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Chapter 6

To accompanyQuanti tat ive Analys is for Management, Eleventh Edit ion,by Render, Stair, and HannaPower Point slides created by Brian Peterson andXiaodong Wu

Inven tory Con trol Models

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Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-2

Learn ing Object ives

1. Understand the importance of inventorycontrol and ABC analysis.

2. Use the economic order quantity (EOQ) todetermine how much to order.

3. Compute the reorder point (ROP) indetermining when to order more inventory.

4. Handle inventory problems that allowquantity discounts or non-instantaneousreceipt.

After completing this chapter, students will be able to:

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Learn ing Object ives

5. Understand the use of safety stock.

6. Describe the use of material requirements

planning in solving dependent-demandinventory problems.

7. Discuss just-in-time inventory concepts toreduce inventory levels and costs.

8. Discuss enterprise resource planningsystems.

After completing this chapter, students will be able to:

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Chapter Ou tl ine

6.1 Introduction

6.2 Importance of Inventory Control

6.3 Inventory Decisions

6.4 Economic Order Quantity: DeterminingHow Much to Order

6.5 Reorder Point: Determining When to Order

6.6 EOQ Without the Instantaneous ReceiptAssumption

6.7 Quantity Discount Models

6.8 Use of Safety Stock

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Chapter Ou tl ine

6.9 Single-Period Inventory Models

6.10 ABC Analysis

6.11 Dependent Demand: The Case for MaterialRequirements Planning

6.12 Just-in-Time Inventory Control

6.13 Enterprise Resource Planning

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In t roduct ion

Inventory is an expensive and importantasset to many companies.

Inventory is any stored resource used tosatisfy a current or future need.

Common examples are raw materials, work-in-process, and finished goods.

Most companies try to balance high and lowinventory levels with cost minimization as a

goal. Lower inventory levels can reduce costs.

Low inventory levels may result in stockouts anddissatisfied customers.

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7/118Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-7

In t roduct ion

All organizations have some type of inventorycontrol system.

Inventory planning helps determine whatgoods and/or services need to be produced.

Inventory planning helps determine whetherthe organization produces the goods orservices or whether they are purchased fromanother organization.

Inventory planning also involves demandforecasting.

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Controlling

InventoryLevels

In t roduct ion

Forecasting

Parts/ProductDemand

Planning on WhatInventory to Stock

and How to AcquireIt

Feedback Measurementsto Revise Plans and

Forecasts

Figure 6.1

Inventory planning and control

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Impo rtance of Invento ry Con trol

Five uses of inventory: The decoupling function

Storing resources

Irregular supply and demand Quantity discounts

Avoiding stockouts and shortages

Decouple manufacturing processes.

Inventory is used as a buffer between stagesin a manufacturing process.

This reduces delays and improves efficiency.

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Storing resources. Seasonal products may be stored to satisfy

off-season demand.

Materials can be stored as raw materials, work-in-process, or finished goods.

Labor can be stored as a component ofpartially completed subassemblies.

Compensate for irregular supply anddemand. Demand and supply may not be constant over

time.

Inventory can be used to buffer the variability.

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Take advantage of quantity discounts. Lower prices may be available for larger

orders.

Extra costs associated with holding moreinventory must be balanced against lowerpurchase price.

Avoid stockouts and shortages. Stockouts may result in lost sales.

Dissatisfied customers may choose to buyfrom another supplier.

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Invento ry Decis ions

There are two fundamental decisions incontrolling inventory: How much to order.

When to order. The major objective is to minimize total

inventory costs.

Common inventory costs are:

Cost of the items (purchase or material cost). Cost of ordering.

Cost of carrying, or holding, inventory.

Cost of stockouts.

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Inven tory Cos t Facto rs

ORDERING COST FACTORS CARRYING COST FACTORS

Developing and sending purchase orders Cost of capital

Processing and inspecting incominginventory

Taxes

Bill paying Insurance

Inventory inquiries Spoilage

Utilities, phone bills, and so on, for thepurchasing department

Theft

Salaries and wages for the purchasingdepartment employees

Obsolescence

Supplies, such as forms and paper, for thepurchasing department Salaries and wages for warehouseemployees

Utilities and building costs for thewarehouse

Supplies, such as forms and paper, for thewarehouse

Table 6.1

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Inven tory Cos t Facto rs

Ordering costs are generally independent oforder quantity. Many involve personnel time.

