Continuing Bath and Body Works as a model, describe how you would develop a master schedule. Make sure you describe the relationship between the production plan and the customer demand forecast. The f
OR-N ot esJ E Beas le y
O R-N otes a re a serie s of int roduc tor y not es on t opics t ha t f all unde r t he br oad he adi ng of the fie ld of ope ra tions
r e se arc h ( OR). T hey w ere or igi na lly us ed by m e i n a n introduc tor y O R cour se I gi ve at I m pe ria l C olle ge . T hey a re
now ava ila bl e f or us e by a ny stude nts a nd t eache rs i nt ere ste d i n O R subj ect t o t he fol low ing c ondi tions .
A ful l l is t of the topi cs a va ila bl e i n O R-N otes c an be found he re .
M aste r p rod uction sch ed ule
I n tr od uction
T he m aste r pr oduc tion s che dul e ( als o c om monl y refe rre d t o a s t he M PS) i s e ffe ctive ly t he pl an t hat t he com pany
has de velope d for pr oduc tion, s ta ffing, i nventor y, e tc .
It ha s a s i nput a va rie ty of data , e .g. f orecast de mand, pr oduction c osts , i nve ntor y c osts , e tc a nd a s out put a
produc tion pl an de ta iling a mount s t o be produc ed, s ta ffing l eve ls , e tc f or each of a num ber of tim e pe riods .
Thi s pr oduc tion pl an:
ope ra te s a t a n aggr egat e leve l ( tha t i s i t doe s not usually go i nto gr eat de ta il a bout parts t o be used, e tc -
he nce t he na me aggr egat e pl anni ng ); a nd
is c os t dr iv en , t ha t i s i t a tte m pts t o m eet t he spe cif ie d r equi re m ent s a t m ini mum cos t.
T he ide a of a m aste r pr oduc tion s che dul e c an be st be illus tr a te d by m eans of an e xample.
E xam ple
I n our exa mple w e ha ve jus t a singl e pr oduc t be ing pr oduced.
P roduc tion t ake s pl ace e ach pe riod ( week) eithe r i n t he nor mal ( re gul ar) pr oduc tion s hift or in ove rtim e a ssoc ia te d
w ith t hat s hi ft. T here i s onl y one shi ft ( i.e . not opera ting a tw o/thr ee s hi ft s ys te m - s uc h a s w ith " round- the -c loc k"
wor king) .
Com plete d i te m s c an a ls o be "bought -in" from a subc ontra ctor (at a cos t) .
W e a re a llow ed t o hi re /f ir e w orke rs ( aga in a t a cos t) . B ackor ders a re a ls o a llow ed ( re call he re t ha t ba ckor ders a re
c us tom er or ders t ha t c annot be satis fie d i n the requi re d pe riod, but the cus tom er a llow s t he or der t o r em ain ope n to
be ful fille d i n a late r pe riod) . Lost s ale s a re not allow ed.
T he di agr am be low illus tr a te s t he situa tion a nd the type s of factor w ith w hich w e a re de aling gr aphi cally . The da ta f or the exa mple w e c ons ide r i s a s be low , w here w e ha ve show n the ini tia l da ta e nt ry s cre en f rom the
pa cka ge .
In t he above scre en w e ha ve chos en t he "G ene ra l L P M ode l" . T his i s t he m ost ge nera l of the opt ions allow ed by
the pa cka ge. L P s ta nds for line ar pr ogr am ming a nd i s a ge nera lis e d w ay of mode lling de cis ion pr oblem s. T o e ase
da ta e nt ry w e ha ve not cros se d t he "Part T im e A llow ed" box - if w e ha d then w e w oul d ha ve ha d the opt ion of
de aling w ith pa rt t im e e m ploye es. We ha ve als o not cros se d t he "Los t S ale s A llow ed" box - if w e ha d then w e w oul d ha ve allow ed l ost s ale s. I n
ge nera l a com pany m ay a llow los t s ale s be caus e t he com pany f inds tha t c us tom ers s im ply do not backor der - i.e . a
los t s ale i s a ut om atic i f t he pr oduc t i s not im medi ate ly a vaila bl e; or the com pany i s pr epa re d t o a llow los t s ale s a s i t
m ay be bette r t o a llow orders t o be los t t ha n t o a llow suc h or ders t o be com e ba ckor ders ( the re by i ncurring
ba ckor der c os ts ).
