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Managing Economies of Scale in
a Supply Chain: Cycle InventoryChapter 11
GROUP Members:Avinash Kumar MahtoAbhishek AnandAnnant Singh Raunkali Jay Shah
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Learning Objectives
1. alance the appropriate costs to choosethe optimal lot si!e an" cycle inventory ina supply chain.
#. $n"erstan" the impact of %uantity
"iscounts on lot si!e an" cycle inventory.&. 'evise appropriate "iscounting schemes
for a supply chain.(. $n"erstan" the impact of tra"e
promotions on lot si!e an" cycle inventory.). I"entify managerial levers that re"uce lot
si!e an" cycle inventory in a supply chain*ithout increasing cost.
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+ole of Cycle Inventoryin a Supply Chain
• Lot or batch size is the %uantity that a stage of asupply chain either pro"uces or purchases at atime
•
Cycle inventory is the average inventory in asupply chain "ue to either pro"uction orpurchases in lot si!es that are larger than those"eman"e" by the customer
,: ,uantity in a lot or batch si!e': 'eman" per unit time
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+ole of Cycle Inventoryin a Supply Chain
Cycle inventory = lot size2
= Q2
Average flow time =average inventory
average flow rate
-verage o*time resultingfrom cycleinventory
= cycle inventorydemand
= Q2D
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+ole of Cycle Inventoryin a Supply Chain
• Average price paid per unit purchased isa /ey cost in the lot0si!ing "ecision
Material cost C •
Fixed ordering cost inclu"es all coststhat "o not vary *ith the si!e of theor"er but are incurre" each time anor"er is place"
2i3e" or"ering cost S • Holding cost is the cost of carrying one
unit in inventory for a speci4e" perio" oftime
5ol"ing cost H hC
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+ole of Cycle Inventoryin a Supply Chain
Economies of scale e3ploite" inthree typical situations
1. - 43e" cost is incurre" each time anor"er is place" or pro"uce"
#. 6he supplier o7ers price "iscountsbase" on the %uantity purchase" per
lot
&. 6he supplier o7ers short0term price"iscounts or hol"s tra"e promotions
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Estimating Cycle Inventory+elate" Costs in 8ractice
Inventory 5ol"ing Cost
◦ Obsolescence cost
◦ 5an"ling cost
◦
Occupancy cost◦ Miscellaneous costs 6heft9 security9 "amage9 ta39 insurance
Or"ering Cost
◦ uyer time
◦ 6ransportation costs◦ +eceiving costs
◦ Other costs
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Economies of Scaleto E3ploit 2i3e" Costs
• Lot si!ing for a single pro"uct EO,; D -nnual "eman" of the pro"uctS = 2i3e" cost incurre" per or"erC = Cost per unit H = 5ol"ing cost per year as afraction of pro"uct cost
•
asic assumptions –'eman" is stea"y at D units per unit time –
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Lot Si!ing for a Single8ro"uct
Annual material cost =CD
Number of orders per year = DQ
Annual ordering cost = DQ
÷S
Annual holding cost = Q
2
÷H =
Q
2
÷hC
Total annual cost TC =CD+ DQ
÷S+
Q
2
÷hC
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Lot Si!ing for a Single8ro"uct
2igure 110#
