Chap015.ppt Independent-Demand Inventory

7/30/2019 Chap015.ppt Independent-Demand Inventory

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McGraw-Hill/Irwin

The McGraw-Hill Companies, Inc. 2007, All Rights Reserved

Independent-Demand

Inventory

Chapter 15


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Chapter 15 Outline

Introduction

Purpose of Inventories

Inventory Cost Structures

Independent versus Dependent DemandEconomic Order Quantity

Continuous Review System

Periodic Review System

Using P and Q System in Practice

ABC Inventory Management


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Introduction

Inventory: a stock of materials used to

facilitate production or to satisfy customer

demand.

Types of inventory

Raw materials (RM)

Work in process (WIP)

Finished goods (FG)

Maintenance, repair & operating supplies (MRO)


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A Material-Flow Process

Work in

process

Work in

process

Work in

process

Finished

goods

Raw

MaterialsVendors Customer

Productive Process


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A Water Tank Analogy for Inventory

Supply Rate

Inventory Level

Demand Rate

InventoryLevel


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Purpose of Inventories (1)

To protect against uncertaintiesin demand (finished goods, MRO)

supply (RM, MRO)

lead times (RM/PP or WIP)schedule changes (WIP)

To allow economic production and purchase

(as in discounts for buying RM/PP in bulk)


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Purpose of Inventories (2)

To cover anticipated changes in demand (asin a level strategy) or supply

finished goods

RM/PP

To provide for transit (pipeline inventories)

RM/PP

finished goodsWIP (independence of operations)


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Inventory Cost Structures (1)

Item or SKU cost

Expressed as cost per unit or SKU. Gets into

LIFO and FIFO issues.

Problem can be compounded by quantity

discounts.


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Ordering (or setup) cost

Paperwork, worker time (ordering)

worker time, downtime (setup)Typically expressed as a fixed cost per order or

setup.


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Carrying (or holding) cost: Cost of capital (market rate or internal rate of return) Cost of storage (building, utilities, insurance, handling)

Cost of obsolescence, deterioration, and loss(shrinkage)

Management cost (record keeping, counting)

Typically expressed as a percentage of SKU cost.Average in U.S. is estimated to be 35 percentperyear.

Businesses often use only cost of capital(understatement).


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How the 35 percent carrying cost is distributedCost of Capital9-20 percent

Obsolescence2-5 percent

Storage2-5 percent

Material Handling1-3 percent

Shrinkage1-3 percent

Taxes & Insurance1-3 percent

Source: Mark Williams, APICS Instructor Listserv, 22 January 2001


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Stock out cost (back order or lost sales)

record maintenance

lost income

customer dissatisfaction

Typically expressed as a fixed cost per backorderor as a function of aging of backorders.


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Two Forms of Demand (1)

Independent demand(this chapter)

finished goods, spare parts, MRO

based on market demandrequires forecasting

managed using replenishment philosophy, i.e.

reorder when reach a pre-specified level.


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Two Forms of Demand (2)

Dependent demand(next two chapters)

parts that go into the finished products, RM/PP

orWIP

dependent demand is a known function ofindependent demand

calculate instead of forecast

Managed using a requirements philosophy,i.e. only ordered as needed for higher level

components or products.


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Independent versus Dependent

Demand

A pattern plus random influences Lumpy because of production lots


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Economic Order Quantity (EOQ)

Developed in 1915 by F.W. HarrisAnswers the question How much do I order?

Used forindependent demanditems.

Objective is to find order quantity (Q) that minimizesthe total cost (TC) of managing inventory.

Must be calculated separately for each SKU.

Widely used and very robust (i.e. works well in a lotof situations, even when its assumptions dont holdexactly).


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Economic Order Quantity (EOQ)

Basic Model Assumptions

Demand rate is constant, recurring, and known.

Lead time is constant and known.

No stockouts allowed.

Material is ordered or produced in a lot or batchand the lot is received all at once

Costs are constant Unit cost is constant (no quantity discounts)

Carrying cost is a constant per unit (SKU) Ordering (setup) cost per order is fixed

The item is a single product or SKU.


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EOQ Lot Size Choice

There is a trade-off between frequency of

ordering (or the size of the order) and the

inventory level.

Frequent orders (small lot size) lead to a lower

average inventory size, i.e. higher ordering cost

and lower holding cost.

Fewer orders (large lot size) lead to a largeraverage inventory size, i.e. lower ordering cost and

higher holding cost.


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EOQ Inventory Levels

(sawtooth model)

Time

Lot size = Q

Order

Interval

Average I nventory

Level = Q/2


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Notations and measurement

units in EOQD= Demand rate, units per year

S= Cost per order placed, or setup cost,

dollars per order

C= Unit cost, dollars per unit

i= Carrying rate, percent of value per year

Q= Lot size, unitsTC= total of ordering cost plus carrying cost


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Cost Equations in EOQ

Ordering cost = (cost per order) x orders per

year) = SD/Q

Carrying cost per year = (annual carrying rate) x

(unit cost) x average inventory = iCQ/2

Total annual cost (TC) = ordering cost per year

+ carrying cost per year = SD/Q + iCQ/2


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Total Cost of Inventory


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TC and EOQ

TC = ordering cost + holding cost

= S*(D/Q) + iC*(Q/2)