The amount of work is the same no matter thesize of the order.

Carrying costs generally varies with theamount of inventory, or the order size. The labor, space, and other costs increase as the

order size increases.

The actual cost of items purchased can varyif there are quantity discounts available.

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Econom ic Order Quant i ty

The econom ic order quant i ty(EOQ) modelis one of the oldest and most commonlyknown inventory control techniques.

It is easy to use but has a number ofimportant assumptions.

Objective is to minimize total cost ofinventory.

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Econom ic Order Quant i ty

Assumptions:1. Demand is known and constant.

2. Lead time is known and constant.

3. Receipt of inventory is instantaneous.

4. Purchase cost per unit is constantthroughout the year.

5. The only variable costs are the cost ofplacing an order, ordering cos t, and the cost

of holding or storing inventory over time,hold ingorcarry ing cost, and these areconstant throughout the year.

6. Orders are placed so that stockouts orshortages are avoided completely.

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Invento ry Usage Over Time

Time

InventoryLevel

MinimumInventory

0

Order Quantity = Q=Maximum Inventory Level

Figure 6.2

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Invento ry Costs in the EOQ Situat ion

Computing Average Inventory

2levelinventoryAverage

QINVENTORY LEVEL

DAY BEGINNING ENDING AVERAGE

April 1 (order received) 10 8 9

April 2 8 6 7

April 3 6 4 5

April 4 4 2 3April 5 2 0 1

Maximum level April 1 = 10 unitsTotal of daily averages = 9 + 7 + 5 + 3 + 1 = 25Number of days = 5Average inventory level = 25/5 = 5 units Table 6.2

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Inventory Costs in theEOQSituat ion

Mathematical equations can be developed using:

Q= number of pieces to orderEOQ = Q* = optimal number of pieces to order

D= annual demand in units for the inventory item

Co= ordering cost of each orderCh= holding or carrying cost per unit per year

Annual ordering cost Number of

orders placed

per year

Orderingcost per

order

oC

Q

D

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Mathematical equations can be developed using:

Q= number of pieces to orderEOQ = Q* = optimal number of pieces to order

D= annual demand in units for the inventory item

Co= ordering cost of each orderCh= holding or carrying cost per unit per year

Annual holding cost Average

inventory

Carryingcost per unit

per year

hC

Q

2

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MinimumTotalCost

Optimal

OrderQuantity

Curve of Total Costof Carrying

and Ordering

Carrying Cost Curve

Ordering Cost Curve

Cost

Order QuantityFigure 6.3

Total Cost as a Function of Order Quantity

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Finding theEOQ

According to the graph, when the EOQ assumptionsare met, total cost is minimized when annualordering cost equals annual holding cost.

ho CQ

CQ

D

2Solving forQ

hoCQDC

22 22

QC

DC

h

o *

EOQ QQ

C

DC

h

o 2

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Econom ic Order Quant i ty (EOQ) Model

hC

Q

2costholdingAnnual

oC

Q

DcostorderingAnnual

h

o

C

DCQ

2*EOQ

Summary of equations:

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Sumco Pump Company

Sumco Pump Company sells pump housings toother companies.

The firm would like to reduce inventory costs byfinding optimal order quantity.

Annual demand = 1,000 units Ordering cost = $10 per order

Average carrying cost per unit per year = $0.50

units20000040500

10000122 ,.

))(,(*

h

o

CDCQ

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Sumco Pump Company

Total annual cost = Order cost + Holding cost

hoC

QC

Q

DTC

2

).()(,

502

20010

200

0001 1005050 $$$

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Sumco Pump Company

Program 6.1A

Input Data and Excel QM formulas for theSumco Pump Company Example

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Sumco Pump Company

Program 6.1B

Excel QMSolution forthe SumcoPump

CompanyExample

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Purchase Cost o f Invento ry Items

Total inventory cost can be written to include thecost of purchased items.

Given the EOQ assumptions, the annual purchasecost is constant at DCno matter the order

policy, where Cis the purchase cost per unit.

Dis the annual demand in units.

At times it may be useful to know the average

dollar level of inventory:

2leveldollarAverage

)(CQ

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Purchase Cost o f Invento ry Items

Inventory carrying cost is often expressed as anannual percentage of the unit cost or price of theinventory.

This requires a new variable.

Annual inventory holding charge asa percentage of unit price or costI

The cost of storing inventory for one year is then

ICCh thus,

IC

DCQ o

2*

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Sensi t iv i ty Analys is w i th theEOQModel

The EOQ model assumes all values are know andfixed over time.

