Independent Demand Inventory Planning CHAPTER FOURTEEN McGraw-Hill/Irwin Copyright © 2011 by the...

Independent Demand Inventory Planning

CHAPTER FOURTEEN

McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.

*** Important note ****** Important note ****** Important note ****** Important note ***

• Since the text contains advanced materials on inventory management, which will confuse you, do not refer to the text.

• Notations and method should be used consistently as this slides do.

Types of InventoryTypes of Inventory

• Inventory: supply of items held to meet demand

Customers

Suppliers

Raw Material ComponentsMRO

Maintenance, repair & operating supplies

Distribution

Work in Process (WIP)

Finished Goods (FGI)

Customers

Suppliers

Raw Material ComponentsMRO

Maintenance, repair & operating supplies

Distribution

Work in Process (WIP)

Finished Goods (FGI)

Transportation

7–7–33

Inventory Control ObjectivesInventory Control Objectives

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

–When do I order?–How much do I order?–Where do I deploy the inventory?

Where?

How much?

When

?

14–14–44

Functions of InventoryFunctions of InventoryFunctions of InventoryFunctions of Inventory

• To meet anticipated demand

• To smooth production requirements

• To decouple operations

• To protect against stock-outs

Functions of Inventory (Cont’d)Functions of Inventory (Cont’d)Functions of Inventory (Cont’d)Functions of Inventory (Cont’d)

• To help hedge against price increases

• To permit operations through WIP

• To take advantage of quantity discounts

Disadvantages of InventoriesDisadvantages of InventoriesDisadvantages of InventoriesDisadvantages of Inventories

Difficult to Control

Determining optimal amounts

Storage and maintenance

Handling inventory is a non-value added

activity

Inventory ManagementInventory Management

• Independent Demand: demand is beyond control of the organization

• Dependent Demand: demand is driven by demand of another item

14–14–88

Inventory Counting SystemsInventory Counting SystemsInventory Counting SystemsInventory Counting Systems

• Periodic inventory SystemPhysical count of items made at periodic intervals

• Perpetual Inventory System System that keeps track System that keeps track of inventory continuously, thus of inventory continuously, thus monitoringmonitoringcurrent levels of current levels of each itemeach item

Bullwhip EffectBullwhip EffectBullwhip EffectBullwhip Effect

Inventory oscillations become progressivelylarger looking backward through the supply chain

Managing Inventory Across the Supply ChainManaging Inventory Across the Supply ChainManaging Inventory Across the Supply ChainManaging Inventory Across the Supply Chain

• Collaborative planning, forecasting and replenishment (CPFR): supply chain partners sharing information

• Vendor-managed Inventory (VMI): the vendor is responsible for managing inventory for the customer

–Vendor monitors and replenishes inventory balances

–Customer saves holding costs

–Vendor has higher visibility of inventory usage

7–7–1111

P&G:

Cross-docking:

Inventory Management in the supply Inventory Management in the supply chain : Example (Wal-Mart)chain : Example (Wal-Mart)

Inventory Management in the supply Inventory Management in the supply chain : Example (Wal-Mart)chain : Example (Wal-Mart)

Managing Inventory – ABC AnalysisManaging Inventory – ABC AnalysisManaging Inventory – ABC AnalysisManaging Inventory – ABC Analysis

• ABC analysis: ranking inventory by importance• Pareto’s Law: small percentage of items have a

large impact profit

CItems B

ItemsAItems

0 20 50 100Cumulative Percentage of Items

10095

80

50

0

CumulativePercentage of Revenue

7–7–1313

Financial Impact of InventoryFinancial Impact of Inventory

• Set-up (Ordering)Cost–Purchased items: placing and receiving orders

• Holding (Carrying ) Costs–Opportunity cost (including cost of capital)–Storage and warehouse management–Taxes and insurance–Obsolescence, spoilage, & shrinkage–Material handling, tracking and management

7–7–1414

Carrying costO

rder

ing

cost

Total Inventory Costs Total Inventory Costs

• Total Inventory Costs: sum of all relevant annual inventory costs. i.e. total set-up cost + total holding cost.

