inventory models. inventory models help to decide help to decide how much to order how much to order...
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Inventory ModelsInventory Models
Inventory modelsInventory models
Help to decide Help to decide
How much to orderHow much to order
When to orderWhen to order
Basic EOQ modelBasic EOQ model
POQ modelPOQ model
Basic EOQ modelBasic EOQ model
AssumptionsAssumptions Known and constant Known and constant demanddemand Known and constant Known and constant lead timelead time Instantaneous receiptInstantaneous receipt of materialof material NoNo quantityquantity discountsdiscounts OnlyOnly order (setup) costorder (setup) cost and and holding holding
costcost NoNo stockoutsstockouts
Basic EOQ modelBasic EOQ model
Receive an orderReceive an order
Use the inventory at a constant Use the inventory at a constant
raterate
Reorder same amountReorder same amount
Instantaneously receive the orderInstantaneously receive the order
Economic Order Economic Order QuantityQuantity
On
-han
d i
nve
nto
ry (
un
its)
Time
Economic Order Economic Order QuantityQuantity
On
-han
d i
nve
nto
ry (
un
its)
Time
Economic Order Economic Order QuantityQuantity
On
-han
d i
nve
nto
ry (
un
its)
Time
Receive order
Q
Economic Order Economic Order QuantityQuantity
On
-han
d i
nve
nto
ry (
un
its)
Time
Receive order
Q
1 cycle
Economic Order Economic Order QuantityQuantity
On
-han
d i
nve
nto
ry (
un
its)
Time
Receive order
Q
1 cycle
Economic Order Economic Order QuantityQuantity
On
-han
d i
nve
nto
ry (
un
its)
Time
Receive order
Inventory depletion (demand rate)
Q
1 cycle
Economic Order Economic Order QuantityQuantity
On
-han
d i
nve
nto
ry (
un
its)
Time
Receive order
Inventory depletion (demand rate)
Q
1 cycle
Economic Order Economic Order QuantityQuantity
On
-han
d i
nve
nto
ry (
un
its)
Time
Averagecycleinventory
Q
Q—2
1 cycle
Receive order
Inventory depletion (demand rate)
Total Cost = Holding Cost + Order Total Cost = Holding Cost + Order CostCost
Total Cost = Holding Cost + Total Cost = Holding Cost + Order CostOrder Cost
An
nu
al c
os
t (d
olla
rs)
Lot Size (Q)
An
nu
al c
os
t (d
olla
rs)
Lot Size (Q)
Holding cost (HC)
Total Cost = Holding Cost + Order CostTotal Cost = Holding Cost + Order Cost
More units must be stored if more are orderedMore units must be stored if more are ordered
Purchase OrderDescription Qty.Microwave 1
Order quantityOrder quantity
Purchase OrderDescription Qty.Microwave 1000
Order quantityOrder quantity
Why Holding Costs Why Holding Costs IncreaseIncrease
An
nu
al c
os
t (d
olla
rs)
Lot Size (Q)
Holding cost (HC)
Ordering cost (OC)
Total Cost = Holding Cost + Order CostTotal Cost = Holding Cost + Order Cost
If we order more when we place If we order more when we place
an order, then we order fewer an order, then we order fewer
times over the year.times over the year.
Example: You expect to order Example: You expect to order
10 microwave ovens over a year 10 microwave ovens over a year
for a retail store like Sears. It for a retail store like Sears. It
cost $10 to place an order.cost $10 to place an order.
Why Order Costs Why Order Costs DecreaseDecrease
Order Cost $10Order Cost $10
Purchase OrderDescription Qty.Microwave 10
Order cost $10Order cost $10
Purchase OrderDescription Qty.
1Microwave
If you order 1 microwave, how
many orders will you place over the
year? what is the ordering cost?
What is the ordering cost per
microwave?
If you order 10 microwaves, how
many orders will you place over
the year? What is the ordering
cost? What is the ordering cost
per microwave?
An
nu
al c
os
t (d
olla
rs)
Lot Size (Q)
Ordering cost (OC)
Holding cost (HC)
Total cost = HC + OC
Total Cost = Holding Cost + Order CostTotal Cost = Holding Cost + Order Cost
Gift ShopGift Shop A museum of natural history is having A museum of natural history is having
problems managing their inventories. problems managing their inventories. Low inventory turnover is squeezing profit Low inventory turnover is squeezing profit margins and causing cash-flow problems.margins and causing cash-flow problems.