Generally, however, some values are estimated ormay change.

Determining the effects of these changes iscalled sensit iv i ty analysis .

Because of the square root in the formula,changes in the inputs result in relatively small

changes in the order quantity.

h

o

C

DC2EOQ

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Sensi t iv i ty Analys is w i th theEOQModel

In the Sumco Pump example:

units200500

1000012 .

))(,(EOQ

If the ordering cost were increased four times from$10 to $40, the order quantity would only double

units400500

4000012 .

))(,(

EOQ

In general, the EOQ changes by the square rootof the change to any of the inputs.

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Reorder Poin t :Determ ining When To Order

Once the order quantity is determined, thenext decision is when to order.

The time between placing an order and itsreceipt is called the

lead t ime(L ) or

del ivery t im e.

When to order is generally expressed as areorder po int(ROP).

Demandper day

Lead time for anew order in daysROP

dL

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Procomps Computer Chips

Demand for the computer chip is 8,000 per year.

Daily demand is 40 units.

Delivery takes three working days.

ROPdL 40 units per day 3 days 120 units

An order based on the EOQ calculation is placedwhen the inventory reaches 120 units.

The order arrives 3 days later just as theinventory is depleted.

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Reorder Poin t Graphs

Figure 6.4

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EOQ Without The Ins tantaneousReceip t Assumpt ion

When inventory accumulates over time, theinstantaneous receiptassumption does not apply.

Daily demand rate must be taken into account.

The revised model is often called the product ionrun model.

Figure 6.5

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Annual Carry ing Cos t forProduct ion Run Model

In production runs, setup costreplaces orderingcost.

The model uses the following variables:

Q number of pieces per order, orproduction run

Cs setup costCh holding or carrying cost per unit per

yearp daily production rated daily demand ratet length of production run in days

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Maximum inventory level (Total produced during the production run)

(Total used during the production run)

(Daily production rate)(Number of days production) (Daily demand)(Number of days production)

(pt) (dt)

since Total produced Qpt

we know p

Qt

Maximuminventory

level

p

dQ

p

Qd

p

Qpdtpt 1

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Since the average inventory is one-half the maximum:

p

dQ1

2

inventoryAverage

and

hCp

dQ

12costholdingAnnual

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Annual Setup Cost forProduct ion Run Model

sCQ

D

costsetupAnnual

Setup cost replaces ordering cost when a product isproduced over time.

replaces

o

CQ

DcostorderingAnnual

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Determ ining the Opt imalProduct ion Quant i ty

By setting setup costs equal to holding costs, wecan solve for the optimal order quantity

Annual holding cost Annual setup cost

shC

Q

DC

p

dQ

12

Solving for Q, we get

p

dC

DCQ

h

s

1

2*

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Produc t ion Run Model

Summary of equations

p

dC

DCQ

h

s

1

2quantityproductionOptimal *

sC

Q

DcostsetupAnnual

hC

p

dQ

12

costholdingAnnual

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Brown Manu factur ing

Brown Manufacturing produces commercialrefrigeration units in batches.

Annual demand D 10,000 units

Setup cost Cs $100Carrying cost Ch $0.50 per unit per year

Daily production rate p 80 units dailyDaily demand rate d 60 units daily

1. How many units should Brown produce in each batch?2. How long should the production part of the cycle last?

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Brown Manu factur ing Example

p

dC

DCQ

h

s

1

2*1. 2.

80

60150

100000102

.

,*Q

000000164

1500000002 ,,

.

,,

units4,000

days50

80

0004 ,p

QcycleProduction

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Program 6.2A

Excel QM Formulas and Input Data for the BrownManufacturing Problem

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Program 6.2B

The Solution Results for the Brown ManufacturingProblem Using Excel QM

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Quant i ty Discount Models

Quantity discounts are commonly available. The basic EOQ model is adjusted by adding in the

purchase or materials cost.

Total cost

Material cost + Ordering cost + Holding cost

hoC

QC

Q

DDC

2costTotal

where

D annual demand in unitsCo ordering cost of each orderC cost per unitCh holding or carrying cost per unit per year

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Quantity discounts are commonly available. The basic EOQ model is adjusted by adding in the

purchase or materials cost.

