inventory management ppt
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Inventory ManagementInventory Management
Demand Demand raterate
TimeTimeLead Lead timetime
Lead Lead timetime
Order Order placedplaced
Order Order placedplaced
Order Order receiptreceipt
Order Order receiptreceipt
Inve
nto
ry L
evel
Inve
nto
ry L
evel
Reorder point, Reorder point, RR
Order quantity, Order quantity, QQ
00
CCoo - cost of placing order - cost of placing order DD - annual demand - annual demand
CCcc - annual per-unit carrying cost - annual per-unit carrying cost QQ - order quantity - order quantity
Annual ordering cost =Annual ordering cost =CCooDD
Annual carrying cost =Annual carrying cost =CCccQQ
22
Total cost = +Total cost = +CCooDD
CCccQQ
22
TC = +CoD
Q
CcQ
2
= +CoD
Q2
Cc
2
TC
Q
0 = +C0D
Q2
Cc
2
Qopt =2CoD
Cc
Deriving Qopt Proving equality of costs at optimal point
=CoD
Q
CcQ
2
Q2 =2CoD
Cc
Qopt =2CoD
Cc
Order Quantity, Order Quantity, QQ
Annual Annual cost ($)cost ($) Total CostTotal Cost
Carrying Cost =Carrying Cost =CCccQQ
22
Slope = 0Slope = 0
Minimum Minimum total costtotal cost
Optimal orderOptimal order QQoptopt
Ordering Cost =Ordering Cost =CCooDD
QQ(1-(1-d/pd/p))
InventoryInventorylevellevel
(1-(1-d/pd/p))QQ22
TimeTime00
OrderOrderreceipt periodreceipt period
BeginBeginorderorder
receiptreceipt
EndEndorderorder
receiptreceipt
MaximumMaximuminventory inventory levellevel
AverageAverageinventory inventory levellevel
pp = production rate = production rate dd = demand rate = demand rate
Maximum inventory level =Maximum inventory level = QQ - - dd
== QQ 1 - 1 -
QQpp
ddpp
Average inventory level = Average inventory level = 1 - 1 -QQ22
ddpp
TCTC = + 1 - = + 1 -ddpp
CCooDD
CCccQQ
22
QQoptopt = =22CCooDD
CCcc 1 - 1 - ddpp
TCTC = + + = + + PDPDCCooDD
CCccQQ
22
wherewherewherewhere PP = per unit price of the item = per unit price of the itemDD = annual demand = annual demand
PP = per unit price of the item = per unit price of the itemDD = annual demand = annual demand
QQoptopt
Carrying cost Carrying cost
Ordering cost Ordering cost
Inve
ntor
y co
st (
$)In
vent
ory
cost
($)
QQ((dd1 1 ) = 100) = 100 QQ((dd2 2 ) = 200) = 200
TC TC ((dd2 2 = $6 ) = $6 )
TCTC ( (dd1 1 = $8 )= $8 )
TC TC = ($10 )= ($10 ) ORDER SIZE PRICE
0 - 99 $10
100 – 199 8 (d1)
200+ 6 (d2)
RR = = dLdL
ReorderReorderpoint, point, RR
LTLT
TimeTimeLTLT
Inve
nto
ry le
vel
Inve
nto
ry le
vel
00
ReorderReorderpoint, point, RR
LTLT
TimeTimeLTLT
Inve
nto
ry le
vel
Inve
nto
ry le
vel
00
Safety Stock
RR = = dLdL + + zzdd L L
wherewhere
dd == average daily demandaverage daily demandLL == lead timelead time
dd == the standard deviation of daily demand the standard deviation of daily demand zz == number of standard deviationsnumber of standard deviations
corresponding to the service levelcorresponding to the service levelprobabilityprobability
zzdd L L == safety stocksafety stock
wherewhere
dd == average daily demandaverage daily demandLL == lead timelead time
dd == the standard deviation of daily demand the standard deviation of daily demand zz == number of standard deviationsnumber of standard deviations
corresponding to the service levelcorresponding to the service levelprobabilityprobability
zzdd L L == safety stocksafety stock
Probability of Probability of meeting demand during meeting demand during lead time = service levellead time = service level
Probability of Probability of a stockouta stockout
RR
Safety stock
ddLLDemandDemand
zd L
The carpet store wants a reorder point with a 95% The carpet store wants a reorder point with a 95% service level and a 5% stockout probabilityservice level and a 5% stockout probability
dd = 30 yards per day= 30 yards per dayLL = 10 days= 10 days
dd = 5 yards per day= 5 yards per day
For a 95% service level, For a 95% service level, zz = 1.65 = 1.65
RR = = dLdL + + zz dd L L
= 30(10) + (1.65)(5)( 10)= 30(10) + (1.65)(5)( 10)
= 326.1 yards= 326.1 yards
Safety stockSafety stock = = zz dd L L
= (1.65)(5)( 10)= (1.65)(5)( 10)
= 26.1 yards= 26.1 yards
QQ = = dd((ttbb + + LL) + ) + zzdd ttbb + + LL - - II
wherewhere
dd = average demand rate= average demand ratettbb = the fixed time between orders= the fixed time between orders
LL = lead time= lead timedd = standard deviation of demand= standard deviation of demand
zzdd ttbb + + LL = safety stock= safety stock
II = inventory level= inventory level