Inventory

Chapter. 8 Independent Demand -Inventory

Prepared by :

Arya Wirabhuana, ST, M.Sc

Inventory System

Defined

Inventory is the stock of any item or resource used

in an organization. These items or resources can

include: raw materials, finished products,

component parts, supplies, and work-in-process.

An inventory system is the set of policies and

controls that monitor levels of inventory and

determines what levels should be maintained,

when stock should be replenished, and how large

orders should be.

A Water Tank Analogy for Inventory

Supply Rate

Inventory Level

Demand Rate

Inventory Level

Inventory Cost Structures

Item cost

Ordering (or setup) cost

Carrying (or holding) cost:

– Cost of capital

– Cost of storage

– Cost of obsolescence, deterioration, and loss

Stock out cost

7

Classifying Inventory Models

Fixed-Order Quantity Models

– Event triggered

Fixed-Time Period Models

– Time triggered

Economic Order Quantity (EOQ)

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 batch and

the lot is received all at once

Unit cost is constant (no quantity discounts)

Carrying cost depends linearly on the average level of

inventory

Ordering (setup) cost per order is fixed

The item is a single product

EOQ Inventory Levels

Time

Lot size = Q

Order

Interval

Average Inventory

Level = Q/2

Total Cost of Inventory

Basic Fixed-Order Quantity (EOQ) Model Formula

TC = DC + D

Q S +

Q

2 H

Total Annual Cost =

Annual

Purchase

Cost

Annual

Ordering

Cost

Annual

Holding

Cost + +

TC = Total annual cost

D = Demand

C = Cost per unit

Q = Order quantity

S = Cost of placing an order

or setup cost

R = Reorder point

L = Lead time

H = Annual holding and storage

cost per unit of inventory

Continuous Review System

Assumption of “constant demand” is relaxed.

Monitoring of “on hand” stock position in a

continuous system

Q system (another name for continuous

review system)

A Continuous Review (Q) System

R = Reorder Point

Q = Order Quantity

L = Lead time

Periodic Review System

All assumption of EOQ (except that demand

is constant and “no stockout”) remains in

effect.

Also known as “P System” or “Fixed-order-

Interval System”

A Periodic Review (P) System

“Time Between Orders (P) and

Target Level (T) Calculation

DCi

SP

2

'' smT Where:

m’ = average demand over P+L

s’ = safety stock

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.

Special Purpose Model: Price-Break

Model Formula

Cost Holding Annual

Cost) Setupor der Demand)(Or 2(Annual =

iC

2DS = QOPT

Based on the same assumptions as the EOQ model,

the price-break model has a similar Qopt formula:

i = percentage of unit cost attributed to carrying inventory

C = cost per unit

Since “C” changes for each price-break, the formula above will

have to be used with each price-break cost value.

Price-Break Example Problem Data

(Part 1)

A company has a chance to reduce their inventory

ordering costs by placing larger quantity orders using the

price-break order quantity schedule below. What should

their optimal order quantity be if this company purchases

this single inventory item with an e-mail ordering cost of

$4, a carrying cost rate of 2% of the inventory cost of the

item, and an annual demand of 10,000 units?

Order Quantity(units) Price/unit($)

0 to 2,499 $1.20

2,500 to 3,999 1.00

4,000 or more .98

Price-Break Example Solution (Part 2)

units 1,826 = 0.02(1.20)

4)2(10,000)( =

iC

2DS = QOPT

Annual Demand (D)= 10,000 units

Cost to place an order (S)= $4

First, plug data into formula for each price-break value of “C”.

units 2,000 = 0.02(1.00)

4)2(10,000)( =

iC

2DS = QOPT

units 2,020 = 0.02(0.98)

4)2(10,000)( =

iC

2DS = QOPT

Carrying cost % of total cost (i)= 2%

Cost per unit (C) = $1.20, $1.00, $0.98

Interval from 0 to 2499, the

Qopt value is feasible.

Interval from 2500-3999, the

Qopt value is not feasible.

Interval from 4000 & more, the

Qopt value is not feasible.

Next, determine if the computed Qopt values are feasible or not.

Price-Break Example Solution (Part 3)

Since the feasible solution occurred in the first price-break,

it means that all the other true Qopt values occur at the

beginnings of each price-break interval. Why?

0 1826 2500 4000 Order Quantity

Total

annual

costs So the candidates

for the price-breaks

are 1826, 2500,

and 4000 units.

Because the total annual cost function is a

“u” shaped function.

Annual Usage of Items by Dollar Value

Item

Annual Usage in

Units Unit Cost Dollar Usage

Percentage of

Total 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%

ABC Chart

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.