T he rem aini ng boxe s ha ve be en c ros se d a nd s o we c an de al w ith:
ove rtim e
hiring/ fir ing
s ubc ontra cting
ba ckor ders
In our exa mple a bove we ha ve jus t 4 pe riods (w eeks ) - thi s i s our tim e h or iz on ( pl anni ng pe riod) . W e a re de aling
w ith e m ploy ees w orking hour s in e ach w eek. T wo e mploye e hour s a re r equi re d t o pr oduc e one unit of each
pr oduc t a nd t he ini tia l num ber of em ploye es i s 10. A t t he sta rt of the pl anni ng pe riod t here i s no i nitia l i nve ntor y
(nor are t he re a ny ba ckor ders ).
T he da ta f or our exa mple e nt ere d i nto t he pa cka ge in t he light of the choi ces m ade at t he ini tia l s cre en i s a s be low :
The m eani ng of each of the se l ine s of da ta i s gi ven be low :
For ecas t D em an d - thi s i s t he for ecast de mand f or the pr oduc t i n e ach of our 4 pe riods (w eeks ).
I n itial N um be r of Employ ee - thi s i s t he ini tia l num ber of em ploye es i n e ach w eek, he re j us t t he 10 e mploye es w e
have cur re nt ly .
R egu lar Tim e C apac ity i n H ou r pe r E mploy ee - thi s i s how many r egul ar hour s e ach e mploye e w orks pe r w eek,
he re 35 hour s
Regu lar Tim e C ost pe r H ou r - thi s i s t he cos t pe r hour of regul ar t im e w orke d, he re £15 Unde rtim e C ost pe r H ou r - thi s i s t he cos t pe r hour of not using a worke r t o t heir f ul l r egul ar c apa city , he re z ero
O vertim e C apac ity i n H ou r pe r E mploy ee - thi s i s t he m axi mum num ber of hour s e ach e mploye e c an w ork i n
ove rtim e pe r w eek, he re 10 hour s
Overtim e C ost pe r H ou r - t hi s i s t he cos t pe r hour of ove rtim e, he re £25
H ir in g C ost pe r E mploy ee - thi s i s t he cos t of hiring one em ploye e, he re £500
D is m is sal C ost pe r E mploy ee - thi s i s t he cos t of dism is sing ( fir ing) one em ploye e, he re £2000
M axi mum /M in im um N um be r of Employ ee A llow ed - he re w e c an s et l im its on t he m axi mum and m ini mum
num ber of em ploye es, he re M signi fie s t he re i s no l im it on t he m axi mum num ber a nd t he m ini mum num ber i s 8. I n
genera l t he re m ay be an uppe r l im it on t he num ber of em ploye es due to phys ic al c apa city c ons tr a int s.
In itial Inven tor y ( +) or Backor der ( -) - the ini tia l i nve ntor y a vaila bl e or ba ckor ders out sta ndi ng, he re z ero
M axi mum /M in im um E ndi ng I nven tor y - he re w e c an s et l im its on t he m axi mum and m ini mum num ber of
pr oduc t uni ts i n s toc k a t t he end of each w eek, he re M signi fie s t he re i s no l im it on t he m axi mum num ber a nd t he
mini mum num ber i s z ero. I n ge nera l t he re m ay be an uppe r l im it be caus e w e ha ve a lim ite d s pace i n w hich t o s tor e
stoc k. T he m ini mum num ber c or re sponds to s afe ty s toc k t hat m ay be kept in c ase of unf orese en de mand.
U nit I nven tor y H olding C ost - thi s i s t he cos t of hol ding one unit i n s toc k a t t he end of each pe riod, he re £3
M axi mum S ubc on tr ac tin g A llow ed - thi s i s t he m axi mum num ber of produc t uni ts w e a re a llow ed t o buy i n from
the ext erna l s ubc ontra ctor , he re t he re i s no l im it on t he am ount tha t m ay be bought in. I n ge nera l t he re m ay be a
lim it on t he tot al a m ount the subc ontra ctor can s uppl y to us each pe riod.
U nit S ubc on tr ac tin g C ost - thi s i s t he cos t of each uni t bought from the ext erna l s ubc ontra ctor , he re £60
M axi mum B ackor der A llow ed - thi s i s t he m axi mum num ber of ba ckor ders a llow ed a t t he end of each pe riod,
he re t he re i s no l im it on t he num ber of ba ckor ders t ha t c an be held a t t he end of each pe riod.
U nit B ackor der C ost - t hi s i s t he cos t of each ba ckor der out sta ndi ng a t t he end of each pe riod, he re t he M signi fie s
tha t e ach ba ckor der i s ve ry e xpe nsive . T he effe ct of M he re w ill be to e nsure t ha t ( if a t a ll pos sibl e) ba ckor ders w ill
be avoi ded.