14–14–1515


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

I = % carrying cost per year

14–14–1616


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

Example: H =$2/item/year

14–14–1717


If we need 3,000 units per year at a unit price of $20 and we order 500 each time, at a cost of $50 per order 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

14–14–1818


If we need 3,000 units per year at a units price of $20 and we order 200 each time, at a cost of $50 per order 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 14-214–14–1919

Economic Order Quantity (EOQ) Economic Order Quantity (EOQ)

• Economic Order Quantity (EOQ): minimizes total acquisition costs; point at which holding and orders costs are equal

• How much to order

H

DSor

IC

DSEOQ

22D = Annual Demand

S= Ordering costI= Percent of unit costC = Unit cost

H= IC= holding cost of item per year

14–14–2020

EOQ ModelEOQ ModelEOQ ModelEOQ Model

Averageinventory

1 year

Q

0TimeMany orders but low average inventory

Averageinventory

1 year

Q

0 TimeFew orders but high average inventory


Carrying Cost

Order Quantity (Q)

Cos

t

Order Cost

Carrying + Order

EOQ14–14–2222


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

IC

DSEOQ

2

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

I = 20%

86.27320.0*20

50*3000*2

Example 14-314–14–2323

What is the optimal order quantity?

Example : D=48,000 units/year

S= $20/order

I= 18%, c=$100

EOQ ExampleEOQ ExampleEOQ ExampleEOQ Example

Example : D=12,000 units/year

S= $60/order, H= $10/unit/year

Q= order quantity,

Q*=optimal order quantity

What is the optimal order quantity?

EOQ theoremEOQ theoremEOQ theoremEOQ theorem

Production Order Quantity Model

= POQ Model

It is also called Economic Production Quantity Model

= EPQ Model

Production Order Quantity ModelProduction Order Quantity ModelProduction Order Quantity ModelProduction Order Quantity Model

■ Suited for Production Environment

■ Provides Production lot size

POQ ModelPOQ ModelPOQ ModelPOQ Model

POQ Model: Inventory Levels

POQ Model: POQ Model: Inventory LevelsInventory Levels

TimeTime

Inventory LevelInventory Level

Production Production Portion of Portion of

CycleCycle

Max. Inventory Max. Inventory Q·(1Q·(1-- d/p)d/p)

Q*Q*

Supply Supply BeginsBegins

Supply Supply EndsEnds

Inventory level with no demandInventory level with no demand

Demand portion of Demand portion of cycle with no supplycycle with no supply

Let,

D= Demand per year

S= Setup cost

H=Holding cost

d=demand per day

p=production per day

POQ Model EquationsPOQ Model EquationsPOQ Model EquationsPOQ Model Equations

■ Optimal order quantity or production lot size

■ Max. Inventory level

■ Setup cost

■ Holding cost

POQ Model EquationsPOQ Model EquationsPOQ Model EquationsPOQ Model Equations

Production Order Quantity Production Order Quantity

pd

IC

DSPOQ

1

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

I= 25%

C = $10d = 2,000 p = 5,000

515,3684.514,36

000,5000,2

110$*%25

000,2$*000,500*2

Example 14-6 14–14–3030

■ The Watkins Chemical Company produces a chemical compound that is used as a lawn fertilizer. The compound can be produced at a rate of 10,000 pounds per day. Demand for the compound is 0.6 million pounds per year. The fixed cost of setting up for a production run of the chemical is $1,500, and the variable cost of production is $3.50 per pound. The company uses an annual interest rate of 22% to account for the cost of capital, and the annual costs of storage and handling of the chemical amount to 12% of the value. Assume that there are 250 working days in a year. What is the optimal lot size, maximum inventory level, and total cost?