A Class A item, a birdfeeder is also a top-A Class A item, a birdfeeder is also a top-selling item.selling item. Sales: Sales: 18 units/week18 units/week Purchase cost: Purchase cost: $60$60 Order cost: Order cost: $45$45 Annual holding cost: 25% of purchase costAnnual holding cost: 25% of purchase cost 52-week year52-week year
Management has been ordering in lots of Management has been ordering in lots of 390 units.390 units.
Q – order quantityQ – order quantity
TC – Total costTC – Total cost AnnualAnnual MonthlyMonthly ????
What is the annual cost What is the annual cost of the current policy?of the current policy?
Time
Q
Holding CostHolding Cost
HQ
ingCostAnnualHold
2
)//)(( yearunittHoldingCosryAveInvento
ingCostAnnualHold
Holding costHolding cost
| | | | | | | |50 100 150 200 250 300 350 400
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Holding cost = (H)Q2
An
nu
al c
ost
(d
oll
ars)
Ordering costOrdering cost
)(OrderCostityOrderQuant
ndAnnualDemarCostAnnualOrde
SQ
DrCostAnnualOrde
Holding & Holding & Ordering CostOrdering Cost
| | | | | | | |50 100 150 200 250 300 350 400
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Holding cost = (H)Q2
Ordering cost = (S)DQ
An
nu
al c
ost
(d
oll
ars)
Total CostTotal Cost
| | | | | | | |50 100 150 200 250 300 350 400
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Total cost = (H) + (S)DQ
Q2
Holding cost = (H)Q2
Ordering cost = (S)DQ
An
nu
al c
ost
(d
oll
ars)
Total cost:Total cost:
HQ
SQ
DTC
2
ngCostTotalHoldiCostTotalOrderTotalCost
What is the annual cost of the What is the annual cost of the current policy?current policy?
HQ
SQ
DTC
2D – Total demand
Q – Order quantity
S – Setup/order cost
H – Holding cost
What is the annual cost of the What is the annual cost of the current policy?current policy?
HQ
SQ
DTC
2D – Total demand
936/year
Q – Order quantity 390/order
S – Setup/order cost $45/order
H – Holding cost = 0.25*60= $15/unit/year
152
39045
390
936TC
2925108TC
3033TC
Total Cost for Q = 390Total Cost for Q = 390A
nn
ual
co
st (
do
llar
s)
| | | | | | | |50 100 150 200 250 300 350 400
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Currentcost
CurrentQ
Total cost = (H) + (S)DQ
Q2
Holding cost = (H)Q2
Ordering cost = (S)DQ
Can the gift shop do Can the gift shop do better?better?
An
nu
al c
ost
(d
oll
ars)
| | | | | | | |50 100 150 200 250 300 350 400
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Currentcost
CurrentQ
Total cost = (H) + (S)DQ
Q2
Holding cost = (H)Q2
Ordering cost = (S)DQ
Economic Order Quantity – Economic Order Quantity – Q*Q*
An
nu
al c
ost
(d
oll
ars)
| | | | | | | |50 100 150 200 250 300 350 400
Lot Size (Q)
3000 —
2000 —
1000 —
0 —
Q*
Setup cost = Holding Cost
Economic Order Quantity (EOQ) – Economic Order Quantity (EOQ) – Q*Q*
H
DSQ
2*
15
)45)(936(2* Q orderunits /7594.74
Total Cost of Economic Total Cost of Economic Order Quantity (EOQ) – Q*Order Quantity (EOQ) – Q*
152
7545
75
936TC
HQ
SQ
DTC
2
*
*
10.1124TC 3033TCWhen Q = 390
When to order?When to order?
Reorder point (ROP)Reorder point (ROP)
Lead time – amount of time from order Lead time – amount of time from order
placement to receipt of goodsplacement to receipt of goods
Lead time demand – the demand the Lead time demand – the demand the
occurs during the lead timeoccurs during the lead time
Reorder pointReorder point
Orderreceived
OH
On
-han
d i
nve
nto
ry
Reorder pointReorder point
Orderreceived
OH
TBO
On
-han
d i
nve
nto
ry
Time between orders
Reorder pointReorder point
Orderreceived
OH
TBO
L
On
-han
d i
nve
nto
ry
Lead time
Reorder pointReorder point
Orderreceived
OH
Orderplaced
TBO
L
ROn
-han
d i
nve
nto
ry
Gift shop reorder pointGift shop reorder point
Demand: 18 birdfeeders/weekDemand: 18 birdfeeders/week
Lead time: 2 weeksLead time: 2 weeks
Lead time demand: 36 birdfeedersLead time demand: 36 birdfeeders
ROP: 36 birdfeedersROP: 36 birdfeeders
Gift shop order policyGift shop order policy
Place order when the on-hand Place order when the on-hand inventory is 36 birdfeeders.inventory is 36 birdfeeders.