Total cost

Material cost + Ordering cost + Holding cost

hoC

QC

Q

DDC

2costTotal

where

D annual demand in unitsCo ordering cost of each orderC cost per unitCh holding or carrying cost per unit per year

Holding cost ChI C

I holding cost as a percentage of the unit cost (C)

Because unit cost is now variable,

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A typical quantity discount schedule can look likethe table below.

However, buying at the lowest unit cost is notalways the best choice.

DISCOUNTNUMBER

DISCOUNTQUANTITY DISCOUNT (%)

DISCOUNTCOST ($)

1 0 to 999 0 5.00

2 1,000 to 1,999 4 4.80

3 2,000 and over 5 4.75

Table 6.3

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Total cost curve for the quantity discount model

Figure 6.6

TC Curve forDiscount 1

TC Curve for Discount 3TotalCost

$

Order Quantity

0 1,000 2,000

TC Curve for Discount 2

EOQ for Discount 2

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Brass Department Store

Brass Department Store stocks toy race cars. Their supplier has given them the quantity

discount schedule shown in Table 6.3. Annual demand is 5,000 cars, ordering cost is $49, and

holding cost is 20% of the cost of the car

The first step is to compute EOQ values for eachdiscount.

orderpercars70000520

49000521

).)(.(

))(,)((EOQ


49000522

).)(.(

))(,)((EOQ


49000523

).)(.(

))(,)((EOQ

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Brass Department Store Example

The second step is adjust quantities below theallowable discount range.

The EOQ for discount 1 is allowable.

The EOQs for discounts 2 and 3 are outside the

allowable range and have to be adjusted to thesmallest quantity possible to purchase andreceive the discount:

Q1 700Q2 1,000Q3 2,000

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The third step is to compute the total cost for eachquantity.

DISCOUNTNUMBER

UNITPRICE

(C)

ORDERQUANTITY

(Q)

ANNUALMATERIALCOST ($)

= DC

ANNUALORDERINGCOST ($)= (D/Q)Co

ANNUALCARRYINGCOST ($)= (Q/2)Ch TOTAL ($)

1 $5.00 700 25,000 350.00 350.00 25,700.00

2 4.80 1,000 24,000 245.00 480.00 24,725.00

3 4.75 2,000 23,750 122.50 950.00 24,822.50

The final step is to choose the alternative with thelowest total cost.

Table 6.4

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Program 6.3A

Excel QMs Formulas and the Input Data for the BrassDepartment Store Quantity Discount Problem

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Program 6.3B

Excel QMs Solution to the Brass DepartmentStore Problem

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Use of Safety Stock

If demand or the lead time are uncertain,the exact ROP will not be known withcertainty.

To prevent s tockouts, it is necessary tocarry extra inventory called safety stock.

Safety stock can prevent stockouts whendemand is unusually high.

Safety stock can be implemented byadjusting the ROP.

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Use of Safety Stock

The basic ROP equation is

ROPdLd daily demand (or average daily demand)L order lead time or the number of

working days it takes to deliver an order(or average lead time)

A safety stock variable is added to the equationto accommodate uncertain demand during leadtime

ROP dL + SSwhere

SS safety stock

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Use of Safety Stock

Figure 6.7

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ROP wi th Known Stockout Costs

With a fixed EOQ and an ROP for placing orders,stockouts can only occur during lead time.

Our objective is to find the safety stock quantitythat will minimize the total of stockout cost and

holding cost. We need to know the stockout cost per unit and

the probability distribution of demand during leadtime.

Estimating stockout costs can be difficult asthere may be direct and indirect costs.

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Safety Stock w i th UnknownStockou t Costs

There are many situations when stockout costsare unknown.

An alternative approach to determining safetystock levels is to use a servic e level.

A service level is the percent of time you will notbe out of stock of a particular item.

Service level 1 Probability of a stockoutor

Probability of a stockout 1 Service level

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Hinsdale Company

Inventory demand during lead time is normallydistributed.

Mean demand during lead time is 350 units with astandard deviation of 10.

The company wants stockouts to occur only 5%of the time.

350 X ?

SS

5% Area ofNormal Curve

Figure 6.8

Mean demand 350dLT Standard deviation 10

X

Mean demand + Safety stockSS Safety stock XZ

XZ

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Hinsdale Company Example

350 X ?

SS

5% Area ofNormal Curve

From Appendix A we find Z 1.65 SSX

Solving for safety stock:

SS 1.65(10) 16.5 units, or 17 units

X = ROP = 350+16.5 = 366.5 units

Figure 6.9

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Hinsdale Company

Different safety stock levels will be generated fordifferent service levels.

