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Independent

Demand InventoryPlanning

CHAPTER FOURTEEN

McGraw-Hill/Irwin Copyri ght 2011 by the McGraw-H il l Companies, Inc. Al l r ights reserved.

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*** Important note ***

Since the text contains advancedmaterials on inventory management,

which will confuse you, do not refer to thetext.

Notations and method should be used

consistently as this slides do.

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Types of Inventory

Inventory: supply of items held to meet demand

Customers

Suppliers

Raw Material ComponentsMRO

Maintenance, repair &operating supplies

Distribution

Work inProcess (WIP)

FinishedGoods (FGI)

Customers

Suppliers

Raw Material ComponentsMRO

Maintenance, repair &operating supplies

Distribution

Work inProcess (WIP)

FinishedGoods (FGI)

Transportation

73

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Inventory Control Objectives

We need to answer the following questionsin order to balance supply and demand,and balance costs and service levels.

Whendo I order?How muchdo I order?

Wheredo I deploy the inventory?

Howmuch?

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Functions of Inventory

To meet anticipated demand

To smooth production requirements

To decouple operations

To protect against stock-outs

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Functions of Inventory (Contd)

To help hedge against price increases

To permit operations through WIP

To take advantage of quantity discounts

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Disadvantages of Inventories

Difficult to Control

Determining optimal amountsStorage and maintenance

Handling inventory is a non-value added

activity

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Inventory Management

Ind ependent Demand: demand isbeyond control of the organization

Dependent Demand: demand isdriven by demand of another item

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Inventory Counting Systems

Periodic inventory System

Physical count of items made at periodic intervals

Perpetual Inventory SystemSystem that keeps trackof inventory continuously, thusmonitoring

current levels ofeach item

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Bullwhip Effect

Inventory oscillations become progressivelylarger looking backward through the supply chain

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Managing Inventory Across the Supply Chain

Col labo rative planning , forecast ing andreplenishment (CPFR): supply chain partnerssharing information

Vendor-managed Inventory (VMI): the vendor isresponsible for managing inventory for the customer

Vendor monitors and replenishes inventory balances

Customer saves holding costs

Vendor has higher visibility of inventory usage

711

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P&G:

Cross-docking:

Inventory Management in the supply

chain : Example (Wal-Mart)

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Managing InventoryABC Analysis

ABC analysis: ranking inventory by importance Paretos Law: small percentage of items have a

large impact profit

CItemsB

ItemsA

Items

0 20 50 100Cumulative Percentage of Items

100

95

80

50

0

CumulativePercentage

of Revenue

713

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Financial Impact of Inventory

Set-up (Ordering)CostPurchased items: placing and receiving orders

Holding (Carry ing ) Cos tsOpportunity cost (including cost of capital)Storage and warehouse managementTaxes and insurance

Obsolescence, spoilage, & shrinkageMaterial handling, tracking and management

714

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Total Inventory Costs

Total Invento ry Costs: sum of all relevantannual inventory costs. i.e. total set-up cost

+ total holding cost.

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Total Inventory Costs

TIC = annual ordering cost + annual carrying cost= (D/Q)(S) + (Q/2)(IC)

N = D/Q

A = Q/2

Where:N = orders per year A = average inventory level

D = annual demand S = order cost per orderQ = order quantity C = unit cost

I = % carrying cost per year

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Total Inventory Costs

Note that frequently holding cost is given as a singlenumber meaning H = IC

Example: H=$2/item/year

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Total Inventory Costs

If we need 3,000 units per year at a unit price of $20and we order 500 each time, at a cost of $50 perorder with a carrying cost of 20%, what is the TIC?

N = D/Q = 3000 / 500 = 6 order per year

A = Q/2 = 500 / 2 = 250 average inventory

TIC= ordering cost + carrying cost

= S (D/Q) + (IC)(Q/2)

= $50 (3000/500) + ($20*0.20)*(500/2) = $1,300

Where:N = D/Q Q = 500 A = Q/2 C = $20D = 3,000 S = $50 I= 0.20

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Total Inventory Costs

If we need 3,000 units per year at a units price of $20and we order 200each time, at a cost of $50 perorder with a carrying cost of 20%, what is the TIC?

