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Inventory Management
12
For Operations Management, 9ebyKrajewski/Ritzman/Malhotra 2010 Pearson Education
Homework: 1, 3(assume 250
working days/year), 5, 7, 10, 13,Milligan Workshop
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122
Inventory Management
Concepts Weeks of supply
Turns
ABC Analysis
Q System
Q Systems Total Costs
P System
Q System vs. P System
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Inventory Management
Inventory is a stock of anything held to meet somefuture demand. It is created when the rate of receiptsexceeds the rate of disbursements.
A stock or store of goods.
Inventory Turns (Turnover)COGS/Avg. Inventory Investment
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124
Inventory Management
Weeks of supply = Average aggregate Inventory Value / Weekly Sales (at cost)
IT = COGS / Average aggregate inventory value
The Eagle Machine Company averaged $2M in inventory last year, and theCOGS was $10M. If the company has 52 business weeks per year, how manyweeks of supply are held in inventory? What is the inventory turnover rate?
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10 20 30 40 50 60 70 80 90 100
Percentage of SKUs
Pe
rcentageofdollarvalue
100 90
80
70
60
50
40
30
20
10
0
Class C
Class A
Class B
ABC Analys is
Figure 12.1Typical Chart Using ABC Analysis
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Solved Problem 1
Bookers Book Bindery divides SKUs into three classes,according to their dollar usage. Calculate the usage values ofthe following SKUs and determine which is most likely to beclassified as class A.
SKU Number DescriptionQuantity Used
per Year
Unit Value
($)1 Boxes 500 3.00
2 Cardboard(square feet)
18,000 0.02
3 Cover stock 10,000 0.75
4 Glue (gallons) 75 40.00
5 Inside covers 20,000 0.05
6 Reinforcing tape(meters)
3,000 0.15
7 Signatures 150,000 0.45
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Solved Problem 1
SKUNumber
DescriptionQuantityUsed per
Year
Unit Value($)
Annual DollarUsage ($)
1 Boxes 500 3.00 = 1,500
2 Cardboard
(square feet)
18,000 0.02 = 360
3 Cover stock 10,000 0.75 = 7,500
4 Glue (gallons) 75 40.00 = 3,000
5 Inside covers 20,000 0.05 = 1,000
6 Reinforcing tape(meters)
3,000 0.15 = 450
7 Signatures 150,000 0.45 = 67,500
Total 81,310
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Solved Problem 1
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Solved Problem 1
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Outl ine, Two Major Models
Fixed Quantity Model, Q Continuous Review SystemOrder a fixed amountOrder cycle (time between orders) varies
EOQ, C (holding and ordering costs)
R- Constant demand, constant lead time- Variable demand~N, constant lead time
Fixed Interval Model, P Periodic Review SystemOrder various amountsOrder cycle is fixed or constant
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Invento ry Contro l Systems
Continuous review (Q) systemReorder point system (ROP) and fixed order
quantity system
For independent demand items
Tracks inventory position (IP)
Includes scheduled receipts (SR), on-handinventory (OH), and back orders (BO)
Inventory position = On-hand inventory + Scheduled receiptsBackorders
IP = OH + SR BO
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Some Terms
Constant demand, constant lead time.
EOQ=Economic Order QuantityQ=Order QuantityD=Annual demandS=Order cost per order
H=Annual holding cost per unitTC=Total annual costsTBO=Time between orders, order cycle time
R=Reorder Point, used when LT>0d=demand rate, dbar mean demand rateL=Lead time
Constant means fixed or non-fluctuating.
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Cont inuous Review System
Constant demand, constant lead time.
On-h
andinventory(units)
Time
Averagecycleinventory
Q
Q2
1 cycle
Receiveorder
Inventory depletion(demand rate)
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Select ing the Reorder Poin t
Time
On-handinventory
TBO TBO
L L
TBO
L
Orderplaced
Orderplaced
Orderplaced
IP IPIP
R
OH OHOH
Orderreceived
Orderreceived
Orderreceived
Orderreceived
Figure 12.6 QSystem When Demand and Lead Time Are Constant and Certain
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Cont inuous Review Systems Total Cos ts
Constant demand, constant lead time.