However, the relationship is not linear. You should be aware of what a service level is costing in

terms of carrying the safety stock in inventory.

The relationship between Zand safety stock canbe developed as follows:

2. We also know that SSX1. We know that

XZ

3. Thus SS

Z

4. So we haveSSZ

Z(10)

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Hinsdale Company

Safety Stock at different service levelsSERVICE LEVEL(%)

ZVALUE FROMNORMAL CURVE TABLE

SAFETY STOCK(UNITS)

90 1.28 12.8

91 1.34 13.4

92 1.41 14.1

93 1.48 14.8

94 1.55 15.5

95 1.65 16.5

96 1.75 17.5

97 1.88 18.8

98 2.05 20.5

99 2.33 23.3

99.99 3.72 37.2Table 6.5

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Hinsdale Company

Figure 6.9

Service level versus annual carrying costs

This graph wasdeveloped for aspecific case, but

the general shape ofthe curve is thesame for all service-level problems.

Calcu lat ing Lead Time Demand

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Calcu lat ing Lead Time Demandand Standard Dev iat ion

There are three situations toconsider:Demand is variable but lead time is

constant.Demand is constant but lead time is

variable.

Both demand and lead time are variable.


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Demand is variable but lead time isconstant:

Where:


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Demand is constant but lead time isvariable:

Where:


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Both demand and lead time arevariable.

Notice that this is the most general case and that

the other two cases can be derived from thisformula.

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Hinsdale Company

Suppose for product SKU F5402, daily demand isnormally distributed, with a mean of 15 units and astandard deviation of 3. Lead time is exactly 4 days.To maintain a 97% service level, what is the ROP,

and how much safety stock should be carried?

ROP = 15(4)+1.88(3*2)= 60 + 11.28=71.28

So the average demand during lead time is 60units, and safety stock is 11.28 units.

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Hinsdale Company

Suppose for product SKU B7319, daily demand isconstant at 25 units per day, but lead time isnormally distributed, with a mean of 6 days and astandard deviation of 3. To maintain a 98% service

level, what is the ROP?

ROP = 25(6)+2.05(25*3)= 150+153.75

=303.75

So the average demand during lead time is 150units, and safety stock is 153.75 units.

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Hinsdale Company

Suppose for product SKU F9004, daily demand isnormally distributed, with a mean of 20 units and astandard deviation of 4. Lead time is normallydistributed, with a mean of 5 days and a standard

deviation of 2 days. To maintain a 94% servicelevel, what is the ROP?

ROP = 100+1.55(40.99)= 163.53

Calculat ing Annual Hold ing

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Calculat ing Annual HoldingCost w i th Safety Stock

Under standard assumptions of EOQ,average inventory is just Q/2.

So annual holding cost is: (Q/2)*Ch.

This is not the case with safety stockbecause safety stock is not meant tobe drawn down.

Calculat ing Annual Hold ing

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Calculat ing Annual HoldingCost w i th Safety Stock

Total annual holding cost = holdingcost of regular inventory + holdingcost of safety stock

Where:

THC = total annual holding costQ = order quantityCh = holding cost per unit per yearSS = safety stock

Excel QM Form ulas and Input Data for

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Excel QM Form ulas and Input Data forthe Hinsdale Safety Stock Prob lems

Program 6.4A

Excel QM Solu t ion to the

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Excel QM Solu t ion to theHinsdale Safety Stock Prob lem

Program 6.4B

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Single-Period Invento ry Models

Some products have no future value beyond thecurrent period.

These situations are called news vendorproblems orsingle-per iod inventory m odels.

Analysis uses marginal profit (MP) and marginalloss (ML) and is called marginal analysis.

With a manageable number of states of natureand alternatives, discrete distributions can beused.

When there are a large number of alternatives orstates of nature, the normal distribution may beused.

Marginal Analysis w ith

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Marginal Analysis w ithDiscrete Distr ibu t ions

We stock an additional unit only if the expectedmarginal profit for that unit exceeds the expectedmarginal loss.

P probability that demand will be greaterthan or equal to a given supply (or theprobability of selling at least oneadditional unit).

1P probability that demand will be less thansupply (or the probability that oneadditional unit will not sell).

Marginal Analysis w ith

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Marginal Analysis w ithDiscrete Distr ibu t ions

The expected marginal profit is P(MP) .