N = D/Q = 3000 / 200 = 15 order per year

A = Q/2 = 200 / 2 = 100 average inventory

TIC= ordering cost + carrying cost

= S (D/Q) + ( IC )(Q/2)

= 50 (3000/200) + ($20*0.20)*(200/2) = $1,150

Where:N = D/Q Q = 500 A = Q/2 C = $20D = 3,000 S = $50 I = 0.20

Example 14-21419

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Economic Order Quantity (EOQ)

Econom ic Order Quant i ty (EOQ): minimizestotal acquisition costs; point at which holdingand orders costs are equal

How muchto order

H

DSor

IC

DSEOQ

22D = Annual DemandS= Ordering cost

I= Percent of unit costC = Unit costH= IC= holding cost of item

per year

1420

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EOQ Model

Average

inventory

1 year

Q

0TimeMany orders but low average inventory

Average

inventory

1 year

Q

0TimeFew orders but high average inventory

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Economic Order Quantity (EOQ)

Carrying Cost

Order Quantity (Q)

C

ost

Order Cost

Carrying + Order

EOQ1422

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Economic Order Quantity (EOQ)

If we need 3,000 units per year at a unit price of$20, at a cost of $50 per order with a carryingcost of 20%, what is lowest TIC order quantity?

ICDSEOQ 2

D = 3,000S= $50C = $20I = 20%

86.273

20.0*20

50*3000*2

Example 14-31423

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What is the optimal order quantity?

Example : D=48,000 units/year

S= $20/order

I= 18%, c=$100

EOQ Example

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Example : D=12,000 units/year

S= $60/order, H= $10/unit/yearQ= order quantity,

Q*=optimal order quantity

What is the optimal order quantity?

EOQ theorem

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Production Order Quantity Model

= POQ Model

It is also called Economic Production QuantityModel

= EPQ Model

Production Order Quantity Model

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Suited for Production Environment

Provides Production lot size

POQ Model

POQ Model:Invent ory Levels

POQ Model:POQ Model:Invent ory LevelsInvent ory Levels

TimeTime

Inventory LevelInventory Level

ProductionProductionPortion ofPortion of

CycleCycle

Max. InventoryMax. InventoryQ(1Q(1-- d/p)d/p)

Q*Q*

SupplySupply

BeginsBegins

SupplySupply

EndsEnds

Inventory level with no demandInventory level with no demand

Demand portion ofDemand portion of

cycle with no supplycycle with no supply

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Let,

D= Demand per year

S= Setup cost

H=Holding cost

d=demand per day

p=production per day

POQ Model Equations

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Optimal order quantity or production lot size

Max. Inventory level

Setup cost

Holding cost

POQ Model Equations

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Production Order Quantity

p

dIC

DSPOQ

1

2D = 500,000S= $2,000

I= 25%

C = $10

d = 2,000p = 5,000

515,3684.514,36

000,5

000,2110$*%25

000,2$*000,500*2

Example 14-6 1430

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The Watkins Chemical Company produces achemical compound that is used as a lawn fertilizer.The compound can be produced at a rate of 10,000pounds per day. Demand for the compound is 0.6

million pounds per year. The fixed cost of setting upfor a production run of the chemical is $1,500, and thevariable cost of production is $3.50 per pound. Thecompany uses an annual interest rate of 22% to

account for the cost of capital, and the annual costs ofstorage and handling of the chemical amount to 12%of the value. Assume that there are 250 working daysin a year. What is the optimal lot size, maximuminventory level, and total cost?

POQ Example

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Quantity discounts

All-Units Discount Order Cost Function

Incremental Discount Cost Function

C1=.29

C0=.30

C2=.28

500 1,000 Q

C(Q)

C1=.29

C0=.30

C2=.28

500 1,000 Q

C(Q)

295

150

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Quantity Discount Models

Material cost:Total material cost is affected by the Discount (%)Unit cost if first $5.00, then $4.80,and finally $4.75

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6-34

Quantity Discount Models

Total Cost Curves for each of the 3 discount plans

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All-Units quantity discounts

1. Consider the all-units quantity discount schedule below.

Units Ordered Price Per Unit EOQ at that Price

1-400 $100 200401-800 $90 506

801-1000 $80 700

1001-1250 $70 800

1251-1500 $60 900 1501 $50 1400

What are the possible optimal order quantities?

