Ch 12 Student Krajewski

8/12/2019 Ch 12 Student Krajewski

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121Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall.

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


Concepts Weeks of supply

Turns

ABC Analysis

Q System

Q Systems Total Costs

P System

Q System vs. P System


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123


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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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


7/28127Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall.

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



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



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


On-h

andinventory(units)

Time

Averagecycleinventory

Q

Q2

1 cycle

Receiveorder

Inventory depletion(demand rate)



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



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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



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



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%



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



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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Ch 12 Student Krajewski