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Lot Si!ing for a Single8ro"uct
!ptimal lot size Q" =
2DS
hC
• 6he econoic order !uantity "#Q;
n" = DQ "
= DhC2S
• 6he optimal or"ering fre%uency
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8ro"uction Lot Si!ing
6he entire lot "oes not arrive at the sametime
8ro"uction occurs at a speci4e" rate P
Inventory buil"s up at a rate of P = D
Q$ = 2DS#$– D % $&hC
D
Q$
÷S
-nnual setup cost
#$– D % $& Q$
2
÷hC
-nnual hol"ing cost
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-ggregating Multiple 8ro"uctsin a Single Or"er
Savings in transportation costs
◦ +e"uces 43e" cost for each pro"uct
◦ Lot si!e for each pro"uct can be re"uce"◦ Cycle inventory is re"uce"
Single "elivery from multiple
suppliers or single truc/ "elivering tomultiple retailers
+eceiving an" loa"ing costs re"uce"
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Lot Si!ing *ith Multiple8ro"ucts or Customers
• Or"ering9 transportation9 an"receiving costs gro* *ith thevariety of pro"ucts or pic/up points
• Lot si!es an" or"ering policy thatminimi!e total cost
Di: -nnual "eman" for pro"uct i
S : Or"er cost incurre" each time an or"er isplace"9 in"epen"ent of the variety ofpro"ucts in the or"er
si: -""itional or"er cost incurre" if pro"uct i
is inclu"e" in the or"er
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Multiple 8ro"ucts Or"ere" an"'elivere" In"epen"ently
'eman" D L 1#9>>>?yr9 D M 19#>>?yr9 D H
1#>?yr
Common or"er costS @(9>>>
8ro"uct0speci4c or"er cost s L = @19>>>9 s M @19>>>9 s H = @19>>>
5ol"ing costh = >.#
$nit costC L = @)>>9 C M = @)>>9 C H = @)>>
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Multiple 8ro"ucts Or"ere" an"'elivere" In"epen"ently
Litero Medro !eavyro
'eman" per year 1#9>>> 19#>> 1#>
2i3e" cost?or"er @)9>>> @)9>>> @)9>>>
Optimal or"er si!e 19>A) &(B 11>
Cycle inventory )( 1D& ))
-nnual hol"ingcost
@)(9DD# @1D9 @)9(DD
Or"er fre%uency 11.>?year &.)?year 1.1?year
-nnual or"eringcost
@)(9DD# @1D9 @)9(DD
-verage o* time #.( *ee/s D.) *ee/s #&.D *ee/s
-nnual cost @1>A9)(( @&(9B(# @1>9A)( 6able 1101
• 6otal annual cost @1))91(>
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Lots Or"ere" an" 'elivere" ointly
Annual holding cost = D
LhC
L
2n+ D
%hC
%
2n+ D
HhC
H
2n
S" = S+ sL + s
% + s
H Annual order cost = S" n
Total annual cost = D
LhC
L
2n+ D
%hC
%
2n+ D
HhC
H
2n+ S " n
n" = D
LhC
L + D
%hC
% + D
HhC
H
2S "n" =
DihC
ii=$
& ∑2S "
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8ro"ucts Or"ere" an" 'elivere" ointly
S" = S+ s A
+ s' + s
C = '())) per order
n" = $2))) ×$)) +$2))×$)) +$2) ×$))2 × ()))
= *+(,
-nnual or"er cost A.D) 3 D9>>> @B9#)>
-nnual or"eringan" hol"ing cost @B19)1# F @B91)1 F @B1) F @B9#)>
@1&B9)#
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-ggregation *ith CapacityConstraint
• G.G. Hrainger e3ample
'eman" per pro"uct9 Di = 1>9>>>
5ol"ing cost9 h = >.#
$nit cost per pro"uct9 C i = @)>
Common or"er cost9 S = @)>>
Supplier0speci4c or"er cost9 si = @1>>
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-ggregation *ith CapacityConstraint
S" = S+ s$ + s
2 + s
- + s
. = '*)) per order
n" = D$hC$i=$.
∑ 2S " = . ×$))))× )+2× ,)2 × *)) = $.+*$
Annual order cost = $.+*$× *)).
= '--,.