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6-36

Steps for Solving Quantity Discount

1. Compute EOQ for each discount price:

2. If EOQ < discount minimum level, let Q =minimum.

3. For each EOQ or minimum Q, compute total

cost:TC = DC + (D/Q)(S) + (Q/2)(H)

4. Choose the lowest cost quantity from alllevels.

Q* IC

2DS

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All-Units quantity discounts

A supplier for Lower Florida Keys Health System

has introduced all-units quantity discounts

to encourage larger order quantitiesof a special catheter. The price schedule is:

Order Quantity Price per Unit

0-299 $60.00

300-499 $58.80

500 or more $57.00

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All-Units quantity discounts

The firm estimates that its annual demand

for this item is 936 units, its setup cost is $45per order, and its annual holding cost is 25%of the catheters unit price.

Whats the best order size?

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All-Units quantity discounts

Calculate EOQ

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All-Units quantity discounts

Total cost for the quantity discount case:

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Homework problems for ch 14

Problem 1. The I-75 Carpet Discount storein Washington stocks carpet in its warehouseand sells it through an adjoining showroom.The store keeps several brands and styles ofcarpet in stock; however, its biggest selling

item is Super Shag carpet. The store wantsto determine the optimal order size and totalinventory cost for this brand of carpet givenan estimated annual demand of 10,000 yards

of carpet, annual carrying cost of $0.765 peryard, and an ordering cost of $150.

a) Decide the optimal order quantity

b) Calculate the minimum total annual

inventory cost

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Homework problems for ch 14

Problem 2. Ashlees Beach Chairs companyproduces upscale beach chairs. Annualdemand for the chairs is estimated at 18,000units. The frames are made in batchesbefore the final assembly process. Ashleesframe department can produce 2,500 framesper month. The setup cost is $800 per order,and the annual holding cost is $18 per unit.

The company operates 20 days per month.a) Determine the optimal lot size

b) Calculate the total holding cost

c) Calculate maximum inventory level

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Homework problems for ch 14

Problem 3.Sharp inc, a company thatmarkets painless hypodermic needles tohospitals, would like to reduce its inventorycost by determining the optimal number ofhypodermic needles to obtain per order. Theannual demand is 1,000 units; the holdingcost per unit per year is $0.5. The inventorymanager of Sharp inc, calculated the optimal

order quantity of 200 units.a) What is the ordering cost per order in the

company

b) What is the total ordering cost?

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Homework problems for ch 14

Problem 4 . A produce distributor uses 800packing crates a month, which it purchases ata cost of $10 each. The manager has

assigned an annual carrying cost of 35percent of the purchase price per crate.Ordering costs are $28 each time. Currentlythe manager orders once a month. Howmuch could the firm save annually in orderingand carrying costs by using the EOQ?

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Homework problems for ch 14

Problem 5. Ross Whites machine shop uses 2,500brackets during the course of a year, and this usageis relatively constant throughout the year. Thesebrackets are purchased for $15 each. The holding

cost per bracket per year is 10% of the unit cost andthe ordering cost per order is $18.75. There are 250working days per year.

a) What is EOQ?

b) In minimizing cost, how many orders would bemade each year?

c) What would be the total annual inventorycost?(i.e. addition of total ordering and holding cost)

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Homework problems for ch 14

Problem 6. A hospital buys disposablesurgical packages from Pfishier, Inc.Pfishers price schedule is $50.25 per

package on order of 1 to 199 packages, and$49.00 per packages on orders of 200 ormore packages. Ordering cost is $64 perorder, and annual holding cost is 20 percent

of the per-unit purchase price. Annualdemand is 490 packages. What is the bestpurchase quantity?