Oth er U nit P rodu ction Cost - thi s i s t he cos t of produc ing one unit of the pr oduc t t ha t i s not alr e ady a ccount ed f or
by e mploye e c os ts - he re z ero
C apac ity R equ ir e m en t i n H ou r pe r U nit - thi s i s t he num ber of em ploye e hour s t ha t a re r equi re d t o pr oduc e one
uni t of the pr oduc t, he re 2 hour s
In or der t o e ase unde rs ta ndi ng of the pr obl em m ost of the above data i te m s t ake the sam e va lue in e ach a nd e very
pe riod ( week) . H oweve r i t w oul d be perfe ctly pos sibl e f or the m to ha ve di ffe re nt va lue s i n e ach w eek.
C ons ide r f or a m om ent thi s e xa mple a s w e ha ve de fine d i t s o f ar. W e ha ve a singl e pr oduc t, a re pl anni ng ove r 4
tim e pe riods , ha ve regul ar t im e a nd ove rtim e, c an buy f rom an e xterna l s ubc ontra ctor , a nd a re a llow ed t o hi re a nd
fir e e m ploye es. S om e of the de cis ions we m ust m ake are s how n below : Period 1 2 3 4
Amount to produce using regular time ? ? ? ?
Amount to produce using overtime ? ? ? ?
Amount to purchase from subcontractor ? ? ? ?
Number of backorders ? ? ? ?
Number to hire ? ? ? ?
Number to fire ? ? ? ?
Y ou c an s ee f rom thi s m atr ix t hat t he re a re a lr e ady 24 de cis ions which w e ha ve to m ake . F or suc h pr oblem s
de cis ion m odels ( suc h a s t he de cis ion m odel us ed w ithi n t he packa ge ) a re m uch be tte r a t de cis ion- maki ng t han
peopl e. M oreove r s uc h m odels c an gua ra nt ee t o m ake de cis ions at m in im um cos t , som ethi ng pe ople c annot do.
Note he re t ha t e ve n t he (che ap) pa cka ge us ed he re i s e xt re m ely fle xibl e in t erm s of the situa tions it c an c ons ide r.
S ol ution
T he sol ution t o the pr obl em is s how n below :
It c an be seen t hat w e i m medi ate ly hi re m ore e m ploye es, a nd t hat t he se a re e m ploye d throughout the pl anni ng
period of 4 weeks . N ote t ha t t he num ber hi re d i s 10.57 - i.e . i t i nc lude s a fra ction of an e mploye e. T his of te n
ha ppe ns in a ggr ega te pl anni ng a nd can us ually be ignor ed ( sim ply r ound t o the ne are st a ppr opria te w hol e num ber).
R efle ct t ha t w e a re pr oduc ing a plan f or pr oduc tion ove r a 4 w eek pe riod. I t i s unl ike ly t hat our demand f orecasts
w ill be com plete ly a ccur ate a nd he nce t hi s r oundi ng need not conc ern us undul y.
W ith 10+ 10.57 = 20.57 e mploye es w orking 35 hour s a w eek w e ha ve a regul ar t im e c apa city of 20.57x35 = 720
em ploye e hour s ( appr oximate ly) and a t 2 hour s pe r uni t pr oduc ed t his c or re sponds to a regul ar t im e pr oduc tion of
360 uni ts - pr ecis e ly a s a bove , i.e. ove r t he 4 w eek pl anni ng pe riod w e a re pl anni ng t o work a ll of our em ploye es
to t heir f ul l r egul ar t im e c apa city . A s c an be seen a bove we a re pl anni ng no ove rtim e or subc ontra cting.
N ote t he bui ld i nto i nve ntor y t hat oc cur s i n va rious periods . As i nve ntor y c osts us mone y let us be cle ar a bout why
the above (the m ini mum cos t s ol ution) invol ves bui ld i nto i nve ntor y. I t i s t o m eet f ut ur e de mand. D em and f or the
pr oduc t i nc re ase s ove r t he 4 w eek pl anni ng pe riod ( from 250 t o 450 uni ts ) a nd t he pa cka ge ha s de te rm ine d t hat t he
m os t c os t- e ffe ctive w ay t o e nsure t ha t t hi s de mand i s m et i s t o bui ld i nto i nve ntor y i n e arlie r pe riods . Note t ha t a n alte rna tive str a te gy t o meet t hi s i nc re ase d de mand w ould be to buy f rom the subc ontra ctor , w ere t hi s c he ape r t he
pa cka ge w oul d ha ve adopt ed t hat s tr a te gy .
