Chapter 12 Inventory Management. Reasons to Hold Inventory Meet unexpected demand Smooth seasonal or...
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Transcript of Chapter 12 Inventory Management. Reasons to Hold Inventory Meet unexpected demand Smooth seasonal or...
Chapter 12Chapter 12
Inventory Inventory ManagementManagement
Reasons to Hold Reasons to Hold InventoryInventory
Meet unexpected demandMeet unexpected demandSmooth seasonal or cyclical demandSmooth seasonal or cyclical demandMeet variations in customer demandMeet variations in customer demandTake advantage of Take advantage of
price discountsprice discountsHedge against price Hedge against price
increasesincreasesQuantity discountsQuantity discounts
Inventory CostsInventory Costs
Carrying CostCarrying CostCost of holding an item in inventory,Cost of holding an item in inventory,
May include cost of obsolescence May include cost of obsolescence
Ordering CostOrdering CostCost of replenishing inventoryCost of replenishing inventory
Shortage CostShortage CostTemporary or permanent loss of sales Temporary or permanent loss of sales
when demand cannot be metwhen demand cannot be met
Inventory Control Inventory Control SystemsSystems
Continuous system (fixed-order-Continuous system (fixed-order-quantity)quantity)
Constant amount ordered when Constant amount ordered when inventory declines to predetermined inventory declines to predetermined levellevel
Periodic system (fixed-time-period)Periodic system (fixed-time-period)Order placed for variable amount after Order placed for variable amount after
fixed passage of timefixed passage of time
Assumptions of Basic Assumptions of Basic EEconomic conomic OOrder rder QQuantity uantity
ModelModelDemand is known with certainty Demand is known with certainty
and is constant over timeand is constant over timeNo shortages are allowedNo shortages are allowedLead time for the receipt of orders Lead time for the receipt of orders
is constantis constantThe order quantity is received all The order quantity is received all
at onceat once
The Inventory Order CycleThe Inventory Order Cycle
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
When to OrderWhen to OrderReorder Point is the level of inventory Reorder Point is the level of inventory at which a new order is placed at which a new order is placed
RR = = dLdL
wherewhere
dd = demand rate per period = demand rate per periodLL = lead time = lead time
Reorder Point ExampleReorder Point Example
Demand = 10,000 yards/yearDemand = 10,000 yards/year
Store open 311 days/yearStore open 311 days/year
Daily demand = 10,000 / 311 = 32.154 yards/dayDaily demand = 10,000 / 311 = 32.154 yards/day
Lead time = L = 10 daysLead time = L = 10 days
R = dL = (32.154)(10) = 321.54 yardsR = dL = (32.154)(10) = 321.54 yards
Safety Stocks Safety Stocks
Safety stockSafety stock buffer added to on hand inventory during buffer added to on hand inventory during
lead timelead time
Stockout Stockout an inventory shortagean inventory shortage
Service level Service level probability that the inventory available probability that the inventory available
during lead time will meet demandduring lead time will meet demand
Variable Demand with Variable Demand with a Reorder Pointa Reorder Point
ReorderReorderpoint, point, RR
LTLT
TimeTimeLTLT
Inve
nto
ry le
vel
Inve
nto
ry le
vel
00
Reorder Point with Reorder Point with a Safety Stocka Safety Stock
ReorderReorderpoint, point, RR
LTLT
TimeTimeLTLT
Inve
nto
ry le
vel
Inve
nto
ry le
vel
00
Safety Stock
EOQ Cost ModelEOQ Cost ModelCCoo - 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
EOQ Cost ModelEOQ Cost ModelCCoo - 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 QoptProving equality of costs at optimal point
=CoD
Q
CcQ
2
Q2 =2CoD
Cc
Qopt =2CoD
Cc
EOQ Cost ModelEOQ Cost Model
Slope = 0Slope = 0
Total CostTotal Cost
Order Quantity, Order Quantity, QQ
Annual Annual cost ($)cost ($)
Minimum Minimum total costtotal cost
Optimal orderOptimal order QQoptopt
Carrying Cost =Carrying Cost =CCccQQ
22
Ordering Cost =Ordering Cost =CCooDD
EOQ ExampleEOQ ExampleCCcc = $0.75 per yard = $0.75 per yard CCoo = $150 = $150 DD = 10,000 yards = 10,000 yards
QQoptopt = =22CCooDD
CCcc
QQoptopt = =2(150)(10,000)2(150)(10,000)
(0.75)(0.75)
QQoptopt = 2,000 yards = 2,000 yards
TCTCminmin = + = +CCooDD
CCccQQ
22
TCTCminmin = + = +(150)(10,000)(150)(10,000)
2,0002,000(0.75)(2,000)(0.75)(2,000)
22
TCTCminmin = $750 + $750 = $1,500 = $750 + $750 = $1,500
Orders per year =Orders per year = DD//QQoptopt
== 10,000/2,00010,000/2,000
== 5 orders/year5 orders/year
Order cycle time =Order cycle time = 311 days/(311 days/(DD//QQoptopt))
== 311/5311/5
== 62.2 store days62.2 store days
EOQ with EOQ with Noninstantaneous ReceiptNoninstantaneous Receipt
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
EOQ with EOQ with Noninstantaneous ReceiptNoninstantaneous Receipt
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
Quantity DiscountsQuantity Discounts Price per unit decreases as order Price per unit decreases as order
quantity increasesquantity increases
TCTC = + + = + + PDPDCCooDD
CCccQQ
22
wherewhere
PP = per unit price of the item = per unit price of the itemDD = annual demand = annual demand
Quantity DiscountsQuantity Discounts Price per unit decreases as order Price per unit decreases as order
quantity increasesquantity increases
TCTC = + + = + + PDPDCCooDD
CCccQQ
22
wherewhere
PP = per unit price of the item = per unit price of the itemDD = annual demand = annual demand
ORDER SIZE PRICE
1 - 99 $10
100 - 199 8
200+ 6
Quantity Discount ModelQuantity Discount Model
QQoptopt
Carrying cost Carrying cost
Ordering cost Ordering cost
Inve
nto
ry c
ost
($)
Inve
nto
ry c
ost
($)
QQ((dd1 1 ) = 100) = 100 QQ((dd2 2 ) = 200) = 200
TC TC ((dd2 2 = $6 ) = $6 )
TCTC ( (dd1 1 = $8 )= $8 )
TC TC = ($10 )= ($10 )
Quantity Discount ModelQuantity Discount Model
QQoptopt
Carrying cost Carrying cost
Ordering cost Ordering cost
Inve
nto
ry c
ost
($)
Inve
nto
ry c
ost
($)
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 )