= hC
iQ
2= )+2× ,) × /($
2= '--,,-nnual hol"ing
cost persupplier
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-ggregation *ith CapacityConstraint
6otal re%uire" capacity per truc/ ( 3 BD1
#9B( units
6ruc/ capacity #9)>> units
Or"er %uantity from each supplier #9)>>?(
B#)
Or"er fre%uency increase" to 1>9>>>?B#) 1B
-nnual or"er cost per supplier increases to
@&9B>>
-nnual hol"ing cost per supplier "ecreases to
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Lots Or"ere" an" 'elivere" ointly for a Selecte" Subset
Ste ": I"entify the most fre%uentlyor"ere" pro"uct assuming eachpro"uct is or"ere" in"epen"ently
ni =
hCiDi
2#S+ si&
Ste #: 2or all pro"ucts i ( i9 evaluatethe or"ering fre%uency
ni =
hCiDi
2si
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Lots Or"ere" an" 'elivere" ointly for a Selecte" Subset
Ste $: 2or all i ( i9 evaluate thefre%uency of pro"uct i relative to themost fre%uently or"ere" pro"uct i
to be mi i = n % n
i
Ste %: +ecalculate the or"ering
fre%uency of the most fre%uentlyor"ere" pro"uct i to be n
n= hC
iiD
i=$
l∑2 S+ s
i%
i
i=$
l∑( )
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Lots Or"ere" an" 'elivere" ointly for a Selecte" Subset
Ste &: Evaluate an or"er fre%uency of ni
= n ) mi an" the total cost of such an
or"ering policy
TC = nS+ nisi
i=$
l
∑ + Di2n
i
÷hC
$
i−$
l
∑
Tailored aggregation = higher0"eman"pro"ucts or"ere" more fre%uently an"lo*er0"eman" pro"ucts or"ere" less
fre%uently
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Or"ere" an" 'elivere" ointly =2re%uency Jaries by Or"er
-pplying Step 1
nL =
hCLD
L
2#S+ sL&= $$+)
n%
= hC
%D%
2#S+ s%
&= -+,
nL =
hCHD
H
2#S+ sH
&= $+$
n = $$+)
6hus
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Or"ere" an" 'elivere" ointly =2re%uency Jaries by Or"er
-pplying Step #
n% =
hC%D%
2s% = (+( and nH =
hCHD
H
2sH = 2+.
• -pplying Step &
%
= n
n%
= $$+)
(+(
= 2 and H =
n
nH
= $$+)
2+.
= ,
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Or"ere" an" 'elivere" ointly =2re%uency Jaries by Or"er
Litero Medro !eavyro
'eman" per year D; 1#9>>> 19#>> 1#>
Or"er fre%uency nK; 11.(D?year ).D(?year #.#A?yearOptimal or"er si!e D?nK;
19>(B #>A )#
Cycle inventory )#& 1>(.) #B
-nnual hol"ing cost @)#9&>D @1>9(B1 @#9B1)
-verage o* time #.#D *ee/s (.)& *ee/s 11.&)*ee/s 6able 110&
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Or"ere" an" 'elivere" ointly =2re%uency Jaries by Or"er
-pplying Step (
n= $$+.(
• -pplying Step )
nL = $$+.( % yr n
% = $$+.( % 2 = ,+(. % yr
nH
= $$+.( % , = 2+2* % yr
-nnual or"er cost 6otal annual cost
nS+nLsL +n
%s%
+ nHsH = '/,-0-+, @1&>9DBD
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Economies of Scale toE3ploit ,uantity 'iscounts
Lot size*based discount + "iscountsbase" on %uantity or"ere" in a singlelot
,olue based discount = "iscount isbase" on total %uantity purchase"over a given perio"
6*o common schemes
◦ -ll0unit %uantity "iscounts
◦ Marginal unit %uantity "iscount or multi0
bloc/ tari7s
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,uantity 'iscounts
6*o basic %uestions
1. Ghat is the optimal purchasing "ecisionfor a buyer see/ing to ma3imi!e pro4ts
5o* "oes this "ecision a7ect the supplychain in terms of lot si!es9 cycleinventories9 an" o* times
#. $n"er *hat con"itions shoul" a supplier
o7er %uantity "iscounts Ghat areappropriate pricing sche"ules that asupplier see/ing to ma3imi!e pro4tsshoul" o7er
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-ll0$nit ,uantity 'iscounts
8ricing sche"ule has speci4e" %uantitybrea/ points q>9 q19 9 qr 9 *here q> >
If an or"er is place" that is at least as
large as qi but smaller than qiF19 then eachunit has an average unit cost of C i
$nit cost generally "ecreases as the
%uantity increases9 i.e.9 C > N C 1 N N C r Objective is to "eci"e on a lot si!e that
*ill minimi!e the sum of material9 or"er9an" hol"ing costs
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-ll0$nit ,uantity 'iscounts
2igure 110&
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-ll0$nit ,uantity 'iscounts
Ste ": Evaluate the optimal lot si!e foreach price C i9> i r as follo*s
Qi = 2DS
hCi
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-ll0$nit ,uantity 'iscounts
Ste #: Ge ne3t select the or"er %uantityQi for each price C i
!i ≤Q
i < !
i+$
Qi < !iQi ≥ !
i+$
1.