The expected marginal loss is (1P)(ML).

The optimal decision rule is to stock theadditional unit if:

P(MP) (1 P)ML

With some basic manipulation:

P(MP) MLP(ML)P(MP) + P(ML) ML

P(MP + ML) ML

orMPML

ML

P

Steps of Marginal Analysis w ith

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Steps of Marginal Analysis w ith

Discrete Distr ibu t ions

1. Determine the value of for theproblem.

2. Construct a probability table and add a

cumulative probability column.3. Keep ordering inventory as long as the

probability (P) of selling at least one additional

unit is greater than

MPML

ML

MPML

ML

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Cafdu Donu t

The caf buys donuts each day for $4 per cartonof 2 dozen donuts.

Any cartons not sold are thrown away at the endof the day.

If a carton is sold, the total revenue is $6. The marginal profit per carton is.

MP Marginal profit $6 $4 $2

The marginal loss is $4 per carton since cartonscan not be returned or salvaged.

Caf du Donuts Probability

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Caf du Donut s ProbabilityDistr ibut ion

DAILY SALES(CARTONS OF DOUGHNUTS)

PROBABILITY (P) THAT DEMANDWILL BE AT THIS LEVEL

4 0.05

5 0.15

6 0.15

7 0.20

8 0.25

9 0.10

10 0.10

Total 1.00Table 6.6

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MPMLMLStep 1. Determine the value of for the

decision rule.

Cafdu Donu t Examp le

6706

4

24

4.

$$

$

MPML

ML P670.P

Step 2. Add a new column to the table to reflect theprobability that doughnut sales will be at

each level or greater.

Marg inal Analys is fo r Cafdu

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Marg inal Analys is fo r CafduDonut

DAILY SALES(CARTONS OFDOUGHNUTS)

PROBABILITY (P) THATDEMAND WILL BE ATTHIS LEVEL

PROBABILITY (P) THATDEMAND WILL BE AT THISLEVEL OR GREATER

4 0.05 1.00 0.665 0.15 0.95 0.66

6 0.15 0.80 0.66

7 0.20 0.65

8 0.25 0.45

9 0.10 0.20

10 0.10 0.10

Total 1.00

Table 6.7

C f d D E l

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Cafdu Donu t Examp le

Step 3. Keep ordering additional cartons as longas the probability of selling at least oneadditional carton is greater than P, whichis the indifference probability.

Pat 6 cartons 0.80 > 0.67

Marginal Analys is w i th the

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Marginal Analys is w i th theNormal Distr ibut ion

We first need to find four values:

1. The average or mean sales for the product, 2. The standard deviation of sales,

3. The marginal profit for the product, MP.4. The marginal loss for the product, ML.

We let X* optimal stocking level.

Steps o f Marginal Analysis w ith the

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Steps o f Marginal Analysis w ith the

Normal Distr ibut ion

1. Determine the value of for theproblem.

2. Locate Pon the normal distribution (Appendix

A) and find the associated Z-value.

MPML

ML

to solve for the resulting stocking policy:

ZX *

*X

Z

3. Find X* using the relationship:

Joes Stocking Decision for the

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Joe s Stocking Decision for theChicago Tr ibune

Demand for the Chicago Tr ibuneat JoesNewsstand averages 60 papers a day with astandard deviation of 10.

The marginal loss is 20 cents and the marginal

profit is 30 cents.Step 1. Joe should stock the Tribuneas long asthe probability of selling the last unit is at leastML/(ML + MP):

40050

20

cents30cents20

cents20.

MPML

ML Let P= 0.40.


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Step 2. Using the normal distribution in Figure6.10, we find the appropriate Zvalue

Z= 0.25 standard deviations from the mean

50 X Demand

Area under the Curve is 0.40

Figure 6.10 X*

Optimal Stocking Policy (62 Newspapers)

Area under the Curve is 1 0.40 = 0.60

(Z= 0.25) Mean Daily Sales


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Step 3. In this problem, 60 and 10, so

10

60250

*. X

or

X* 60 + 0.25(10) 62.5, or 62 newspapers

Joe should order 62 newspapers since theprobability of selling 63 newspapers is slightlyless than 0.40


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gChicago Tr ibune

The procedure is the same when P> 0.50. Joe also stocks the Chicago Sun-Times.

Marginal loss is 40 cents and marginal profit is10 cents.