Pe

rce

nt

Usa

ge

0.0%

20.0%

40.0%

60.0%

80.0%

100.0%

120.0%

Cu

mu

lati

ve

% U

sag

e

Percentage of Total Dollar Usage Cumulative Percentage

A B C

Dependent Demand-

Inventory

Attribute MRP Order Point

Demand Dependent Independent

Order philosophy Requirements Replenishment

Forecast Based on master schedule Based on past demand

Control concept Control all items ABC

Objectives Meet manufacturing needs Meet customer needs

Lot sizing Discrete EOQ

Demand pattern Lumpy but predictable Random

Types of inventory Work in process and raw

materials

Finished goods and spare

parts

Attribute MRP Order Point

Demand Dependent Independent

Order philosophy Requirements Replenishment

Forecast Based on master schedule Based on past demand

Control concept Control all items ABC

Objectives Meet manufacturing needs Meet customer needs

Lot sizing Discrete EOQ

Demand pattern Lumpy but predictable Random

Types of inventory Work in process and raw

materials

Finished goods and spare

parts

MRP versus Order-Point Systems

3

Material Requirements Planning

How much of an item is needed?

When is an item needed to complete

– a specified number of units...

– in a specified period of time?

Dependent demand drives MRP

4

Introductory

Example - Dependent Demand

B(4)

E(1) D(2)

C(2)

F(2) D(3)

A

Product Structure Tree for Assembly A

Lead Times

A 1 day

B 2 days

C 1 day

D 3 days

E 4 days

F 1 day

Demand

Day 10 50 A

Day 8 20 B (Spares)

Day 6 15 D (Spares)

Create a schedule to satisfy demand.

LT = 1 day

Day: 1 2 3 4 5 6 7 8 9 10

A Required 50

Order Placement 50

5

D a y : 1 2 3 4 5 6 7 8 9 1 0

A R e q u ire d 5 0

O rd e r P la c e m e n t 5 0

B R e q u ire d 2 0 2 0 0

O rd e r P la c e m e n t 2 0 2 0 0

Spares LT = 2

B(4)

E(1) D(2)

C(2)

F(2) D(3)

A

6

Day: 1 2 3 4 5 6 7 8 9 10

A Required 50

LT=1 Order Placement 50

B Required 20 200

LT=2 Order Placement 20 200

C Required 100


D Required 55 400 300

LT=3 Order Placement 55 400 300

E Required 20 200

LT=4 Order Placement 20 200

F Required 200


B(4)

E(1) D(2)

C(2)

F(2) D(3)

A

40 + 15 spares

Part D: Day 6

7

9

Time Fences

Frozen

– No schedule changes allowed within this window

Moderately Firm

– Specific changes allowed within product groups

as long as parts are available

Flexible

– Significant variation allowed as long as overall

capacity requirements remain at the same levels

10

Time Fences

8 15 26

Weeks

Frozen Moderately

Firm Flexible

Firm Customer Orders

Forecast and available

capacity

Capacity

Firm orders

from known

customers

Forecasts

of demand

from random

customers

Aggregate

product

plan

Master

production

schedule

(MPS)

Material

planning

(MRP)

Engineering

design

changes

Bill of

material

file

Inventory

transactions

Inventory

record

file

Reports

12

18

Another MRP Example

A(2) B(1)

D(5) C(2)

X

C(3)

Item On-Hand Lead Time (Weeks)

X 50 2

A 75 3

B 25 1

C 10 2

D 20 2

Requirements include 95 units (80 firm orders and 15 forecast) of X in week 10

plus the following spares:

Spares 1 2 3 4 5 6 7 8 9 10

A 12

B 7

C 10

D 15

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Adding some more terminology

Gross Requirements

On-hand

Net requirements

Planned order receipt

Planned order release

C Gross Requirements 45 36 64

LT=2 On-Hand=10 10

Net Requirements 35 36 64

Planned Order Receipt 35 36 64

Planner Order Release 35 36 64

D Gross Requirements 15 135

LT=2 On-Hand=20 15 5

Net Requirements 130

Planned Order Receipt 130

Planner Order Release 130

A(2) B(1)

D(5) C(2)

X

C(3)

20

Day: 1 2 3 4 5 6 7 8 9 10

X Gross Requirements 95

LT=2 On-Hand=50 50

Net Requirements 45



A Gross Requirements 90 12

LT=3 On-Hand=75 75

Net Requirements 15 12

Planned Order Receipt 15 12

Planner Order Release 15 12

B Gross Requirements 7 45


Net Requirements 27



C Gross Requirements 45 36 54 10

LT=2 On-Hand=10 10

Net Requirements 35 36 54 10

Planned Order Receipt 35 36 54 10

Planner Order Release 35 36 54 10

D Gross Requirements 15 135


Net Requirements 130



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Manufacturing Resource Planning (MRP II)

Goal: Plan and monitor all resources of a

manufacturing firm (closed loop):

– manufacturing

– marketing

– finance

– engineering

Simulate the manufacturing system

Next : Supply Chain Management

Inventory

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