#.
&.
• Case & can be ignore" as it is consi"ere" forQiF1
• 2or Case 1 if 9 then set Qi Qi
• If 9 then a "iscount is not possible
• Set Qi qi to %ualify for the "iscounte"
!i ≤Q
i < !
i+$
Qi < !
i
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-ll0$nit ,uantity 'iscounts
Ste $: Calculate the total annual cost ofor"ering Qi units
Total annual cost TCi = D
Qi
"
÷÷S+
Qi
"
2
÷÷hCi + DCi
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-ll0$nit ,uantity 'iscounts
Ste %: Select Qi *ith the lo*est total
cost TC i
C" = $D
DCr + DS
!r
+ h2!r Cr – 2hDSC
r
• Cuto7 price
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-ll0$nit ,uantity 'iscountE3ample
Order 'uantity Unit Pri(e
>=(9AAA @&.>>
)9>>>=A9AAA @#.AB
1>9>>> or more @#.A#
q> >9 q1 )9>>>9 q# 1>9>>>
C > @&.>>9 C 1 @#.AB9 C # @#.A# D = 1#>9>>>?year9 S = @1>>?lot9 h = >.#
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-ll0$nit ,uantity 'iscountE3ample
Step 1
Q) = 2DS
hC)
= /-2.1 Q$ = 2DS
hC$
= /-/(1 Q2 = 2DS
hC2
= /.$)
Step #
Ignore i = > because Q> B9( N q1 )9>>>2or i = 19 #
Q$
" =Q$ = /-/(1 Q
2
" = !2 = $))))
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-ll0$nit ,uantity 'iscountE3ample
Step &
TC$ = D
Q$"
÷÷S+ Q
$
"
2
÷÷hC$ + DC$ = '-,0*/*1 TC2 = '-,.,2)
Lo*est total cost is for i #
Or"er bottles per lot at @#.A# per
bottle
Q2
" = $))))
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Marginal $nit ,uantity 'iscounts
• %ulti*bloc& tari-s + the arginalcost of a unit that "ecreases at abrea/point
2or each value of i9 > i r 9 let V i be the
cost of or"ering qi units
, i =C
)#!
$ – !
)& +C
$#!
2 – !
$& + ++++C
i –$#!
i – !
i –$&
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Marginal $nit ,uantity 'iscounts
2igure 110(
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Marginal $nit ,uantity 'iscounts
Material cost of each or"er Q is V i F Q =
qi;C i
Annual order cost = DQ
÷S
Annual holding cost = , i + #Q – !
i&C
i h% 2
Annual materials cost = DQ, i + #Q – !
i&C
i
= DQ
÷S+ , i + #Q – !i &C i h % 2
+ DQ, i + #Q – !
i&C
i
6otal annualcost
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Marginal $nit ,uantity 'iscounts
Ste ": Evaluate the optimal lot si!e foreach price C i
!ptimal lot size for Ci is Q
i =
2D#S+, i – !
iCi&
hCi
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Marginal $nit ,uantity 'iscounts
Ste #: Select the or"er %uantity Qi* for
each price C i
f !i ≤Qi ≤ !i+$ then set Qi"
=Qif Q
i < !
i then set Q
i
" = !i
f Qi > !
i+$ then set Qi" = !
i+$
1.#.
&.
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Marginal $nit ,uantity 'iscounts
Ste $: Calculate the total annual costof or"ering Qi*
TCi = D
Qi
"
÷÷S+ , i + #Qi
" – !i&C
i
h % 2 +
D
Qi
" ,
i + #Q
i
" – !i&C
i
Ste %: Select the or"er si!e Qi* *iththe lo*est total cost TC i
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Marginal $nit ,uantity 'iscountE3ample
Original "ata no* a marginal "iscount
Order 'uantity Unit Pri(e
>=(9AAA @&.>>
)9>>>=A9AAA @#.AB
1>9>>> or more @#.A#
q> >9 q1 )9>>>9 q# 1>9>>>
C > @&.>>9 C 1 @#.AB9 C # @#.A#
D = 1#>9>>>?year9 S = @1>>?lot9 h = >.#
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Marginal $nit ,uantity 'iscountE3ample
, ) = )1 ,
$ = -#,))) – )& = '$,)))
, 2 = -#,))) – )& + 2+*/#$)))) – ,)))& = '2*0))
Ste "
Q) =
2D#S+, ) – !