The cos ts a ssoc ia te d w ith t he pa cka ge sol ution c an be seen be low :
The pr oduc tion a nd employm ent str a te gy gi ven a bove is t he min im um cos t str a te gy s inc e t he pa cka ge us es line ar
progr amming t o c alc ul ate a sche dul e f or pr oduc tion a nd sta ffing t hat m eets t he for ecast de mand a nd als o s atis fie s
the ot her c ons tr a int s t ha t w e pl ace upon t he pr obl em at m ini mum cos t. I t w oul d be im pos sibl e t o f ind t he m ini mum
cos t s ol ution m anua lly - cons ide r t he sol ution s how n with a n incre ase i n e mploym ent and w ith va ryi ng a mount s
built i nt o i nve ntor y - coul d that e ve r be produc ed by a pers on i n the tim e ( fra ction of a second) it t ake s t he pa cka ge
to pr oduc e i t?
L eve l an d c has e s tr at egi es
W e m ay be int ere ste d i n a sol ution t hat c ons is ts of a fixe d num ber of worke rs ( a level s tr at egy ). T his c an be seen
be low where w e ha ve fixe d t he m axi mum and m ini mum num ber of em ploye es t o 10 ( the cur re nt num ber) i n e ach
and e very pe riod.
T he sol ution f or thi s l eve l s tr a te gy i s s how n below . It c an be seen t hat w ith t his s ol ution w e us e bot h ove rtim e a nd s ubcontra cting but do not build i nto i nve ntor y. T he
tot al c os t of 63,400 i s m uch m ore t ha n t he pr evi ous (non- le ve l) s tr a te gy w hich ha d a tot al c os t of 49475.71
If w e c ha nge the hi re /f ir e c os ts t o z ero a nd r ese t t he lim its on t he m axi mum /m ini mum num ber of em ploye es t he n
we w ill pr oduc e a c has e s tr at egy ( ra m p w orkforce up/ dow n as r equi re d) . T his s ol ution c an be seen be low . Bac kor derin g
In our origi na l s itua tion c onside re d a bove , with c osts f or hi ring a nd fir ing, w e w ere pr ohi biting ba ckor ders by
m aki ng t hem ve ry e xpe nsive . S uppos e now tha t ba ckor ders c os t us £1 pe r pe riod ( week) . T he effe ct of thi s on t he
sol ution i s s how n below . It c an be seen t hat w e pr oduc e not hing - the che ape st s ol ution i s s im ply t o a llow backor ders t o bui ld up ove r t he
pl anni ng pe riod. T his s eem s s illy a nd f or thi s r eason i t i s us ual t o i nsis t t ha t t he re a re no ba ckor ders out sta ndi ng a t
the end of the pl anni ng pe riod. T his i s a n a ssum ption t hat i s, by c onvention, a pplie d a nd i s a reasona ble a ssum ption
w he n pl anni ng ove r a rela tive ly l ong t im e pe riod. M oreove r unl ess t hi s i s a ssum ed i t c an ha ppen that t he be st t hi ng
for the com pany t o do ove r t he pl anni ng pe riod i s s im ply t o a llow backor ders t o bui ld up ( as a bove ).
T o e nsure t ha t t he re a re no ba ckor ders out sta ndi ng a t t he end of the pl anni ng pe riod w e e nt er a zero f or "M axi mum
Backor ders A llow ed" in t he last pe riod ( week 4) , as be low .
The sol ution i s which i s e ffe ctive ly t he sam e a s t he ini tia l s ol ution w e c ons ide re d. H oweve r t o i llus tr a te t ha t ba ckor ders c an pl ay a
rol e s uppos e t ha t w e:
ha ve a leve l s tr a te gy w ith e xactly 10 e mploye es i n e ach a nd e very pe riod ( week) ; a nd
re str ic t t he subc ontra ctor capa city i n e ach a nd e very pe riod
the n t he input is a s be low :
and t he out put is: whe re ba ckor ders do oc cur sinc e pr oduc tion c apa city ( bot h regul ar t im e a nd ove rtim e) t oge the r w ith s ubc ontra ctor
c apa city i s i ns uffic ie nt to m et de mand i n som e pe riods .
Rollin g h oriz on
In pr actic e w e w oul d pr obably de al w ith t he situa tion de sc ribe d a bove on a "rol ling hor iz on" basis i n t hat w e
woul d ge t a n i nitia l pr oduc tion pl an ba se d on c urre nt da ta a nd t hen, a fte r one tim e pe riod ( sa y) , w e w oul d upda te
our probl em /da ta a nd r esol ve to ge t a revi se d pr oduc tion pl an. I n ot her w ords eve n t hough w e pl an f or a spe cif ic
tim e hor iz on ( here 4 w eeks ) w e w oul d onl y ever i m plem ent the pl an f or the fir s t w eek, s o that w e a re a lw ays
adj us ting our 4 week pl an t o take account of fut ur e c ondi tions as our view of the fut ur e c ha nge s. W e i llus tr a te t hi s
be low .
Period 1 2 3 4 5 6 7 P = plan
P P P P D = do (follow) the plan in a period
D P P P P
D P P P P
D P P P P
