e ms o wo k cen e s
and o se pe iods. Fo his eason, he capaci y o he p oduc ion p og am is aken in o
accoun mo e p ecisely. The ac is bes demons a ed in compa ison o he maximum
p oduc ion a e by p oduc . While APP doesn’ di e be ween p oduc (E) and p oduc (F)
and has maximum p oduc ion a e o 83 uni s he MPS di e s and has a maximum p oduc ion
a e o 71 uni s o p oduc (E) and a maximum p oduc ion a e o 100 o p oduc (F).
Conclusion
MPS is supe io o APP due o he de ailed conside a ion o he capaci y equi emen .
Th ough he use o esou ce p o iles an alloca ion o he capaci y equi emen by wo k cen e
and pe iod based on p oduc s is made, while APP has a ixed p oduc ion a e o all p oduc s.
MPS has a a iable p oduc ion a e o he p oduc s which di e s by he p oduc mix o he
p oduc ion p og am. Fo his eason MPS can use he a ailable capaci y mo e e icien ly han
APP.
161
Li e a u e
[1] CLAUS, T.; HERRMANN, F.; MANITZ, M. (eds.): (2015). P oduk ionsplanung und -
s eue ung: Fo schungsansä ze, Me hoden und de en Anwendungen. Be lin, Heidelbe g:
Sp inge Gable .
[2] DREXL, A.; FLEISCHMANN, B.; GÜNTHER, H.-O.; STADTLER, H.;
TEMPELMEIER, H.: (1994). Konzep ionelle G undlagen kapazi ä so ien ie e PPS-
Sys eme. Zei sch i ü be iebswi scha liche Fo schung. Vol. 46, pp. 1022–1045.
[3] GEBHARD, M.: (2009). Hie a chische P oduk ionsplanung bei Unsiche hei .
1. Au lage. Wiesbaden: Sp inge Gable . DOI: 10.1007/978-3-8349-8227-8
[4] GÜNTHER, H.-O.; TEMPELMEIER, H.: (2014). P oduk ion und Logis ik: Supply
Chain und Ope a ions Managemen . 11. Au lage. No de s ed : Books on Demand.
ISBN 978-3735721952.
[5] HAX, A. C.; MEAL, H. C.: (1975). Hie a chical In eg a ion o P oduc ion Planning and
Scheduling. In: M. A. Geisle (ed.) TIMS s udies in he managemen sciences. Vol. 1.
Logis ics. pp. 53–69. Ams e dam u.a.: No h-Holland.
[6] HERRMANN, F.: (2011). Ope a i e Planung in IT-Sys emen ü die
P oduk ionsplanung und -s eue ung: Wi kung, Auswahl und Eins ellhinweise on
Ve ah en und Pa ame e n. [Mi Online-Se ice] 1. Au lage. Wiesbaden: Vieweg +
Teubne .
[7] STADTLER, H.: (1988). Hie a chische P oduk ionsplanung bei losweise Fe igung.
Physica-Sch i en zu Be iebswi scha . Vol. 23. Heidelbe g: Sp inge .
[8] VITZTHUM, T.; HERRMANN, F.: (2017). E idence o he ele ance o mas e
p oduc ion Scheduling o hie a chical P oduc ion Planning. In: P oceedings o he 31 h
Eu opean Con e ence on Modelling and Simula ion, ECMS 2017. pp. 475–481. ISBN
978-0-9932440-4-9. DOI: 10.7148/2017-0475
[9] VOLLMANN, T. E.; BERRY, W. L.; WHYBARK, D. C.; JACOBS, F. R.: (2004).
Manu ac u ing planning and con ol o supply chain managemen . 5 h ed. McG aw-
Hill in e na ional edi ions. Bos on, Mass.: McG aw-Hill. ISBN 978-0072299908.
Tho s en Vi z hum, M.Sc.; P o . D . habil. Tho s en Claus; P o . D .-Ing. F ank He mann
162
MŮŽE BÝT AGREGOVANÉ PLÁNOVÁNÍ PRODUKCE MODIFIKOVÁNO TAK, ABY BYLO
TAK DOBRÉ JAKO PLÁNOVÁNÍ PROGRAMU HLAVNÍ PRODUKCE?
V om o příspě ku je pomocí případo é s udie zdů azněn ýznam pláno ání p og amu hla ní
p odukce p o hie a chické pláno ání p odukce. Je učiněn pokus o zlepšení ýsledku
ag ego aného celko ého pláno ání změnou jedno li ých pa ame ů ak, aby o odpo ídalo
ýsledku pláno ání p og amu hla ní p odukce. V ámci še ření se ak docílilo něk e ých
zlepšení jedno li ých si uací pláno ání, a šak obecné řešení se ješ ě nepodařilo naléz .
Z láš ě použi í hodného ak o u k edukci kapaci y e spojení se zohledněním p ůběhu ede
ke zlepšení ýsledku. Při pláno ání íce p oduk ů je šak ěžké nají hodný ak o p o
edukci kapaci y, p o ože en je od islý od pop á ky.
KANN DIE AGGREGIERTE GESAMTPLANUNG SO MODIFIZIERT WERDEN, DASS DAS
PLANUNGSERGEBNIS DEM DER HAUPTPRODUKTIONSPROGRAMMPLANUNG
ENTSPRICHT?
In diesem Bei ag wi d anhand eine Falls udie die Bedeu ung de
Haup p oduk ionsp og ammplanung (HPPLAN) ü die hie a chische P oduk ionsplanung
he ausgea bei e we den. Dazu wi d e such das E gebnis de agg egie en Gesam planung
(AGGRPLAN) du ch Ve ände ung einzelne Pa ama e so zu e besse n, dass es dem
E gebnis de HPPLAN en sp ich . Im Rahmen de Un e suchungen konn en dabei
Ve besse ungen ü einzelne Planungssi ua ionen e ziel we den, eine gene elle Lösung
konn e jedoch nich ge unden we den. Insbesonde e de Einsa z eines geeigne en
Kapazi ä s eduk ions ak o s in Ve bindung mi de Be ücksich igung de Du chlau zei üh
zu eine Ve besse ung de Lösung. Bei de Planung on meh als einem P oduk is alle dings
schwie ig einen geeigne en Kapazi ä s eduk ions ak o zu inden, da diese abhängig on de
Nach age is .
CZY ZAGREGOWANE PLANOWANIE PRODUKCJI MOŻE ZOSTAĆ ZMODYFIKOWANE
TAK, BY BYŁO TAK DOBRE JAK PLANOWANIE PROGRAMU GŁÓWNEJ PRODUKCJI?
W niniejszym op acowaniu na pods awie s udium p zypadku wskazano znaczenie planowania
p og amu głównej p odukcji w hie a chicznym planowaniu p odukcji. Podję o p óbę
pop awienia wyniku zag egowanego ogólnego planowania pop zez zmianę poszczególnych
pa ame ów, by odpowiadało o wynikowi planowania p og amu głównej p odukcji.
W amach p zep owadzonych badań osiągnię o pewne udoskonalenia poszczególnych
sy uacji planowania, jednak nie udało się na azie znaleźć kompleksowego ozwiązania.
Wynik pop awia w szczególności zas osowanie odpowiedniego czynnika do zmniejszenia
wielkości w połączeniu z uwzględnieniem p zebiegu. Podczas planowania kilku p oduk ów
udno jednak znaleźć odpowiedni czynnik do zmniejszenia wielkości, ponieważ zależny jes
on od popy u.