)C
)&
hC)
= /-2.
Q$ =2D#S+,
$
– !$
C$
&
hC$
= $$)20
Q2 =
2D#S+, 2 – !
2C
2&
hC2
= $/*/$
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Marginal $nit ,uantity 'iscountE3ample
Ste# Q)
" = !$ = ,))) because Q
) = /-2. > ,)))
Q$
" = !2 = $))))1 Q
2 = Q
2 = $/*/$
Ste$TC
) = D
Q)
"
÷÷S+ , ) + #Q)
" – !)&C
)
h% 2 +
D
Q)
" ,
) + #Q
)
" – !)&C
)
= '-/-*))
TC2 = D
Q2
"
÷÷S+ , 2 + #Q2
" – !2&C
2
h% 2 +
D
Q2
" ,
2 + #Q
2
" – !2&C
2
= '-/)-/,
TC$ = DQ
$
"
÷÷S+ , $ + #Q$
" – !$&C $ h% 2 + DQ$
" , $ + #Q$" – !$&C$ = '-/$(0)
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Ghy ,uantity 'iscounts
,uantity "iscounts can increasethe supply chain surplus for the
follo*ing t*o main reasons1. Improve" coor"ination to increase
total supply chain pro4ts
#. E3traction of surplus through price
"iscrimination
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,uantity 'iscounts forCommo"ity 8ro"ucts
D = 1#>9>>> bottles?year9 S R @1>>9 h R >.#9 C R
@&
S M @#)>9 h M >.#9 C M @#
Q. =
2DS.
h.C
. =2×$2)))) ×$))
)+2× - = /-2.
Annual cost for 3! = D
Q.
÷S
. + Q
.
2
÷h
.C
. = '-(*,
Annual cost for manufacturer = DQ
.
÷S
% + Q.
2
÷h
%C%
= '/))*
-nnual supply chaincost manufacturer F
'O;
@B9>>A F @&9DA) @A9>(
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Locally Optimal Lot Si!es
= D
Q
÷S. +
Q
2
÷h.C. +
D
Q
÷S% +
Q
2
÷h%C%
-nnual cost for'O an"manufacturer
Q" =2D#S
. +S
%&
h.C
. +h%C% = *$/,
Annual cost for 3! = DQ "
÷S. +
Q "
2
÷h.C. = '.),*
Annual cost for manufacturer = DQ "
÷S% +
Q "2
÷h%C% = ',$)/
-nnual supply chaincost manufacturer F
'O;
@)91>B F @(9>)A @A91B)
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'esigning a Suitable Lot Si!e0ase" ,uantity 'iscount
'esign a suitable %uantity "iscount thatgets 'O to or"er in lots of A91B) units*hen its aims to minimi!e only its o*n
total costsManufacturer nee"s to o7er an
incentive of at least @#B( per year to'O in terms of "ecrease" material cost
if 'O or"ers in lots of A91B) units-ppropriate %uantity "iscount is @& if
'O or"ers in lots smaller than A91B)
units an" @#.AAD for or"ers of A91B) or
, i i h
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,uantity 'iscounts Ghen2irm 5as Mar/et 8o*er
'eman" curve &B>9>>> = B>9>>> p
8ro"uction cost C M = @# per bottle
$ro/ . = # p –C
.-/)))) – /)))) p&
$ro/ % = #C. –C% -/)))) – /)))) p&
p to ma3imi!e Prof R p= - +C
.
2
$ro/ %
= #C. –C
%& -/)))) – /)))) - + C.