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Ex: Find EOQ, TBO, and make cost compar isons
Constant demand, constant lead time, LT=0.
Suppose that you are reviewing the inventory policies onan item stocked at a hardware store. The currentpolicy is to replenish inventory by ordering in lots of360 units. Additional information given:
D= 60 units per week, or 3120 units per year
S= $30 per order
H = 25% of selling price, or $20 per unit per year
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Ex: Determ ine ROP
Constant demand, constant lead time, LT>0.
Q=300 units, LT=8 days, TBO=30 days.
On-handinventory(units
)
Time
R
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Cont inuous Review Systems
Time
On-handin
ventory
TBO1 TBO2 TBO3
L1 L2 L3
R
Orderreceived
Orderplaced
Orderplaced
Orderreceived
IP IP
Orderplaced
Orderreceived
Orderreceived
0
IP
Figure 12.7 QSystem When Demand Is Uncertain
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Demand During Lead Time
Averagedemand
duringlead time
Cycle-service level = 85%
Probability of stockout(1.00.85 = 0.15)
zdLT
R
Figure 12.9 Finding Safety Stock with a Normal Probability Distribution for an85 Percent Cycle-Service Level
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Ex: Determ ine EOQ, ROP Q Sys tem
Variable demand~N, constant lead time, LT>0.
The Discount Appliance Store uses a fixed order quantity model. One ofthe companys items has the following characteristics:
Demand = 10 units/wk (assume 52 weeks per year, normally distributed)
Ordering and setup cost (S) = $45/orderHolding cost (H) = $12/unit/year
Lead time (L) = 3 weeks
Standard deviation of demand = 8 units per week
Service level = 70%
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Period ic Review Sys tem (P)
P P
T
L L L
Protection interval
Time
On-handi
nventory
IP3
IP1
IP2
OrderplacedOrderplaced
Orderplaced
Orderreceived
Orderreceived
Orderreceived
IP IPIP
OH OH
Q1Q2
Q3
Figure 12.10PSystem When Demand Is Uncertain
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App l icat ion 12.6, P sys tem
The on-hand inventory is 10 units, and Tis 400. There are noback orders, but one scheduled receipt of 200 units. Now is thetime to review. How much should be reordered?
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Calculat ing Pand T
EXAMPLE 12.7Again, let us return to the bird feeder example. Recall thatdemand for the bird feeder is normally distributed with a meanof 18 units per week and a standard deviation in weekly demandof 5 units. The lead time is 2 weeks, and the business operates52 weeks per year. The Qsystem developed in Example 12.4
called for an EOQ of 75 units and a safety stock of 9 units for acycle-service level of 90 percent. What is the equivalent Psystem? Answers are to be rounded to the nearest integer.
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Calculat ing Pand T
SOLUTIONWe first define Dand then P. Here, Pis the time betweenreviews, expressed in weeks because the data are expressed asdemand per week:
D= (18 units/week)(52 weeks/year) = 936 units
P= (52) =EOQ
D(52) = 4.2 or 4 weeks
75
936
With d= 18 units per week, an alternative approach is tocalculate Pby dividing the EOQ by dto get 75/18 = 4.2 or 4weeks. Either way, we would review the bird feeder inventoryevery 4 weeks.
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Calculat ing Pand T
We now find the standard deviation of demand over theprotection interval (P+ L ) = 6:
Before calculating T, we also need a zvalue. For a 90 percent
cycle-service level z= 1.28. The safety stock becomes
Safety stock = zP+ L= 1.28(12.25) = 15.68 or 16 units
We now solve for T:
= (18 units/week)(6 weeks) + 16 units = 124 units
T= Average demand during the protection interval + Safety stock
= d(P+ L ) + safety stock
units2 25
LPdLP
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Ex: P Syst em, Determ ine the Am oun t to Order
d=30 units per dayd=3 units per dayLT=2 daysService level 99%P=7 days
A=71 units
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Q Model vs . P Model
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IM in A ct ion Video