Order 75 birdfeedersOrder 75 birdfeeders Order received in 2 weeksOrder received in 2 weeks Place next order when the on-hand Place next order when the on-hand
inventory is 36 birdfeedersinventory is 36 birdfeeders
Gift shop order Gift shop order policypolicy
Orderreceived
OH
Orderplaced
2 wks
36On
-han
d i
nve
nto
ry 75
Distribution GameDistribution Game What is the EOQ What is the EOQ
for the central for the central warehouse in the warehouse in the distribution distribution game?game? Order cost: Order cost: S = S =
Holding cost: H = Holding cost: H =
Demand:Demand: D = D =
$200
$14.70/unit/year
2190
Distribution GameDistribution Game
H
DSQ
2*
7.14
)200)(2190(2* Q
unitsQ 2441.244*
Production Order Production Order QuantityQuantity
On
-han
d i
nve
nto
ry
Time
Production Order Production Order QuantityQuantity
Production quantity
On
-han
d i
nve
nto
ry
Q
Time
Production Order Production Order QuantityQuantity
Production quantity
On
-han
d i
nve
nto
ry
Q
Time
Demand during production interval
p – d
Production Order Production Order QuantityQuantity
Production quantity
Demand during production interval
On
-han
d i
nve
nto
ry
Q
Time
p – d
Production Order Production Order QuantityQuantity
Production quantity
Demand during production interval
On
-han
d i
nve
nto
ry
Q
Time
p – d
Production and demand
Demand only
TBO
Production Order Production Order QuantityQuantity
Production quantity
Demand during production interval
Production and demand
Demand only
TBO
On
-han
d i
nve
nto
ry
Q
Time
p – d
Production Order Production Order QuantityQuantity
Production quantity
Demand during production interval
Maximum inventory
Production and demand
Demand only
On
-han
d i
nve
nto
ry
Q
Time
p – d
Production Order Production Order Quantity (POQ Quantity (POQ
Model)Model)
POQ modelPOQ model
AssumptionsAssumptions Known and constant Known and constant demanddemand Known and constant Known and constant lead timelead time Partial receipt of materialPartial receipt of material NoNo quantity quantity discountsdiscounts Only Only order (setup) costorder (setup) cost and and holding holding
costcost No No stockoutsstockouts
POQ modelPOQ model
Producing and shipping product Producing and shipping product simultaneously until production simultaneously until production quantity is reached.quantity is reached.
Ship the inventory at a constant rate Ship the inventory at a constant rate (no production)(no production)
Reorder same amountReorder same amount Begin production and shipping Begin production and shipping
product simultaneouslyproduct simultaneously
POQ ModelPOQ Model
)/1(
2*
pdH
DSQp
D – annual demand
S – Setup cost
H – Holding cost
d – daily demand rate
p – daily production rate
Chemical PlantChemical PlantA plant manager of a chemical plant must A plant manager of a chemical plant must
determine the lot size for a particular determine the lot size for a particular chemical that has a steady demand of 30 chemical that has a steady demand of 30 barrels/day. The production rate is 190 barrels/day. The production rate is 190 barrels/day, annual demand is 10,500 barrels/day, annual demand is 10,500 barrels, setup cost is $200, annual barrels, setup cost is $200, annual holding cost is $0.21/barrel, and the holding cost is $0.21/barrel, and the plant operates 350 days/year. plant operates 350 days/year. Determine the production order Determine the production order quantity.quantity.
Chemical PlantChemical Plant
Demand: Demand:
Setup cost:Setup cost:
Holding cost:Holding cost:
Production:Production:
d = 30 barrels/dayd = 30 barrels/day
D = 10,500 D = 10,500 barrels/yearbarrels/year
$200/setup$200/setup
$0.21/barrel/year$0.21/barrel/year
190 barrels/day190 barrels/day
Chemical PlantChemical Plant
)/1(
2*
pdH
DSQp
)190/301(21.0
)200)(10500(2*
pQ
barrelsQp 48734.4873*