2
÷
= #C
. – 2$0)))) – -))))C
.&
, i 'i Gh
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,uantity 'iscounts Ghen2irm 5as Mar/et 8o*er
C R = @( per bottle9 p @) per bottle
6otal mar/et "eman" &B>9>>> = B>9>>> p = B>9>>>
Prof R ) = (;&B>9>>> = B>9>>> P ); @B>9>>>
Prof M = ( = #;&B>9>>> = B>9>>> P );
@1#>9>>>
Prof SC p = C M ;&B>9>>> = B>9>>> p;
Coor"inate" retail price p= - +C%
2 = - +2
2 = '.
Prof SC @( = @#; 3 1#>9>>> @#(>9>>>
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6*o08art 6ari7
Manufacturer charges its entirepro4t as an up0front franchise fee ff
Sells to the retailer at cost
+etail pricing "ecision is base" onma3imi!ing its pro4ts
E7ectively ma3imi!es thecoor"inate" supply chain pro4t
J l " , tit
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Jolume0ase" ,uantity'iscounts
'esign a volume0base" "iscountscheme that gets the retailer to
purchase an" sell the %uantity sol"*hen the t*o stages coor"inatetheir actions
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Lessons from 'iscounting Schemes
,uantity "iscounts play a role in supply chaincoor"ination an" improve" supply chainpro4ts
'iscount schemes that are optimal are volumebase" an" not lot si!e base" unless themanufacturer has large 43e" costs associate"*ith each lot
Even in the presence of large 43e" costs for
the manufacturer9 a t*o0part tari7 or volume0base" "iscount9 *ith the manufacturerpassing on some of the 43e" cost to theretailer9 optimally coor"inates the supply
chain an" ma3imi!es pro4ts
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Lessons from 'iscounting Schemes
Lot si!e=base" "iscounts ten" to raise thecycle inventory in the supply chain
Jolume0base" "iscounts are compatible *ithsmall lots that re"uce cycle inventory
+etailers *ill ten" to increase the si!e of thelot to*ar" the en" of the evaluation perio"9the hoc&ey stic& phenoenon
Gith multiple retailers *ith "i7erent "eman"curves
optimal "iscount continues to bevolume base" *ith the average price charge"to the retailers "ecreasing as the rate ofpurchase increases
8 i 'i i i ti t M i i
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8rice 'iscrimination to Ma3imi!eSupplier 8ro4ts
2irm charges "i7erential prices toma3imi!e pro4ts
Setting a 43e" price for all units "oes not
ma3imi!e pro4ts for the manufacturerManufacturer can obtain ma3imum pro4ts
by pricing each unit "i7erently base" oncustomersQ marginal evaluation at each
%uantity,uantity "iscounts are one mechanism for
price "iscrimination because customers
pay "i7erent prices base" on the %uantity
Sh t 6 'i ti
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Short06erm 'iscounting: 6ra"e 8romotions
6ra"e promotions are price"iscounts for a limite" perio" oftime
Rey goals1. In"uce retailers to use price
"iscounts9 "isplays9 or a"vertising to
spur sales#. Shift inventory from the
manufacturer to the retailer an" thecustomer
&. 'efen" a bran" against competition
Sh t 6 'i ti
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Short06erm 'iscounting: 6ra"e 8romotions
Impact on the behavior of theretailer an" supply chainperformance
+etailer has t*o primary options1. 8ass through some or all of the
promotion to customers to spur sales
#. 8ass through very little of thepromotion to customers but purchasein greater %uantity "uring thepromotion perio" to e3ploit the
temporary re"uction in price /or0ard
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2or*ar" uying Inventory 8ro4le
2igure 110)
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2or*ar" uy
Costs to be consi"ere" = materialcost9 hol"ing cost9 an" or"er cost
6hree assumptions
1. 6he "iscount is o7ere" once9 *ith nofuture "iscounts
#. 6he retailer ta/es no action to
inuence customer "eman"&. -naly!e a perio" over *hich the
"eman" is an integer multiple of Q1
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2or*ar" uy
Optimal or"er %uantity
Qd = dD#C – d&h
+ CQ"C – d
• +etailers are often a*are of thetiming of the ne3t promotion
4orward buy =Qd –Q "
Impact of 6ra"e 8romotions
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Impact of 6ra"e 8romotionson Lot Si!es
Q B9( bottles9 C @& perbottle
d @>.1)9 D = 1#>9>>>9 h >.#
Cycle inventory at 'O Q?# B9(?# &91B#bottles
-verage o* time Q?# D B9(?# D; >.&1B#monthsQd = dD
#C – d&h
+ CQ "
C – d= )+$, ×$2))))
#-+)) – )+$,& × )+2)+ - × /-2.