Daily sales average 100 copies with a standarddeviation of 10 papers.

80050

40

cents10cents40

cents40.

MPML

ML

Z= 0.84 standard deviations from the mean

From Appendix A:


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gChicago Tr ibune

With 100 and 10

10

100840

*. Xor

X* 100 0.84(10) 91.6, or 91 newspapers

100 X Demand

Area under the

Curve is 0.40

Figure 6.11X*

Optimal Stocking Policy (91 Newspapers)

(Z= 0.84)

ABC A l i

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ABC Analys is

The purpose of ABC analysis is to divide theinventory into three groups based on the overallinventory value of the items.

Group A items account for the major portion ofinventory costs. Typically about 70% of the dollar value but only 10% of

the quantity of items.

Forecasting and inventory management must be donecarefully.

Group B items are more moderately priced. May represent 20% of the cost and 20% of the quantity.

Group C items are very low cost but high volume. It is not cost effective to spend a lot of time managing

these items.

S f ABC A l i

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Summary of ABC Analys is

INVENTORYGROUP

DOLLARUSAGE (%)

INVENTORYITEMS (%)

ARE QUANTITATIVE CONTROLTECHNIQUES USED?

A 70 10 Yes

B 20 20 In some cases

C 10 70 No

Table 6.8

Dependent Demand : The Case for

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pMater ial Requiremen ts Plann ing

All the inventory models discussed so farhave assumed demand for one item isindependent of the demand for any otheritem.

However, in many situations itemsdemand is dependent on demand for oneor more other items.

In these situations,Material Requ iremen tsPlann ing (MRP)can be employed

effectively.

Dependent Demand : The Case for

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pMater ial Requiremen ts Plann ing

Some of the benefits of MRP are:1. Increased customer service levels.

2. Reduced inventory costs.

3. Better inventory planning and scheduling.

4. Higher total sales.

5. Faster response to market changes and shifts.

6. Reduced inventory levels without reducedcustomer service.

Most MRP systems are computerized, butthe basic analysis is straightforward.

Material Struc tu re Tree

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The first step is to develop a bi l l of mater ials(BOM).

The BOM identifies components, descriptions,and the number required for production of oneunit of the final product.

From the BOM we can develop a materialstructure tree.

We use the following data: Demand for product A is 50 units.

Each A requires 2 units of B and 3 units of C. Each B requires 2 units of D and 3 units of E.

Each C requires 1 unit of E and 2 units of F.


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Material structure tree for Item A

ALevel

0

1

2

B(2) C(3)

D(2) E(3) F(2)E(1)

Figure 6.12


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It is clear from the three that the demand for B, C,D, E, and F is completely dependent on thedemand for A.

The material structure tree has three levels: 0, 1,

and 2. Items above a level are called parents.

Items below any level are called components .

The number in parenthesis beside each item

shows how many are required to make the itemabove it.


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We can use the material structure tree and the demandfor Item A to compute demands for the other items.

Part B: 2 number of As 2 50 100.

Part C: 3 number of As 3 50 150.Part D: 2 number of Bs 2 100 200.Part E: 3 number of Bs + 1 number of Cs

3 100 + 1 150 450.Part F: 2 number of Cs 2 150 300.

Gross and Net Mater ial

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Requ iremen ts Plan

Once the materials structure tree is done, weconstruct a gross material requirements plan.

This is a time schedule that shows: when an item must be ordered when there is no

inventory on hand, or

when the production of an item must be started in orderto satisfy the demand for the finished product at aparticular date.

We need lead times for each of the items.

Item A 1 week Item D 1 weekItem B 2 weeks Item E 2 weeksItem C 1 week Item F 3 weeks

Gross Material Requ irements Plan

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for 50 Units o f AWeek

1 2 3 4 5 6

ARequired Date 50

Lead Time = 1 WeekOrder Release 50

BRequired Date 100

Lead Time = 2 WeeksOrder Release 100

CRequired Date 150


DRequired Date 200


ERequired Date 300 150

Lead Time = 2 WeeksOrder Release 300 150

FRequired Date 300

Lead Time = 3 WeeksOrder Release 300

Figure 6.13

Net Material Requ irements Plan

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A net material requirements plan can be constructedfrom the gross materials requirements plan and thefollowing on-hand inventory information:

ITEM ON-HAND INVENTORY

A 10

B 15

C 20

D 10

E 10

F 5

Table 6.9


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Using this data we can construct a planthat includes: Gross requirements.