POQ ExamplePOQ ExamplePOQ ExamplePOQ Example

Quantity discountsQuantity discountsQuantity discountsQuantity discountsA l l - U n i t s D i s c o u n t O r d e r C o s t F u n c t i o n

I n c r e m e n t a l D i s c o u n t C o s t F u n c t i o n

C 1 = . 2 9

C 0 = . 3 0

C 2 = . 2 8

5 0 0 1 , 0 0 0 Q

C(

Q)

C 1 = . 2 9

C 0 = . 3 0

C 2 = . 2 8

5 0 0 1 , 0 0 0 Q

C(

Q)

2 9 5

1 5 0

6-6-3333

Quantity Discount Models Quantity Discount Models Quantity Discount Models 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

6-6-3434

Quantity Discount ModelsQuantity Discount ModelsQuantity Discount ModelsQuantity Discount Models

Total Cost Curves for each of the 3 discount plans

All-Units quantity discountsAll-Units quantity discountsAll-Units quantity discountsAll-Units quantity discounts

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

Units Ordered Price Per Unit EOQ at that Price

1-400 $100 200

401-800 $90 506

801-1000 $80 700

1001-1250 $70 800

1251-1500 $60 900

≥ 1501 $50 1400

What are the possible optimal order quantities?

6-6-3636

Steps for Solving Quantity DiscountSteps for Solving Quantity DiscountSteps for Solving Quantity DiscountSteps 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 all levels.

Q * IC2DS


A supplier for Lower Florida Keys Health System

has introduced all-units quantity discounts

to encourage larger order quantities

of 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


The firm estimates that its annual demand

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

What’s the best order size?


Calculate EOQ


Total cost for the quantity discount case:

Homework problems for ch 14Homework problems for ch 14Homework problems for ch 14Homework problems for ch 14

• Problem 1. The I-75 Carpet Discount store in Washington stocks carpet in its warehouse and sells it through an adjoining showroom. The store keeps several brands and styles of carpet in stock; however, its biggest selling item is Super Shag carpet. The store wants to determine the optimal order size and total inventory cost for this brand of carpet given an estimated annual demand of 10,000 yards of carpet, annual carrying cost of $0.765 per yard, and an ordering cost of $150.

a) Decide the optimal order quantity

b) Calculate the minimum total annual inventory cost


• Problem 2. Ashlee’s Beach Chairs company produces upscale beach chairs. Annual demand for the chairs is estimated at 18,000 units. The frames are made in batches before the final assembly process. Ashlee’s frame department can produce 2,500 frames per 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


Problem 3. Sharp inc, a company that markets painless hypodermic needles to hospitals, would like to reduce its inventory cost by determining the optimal number of hypodermic needles to obtain per order. The annual demand is 1,000 units; the holding cost per unit per year is $0.5. The inventory manager 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?


Problem 4 . A produce distributor uses 800 packing crates a month, which it purchases at a cost of $10 each. The manager has assigned an annual carrying cost of 35 percent of the purchase price per crate. Ordering costs are $28 each time. Currently the manager orders once a month. How much could the firm save annually in ordering and carrying costs by using the EOQ?


Problem 5. Ross White’s machine shop uses 2,500 brackets during the course of a year, and this usage is relatively constant throughout the year. These brackets are purchased for $15 each. The holding cost per bracket per year is 10% of the unit cost and the ordering cost per order is $18.75. There are 250 working days per year.

a) What is EOQ?

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

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


Problem 6. A hospital buys disposable surgical packages from Pfishier, Inc. Pfisher’s price schedule is $50.25 per package on order of 1 to 199 packages, and $49.00 per packages on orders of 200 or more packages. Ordering cost is $64 per order, and annual holding cost is 20 percent of the per-unit purchase price. Annual demand is 490 packages. What is the best purchase quantity?

Independent Demand Inventory Planning CHAPTER FOURTEEN McGraw-Hill/Irwin Copyright © 2011 by the...

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