EOQ =

note: Although we have used annualcosts, any time period is allright. Just be consistent! The same is true for currency

designations.

iC

SDQ

2


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EOQ Example

Sales = 10 cases/week S = $12/orderi = 30 pct/year C = $80/case

_________

EOQ = (2SD)/iC = SQRT[(2*12*10*52)/(80*.3)]

= SQRT[12,480/24] = 22.8 cases/order

TC = ordering cost + holding cost

= S*(D/Q) + iC*(Q/2) = 10(520/22.8) + 24 * 11.4

= 228.70 + 273.60 = $547.28/year

If order 22 cases instead, TC = $547.64; if 23, TC = $547.30


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EOQ Example

Total Inventory Cost

0

200

400

600

800

13 17 21 24 28 32 36 40

Order Size

Dollars


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Relax assumption of constant demand.Demand is assumed to be random.

Check inventory position each time there is a

demand (i.e continuously).If inventory position drops below the reorderpoint, place an order for the EOQ.

Also called fixed-order-quantity or Q system(the fixed order size is EOQ).


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A Continuous Review (Q) System

R = Reorder Point

Q = Order Quantity

L = Lead time


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A Continuous Review (Q) System

Amount to order = EOQOrder when inventory position = reorder point.

Reorder point = lead time * demand/period

= R = lead time demand (when demand is

constant)

Reorder point is independent of EOQ!EOQ tells how much to order.

Reorder pointtells when to order.


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Service Level

When demand is random, the reorder point

must take into account the service level or fill

rate.

Service level has many definitions:

Probability that all orders will be refilled while

waiting for an order to arrive.

Percentage of demand filled from stock in a timeperiod.

Percentage of time the system has stock on hand.


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Probability Distribution of Demand over Lead Time

m = mean demand R = Reorder point s = Safety stock


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Periodic Review System (1)

Instead of reviewing continuously, we review

the inventory position atfixed intervals. For

example, the bread truck visits the grocery

store on the same days every week.

Also known as P system, Fixed-order-

interval system or Fixed-order-period

system


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Periodic Review System (2)

Each time we review the inventory, we either

order or dont. The decision depends upon our

reorder point.

The amount we order may be fixed, or may be

the amount needed to bring us up to a target

(T).


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A Periodic Review (P) System


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Time Between Orders (P) and

Target Level (T) Calculation

DCi

SP

2

'' smT Where:

T = target inventory levelm = average demand over P+L

s = safety stock


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Using P and Q System in Practice

Use P system when orders must be placed at

specified intervals.

Use P systems when multiple items are

ordered from the same supplier (joint-

replenishment).

Use P system for inexpensive items.


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Using P and Q Systems in

PracticeP may be easier to use since levels arereviewed less often.

P requires more safety stock since may only

order at fixed points.

P is more likely to run out since cannot

respond to increases in demand immediately

Either may be more costly: P in safety

stock, Q in monitoring cost.


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Service Level versus Inventory Level (Figure 15.10)

1.1

2.52.42.32.22.12.01.91.81.7

1.61.5

1.31.2

1.0

1.4

75%

80%

85%

90%

95%

100%

105%

150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300

Average Inventory Level

ServiceLevel(%)

z values

100

100

Q


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ABC Inventory Management (1)

Based on Pareto concept (80/20 rule) and

total usage in dollars of each item.

Classification of items as A, B, or C based on

usage.

Purpose is to set priorities on effort used to

manage different SKUs, i.e. to allocate scarce

management resources.


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ABC Inventory Management (2)

A items: 20% of SKUs, 80% of dollars

B items: 30 % of SKUs, 15% of dollars

C items: 50 % of SKUs, 5% of dollars

Three classes is arbitrary; could be any number.

Percents are approximate.

Danger: dollar use may not reflect importance ofany given SKU!


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Annual Usage of Items by Dollar Value (Table 15.4)

Item

Annual Usage in

Units Unit Cost Dollar Usage

Percentage ofTotal Dollar

Usage

1 5,000 1.50$ 7,500$ 2.9%

2 1,500 8.00 12,000 4.7%

3 10,000 10.50 105,000 41.2%4 6,000 2.00 12,000 4.7%

5 7,500 0.50 3,750 1.5%

6 6,000 13.60 81,600 32.0%

7 5,000 0.75 3,750 1.5%

8 4,500 1.25 5,625 2.2%9 7,000 2.50 17,500 6.9%

10 3,000 2.00 6,000 2.4%

Total 254,725$ 100.0%


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ABC Chart for Table 15.4

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

35.0%

40.0%

45.0%

3 6 9 2 4 1 10 8 5 7

Item No.

PercentUsage

0.0%

20.0%

40.0%

60.0%

80.0%

100.0%

120.0%

Cumulative%

Usage

Percentage of Total Dollar Usage Cumulative Percentage

A B C


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Managing A items:

Diamonds


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Summary

IntroductionPurpose of Inventories

Inventory Cost Structures

Independent versus Dependent DemandEconomic Order Quantity


Periodic Review SystemUsing P and Q System in Practice

ABC Inventory Management


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End of Chapter Fifteen

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Chap015.ppt Independent-Demand Inventory