On-hand inventory.

Net requirements.

Planned-order receipts.

Planned-order releases.

The net requirements plan is constructedlike the gross requirements plan.


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for 50 Units o f A

Week LeadTimeItem 1 2 3 4 5 6

A Gross 50 1

On-Hand 10 10

Net 40

Order Receipt 40

Order Release 40

B Gross 80A 2

On-Hand 15 15

Net 65

Order Receipt 65

Order Release 65

Figure 6.14(a)


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for 50 Units o f A


C Gross 120A 1

On-Hand 20 10

Net 100

Order Receipt 100

Order Release 100

D Gross 130B 1

On-Hand 10 10

Net 120

Order Receipt 120

Order Release 120

Figure 6.14(b)


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for 50 Units o f A


E Gross 195B 100C 2

On-Hand 10 10 0

Net 185 100

Order Receipt 185 100

Order Release 185 100

F Gross 200C 3

On-Hand 5 5

Net 195

Order Receipt 195

Order Release 195

Figure 6.14(c)

Two o r More End Produc ts

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Most manufacturing companies have more thanone end item.

In this example, the second product is AA and ithas the following material structure tree:

AA

D(3) F(2)

If we require 10 units of AA, the gross

requirements for parts D and F can be computed:

Part D: 3 number of AAs 3 10 30Part F: 2 number of AAs 2 10 20


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The lead time for AA is one week. The gross requirement for AA is 10 units in week 6

and there are no units on hand.

This new product can be added to the MRP

process. The addition of AA will only change the MRP

schedules for the parts contained in AA.

MRP can also schedule spare parts andcomponents.

These have to be included as gross requirements.

Net Material Requ irements

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Plan , Includ ing AA

Figure 6.15

Just-in -Time (J IT) Invento ry

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Contro l

To achieve greater efficiency in theproduction process, organizations havetried to have less in-process inventory onhand.

This is known as JIT invento ry.

The inventory arrives just in time to beused during the manufacturing process.

One technique of implementing JIT is amanual procedure called kanban.

Just-in-Time Invento ry Con trol

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Just in Time Invento ry Con trol

Kanban in Japanese means card.

With a dual-card kanban system, there is aconveyance kanban, or C-kanban, and a

production kanban, or P-kanban. Kanban systems are quite simple, but they

require considerable discipline.

As there is little inventory to cover

variability, the schedule must be followedexactly.

4 Steps o f Kanban

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4 Steps o f Kanban

1. A user takes a container of parts or inventoryalong with its C-kanban to his or her work area.

When there are no more parts or the container isempty, the user returns the container along with

the C-kanban to the producer area.2. At the producer area, there is a full container of

parts along with a P-kanban.

The user detaches the P-kanban from the fullcontainer and takes the container and the C-

kanban back to his or her area for immediateuse.

4 Steps o f Kanban

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4 Steps o f Kanban

3. The detached P-kanban goes back to theproducer area along with the empty container

The P-kanban is a signal that new parts are to bemanufactured or that new parts are to be placed

in the container and is attached to the containerwhen it is filled .

4. This process repeats itself during the typicalworkday.

The Kanban Sys tem

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The Kanban Sys tem

ProducerArea

StorageArea

UserArea

P-kanbanand

Container

C-kanbanand

Container

4

3 2

1

Figure 6.16

Enterp r ise Resource Planning

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MRP has evolved to include not only the materialsrequired in production, but also the labor hours,material cost, and other resources related toproduction.

In this approach the term MRP II is often used andthe word resourcereplaces the word requirements.

As this concept evolved and sophisticated softwarewas developed, these systems became known asenterpr ise resou rce plann ing(ERP) systems.



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The objective of an ERP System is to reduce costsby integrating all of the operations of a firm.

Starts with the supplier of materials needed andflows through the organization to includeinvoicing the customer of the final product.

Data are entered only once into a database whereit can be quickly and easily accessed by anyone inthe organization.

Benefits include:

Reduced transaction costs. Increased speed and accuracy of information.



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Drawbacks to ERP: The software is expensive to buy and costly to

customize. Small systems can cost hundreds of thousands of

dollars.

Large systems can cost hundreds of millions.

The implementation of an ERP system mayrequire a company to change its normaloperations.

Employees are often resistant to change. Training employees on the use of the new

software can be expensive.


Copyr ight

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Copyr ight

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