-+)) – )+$,= -02-/
Impact of 6ra"e 8romotions
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Impact of 6ra"e 8romotionson Lot Si!es
Cycle inventory at 'O Qd ?# &9#&B?#
1A911 bottles-verage o* time Qd ?# D &9#&B?#>9>>>;
1.A11 months
Gith tra"e promotions
2or*ar" buy Qd = Q &9#&B = B9( &19A1# bottles
5o* Much of a 'iscount Shoul"
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5o* Much of a 'iscount Shoul"the +etailer 8ass 6hrough
8ro4ts for the retailer
Prof R &>>9>>> = B>9>>> p; p = &>>9>>> = B>9>>> p;C R
• Optimal price
p &>>9>>> F B>9>>>C R;?1#>9>>>
• 'eman" *ith no promotion
D R &>9>>> = B>9>>> p B>9>>>
• Optimal price *ith "iscount
p &>>9>>> F B>9>>> 3 #.);?1#>9>>> @&.A#)
D R &>>9>>> 0 B>9>>> p B(9)>>
• 'eman" *ith promotion
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6ra"e 8romotions
6ra"e promotions generallyincrease cycle inventory in asupply chain an" hurt performance
Counter measures
◦ E'L8 every "ay lo* pricing;
◦ 'iscount applies to items sol" to
customers sell0through; not the%uantity purchase" by the retailersell0in;
◦ Scan base" promotions
Managing Multiechelon
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Managing MultiechelonCycle Inventory
Multi0echelon supply chains havemultiple stages *ith possibly manyplayers at each stage
Lac/ of coor"ination in lot si!ing"ecisions across the supply chainresults in high costs an" more cycleinventory than re%uire"
6he goal is to "ecrease total costs bycoor"inating or"ers across the supplychain
Managing Multiechelon
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Managing MultiechelonCycle Inventory
2igure 110B
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Integer +eplenishment 8olicy
'ivi"e all parties *ithin a stage into groups suchthat all parties *ithin a group or"er from thesame supplier an" have the same reor"er interval
Set reor"er intervals across stages such that the
receipt of a replenishment or"er at any stage issynchroni!e" *ith the shipment of areplenishment or"er to at least one of itscustomers
2or customers *ith a longer reor"er interval thanthe supplier9 ma/e the customerQs reor"erinterval an integer multiple of the supplierQsinterval an" synchroni!e replenishment at thet*o stages to facilitate cross0"oc/ing
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Integer +eplenishment 8olicy
2or customers *ith a shorter reor"er interval thanthe supplier9 ma/e the supplierQs reor"er intervalan integer multiple of the customerQs interval an"synchroni!e replenishment at the t*o stages to
facilitate cross0"oc/ing 6he relative fre%uency of reor"ering "epen"s on
the setup cost9 hol"ing cost9 an" "eman" at"i7erent parties
6hese polices ma/e the most sense for supplychains in *hich cycle inventories are large an""eman" is relatively pre"ictable
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Integer +eplenishment 8olicy2igure 110D
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Integer +eplenishment 8olicy
2igure 110
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Summary of Learning Objectives
1. alance the appropriate costs tochoose the optimal lot si!e an" cycleinventory in a supply chain
#. $n"erstan" the impact of %uantity"iscounts on lot si!e an" cycleinventory
&. 'evise appropriate "iscounting
schemes for a supply chain(. $n"erstan" the impact of tra"e
promotions on lot si!e an" cycleinventory
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Summary of Learning Objectives
). I"entify managerial levers that re"ucelot si!e an" cycle inventory in a supplychain *ithout increasing cost
◦
+e"uce 43e" or"ering an" transportationcosts incurre" per or"er
◦ Implement volume0base" "iscountingschemes rather than in"ivi"ual lot si!e=
base" "iscounting schemes◦ Eliminate or re"uce tra"e promotions an"
encourage E'L8 = base tra"e promotions onsell0through rather than sell0in to the retailer
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