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Inventory Management

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Learning Objectives

• Define the term inventory and list the major reasons for holding inventories; and list the main requirements for effective inventory management.

• Discuss the nature and importance of service inventories

• Discuss the objectives of inventory management.

• Describe the A-B-C approach and explain how it is useful.

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Learning Objectives

• Describe the basic EOQ model and its assumptions and solve typical problems.

• Describe the economic production quantity model and solve typical problems.

• Describe reorder point models and solve typical problems.

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• Examples:– Parts in a factory– Paper towels in your cupboard– Customers on hold– Paperwork in secretary’s in-box

• Not limited to physical products

Inventory is DELAY in business process.

What is inventory?

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What is inventory?

TransformationInput OutputRaw materials• Materials received• Customers waiting

in a bank• Paperwork in in-

box

Work-in-Process• Semi-finished

products• Customers at the

counter• Paperwork on

desk

Finished goods• Products waiting

to be shipped• Customers

leaving the bank• Paperwork in out-

box

Within organization:

Between organizations: Goods-in-transit

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Types of Inventories

1. Raw materials & purchased parts

2. Partially completed goods called work in progress (WIP)

3. Finished-goods inventories (manufacturing firms or merchandise, retail stores)

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Types of Inventories (Cont’d)

4. Replacement parts, tools, & supplies

5. Goods-in-transit to warehouses or customers

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Functions of Inventory

• To meet anticipated demand (anticipation stock)

• To maintain continuity of operations (buffer stock)

• To protect against stock-outs, i.e. decrease the risk of shortages due to delayed delivery and unexpected increases in demand, (safety stock)

• To take advantage of quantity discounts

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Objective of Inventory Control

• To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds (limits), there are 2 concerns:

1. Level of customer service

• Right goods (in sufficient quantities)

• Right place

• Right time

2. Costs of ordering and carrying inventory

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• A system to keep track of inventory

• A reliable forecast of demand

• Knowledge of lead times

• Reasonable estimates of

– Holding costs

– Ordering costs

– Shortage costs

• A classification system

Effective Inventory Management

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Inventory Tracking Systems

• Periodic SystemPhysical count of items made at periodic intervals

• Perpetual Inventory System System that keeps track of removals from inventory continuously, thus monitoringcurrent levels of each item

Perpetual = all-time, เป็�นไป็อย่�างต่�อเน� อง ต่ลอดเวลา

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Inventory Tracking Systems (Cont’d)

• Two-Bin System - Two containers of inventory; reorder when the first is empty

• Universal Product Code (UPC) - Bar code printed on a label that hasinformation about the item to which it is attached

0

214800 232087768

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ABC Classification System

Classifying inventory according to some measure of importance and allocating control efforts accordingly.

AA - very important

BB - mod. important

CC - least important Annual $ value of items

AA

BB

CC

High

Low

Low HighPercentage of Items

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ABC Classification SystemItem # Annual demand Unit cost

($)Annual Dollar Value

1 2500 360

2 1000 70

3 2,400 500

4 1500 100

5 700 70

6 1000 1000

7 200 210

8 1000 4000

9 8000 10

10 500 200

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ABC Classification SystemItem Annual Dollar value Classification % items % Annual

Dollar value

8 4,000,000 A 10

3 1,200,000 B 30

6 1,000,000 B

1 900,000 B

4 150,000 C 60

10 C

9 C

2 C

5 C

7 CA item is 10 -20% of the number of items but 60-70% of the annual dollarC item is 50-60% of the number of items but 10-15% of the annual dollarNormally, A items should receive close attention (frequent reviews) while C items should receive only loose control.

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Cycle Counting

• A physical count of items in inventory

• Cycle counting management

– How much accuracy is needed? (± 0.2% for A items, ± 1% B items, and ± 5% C items)

– When should cycle counting be performed?

– Who should do it?

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Inventory Models

• Independent demand – finished goods, items that are ready to be sold– E.g. a computer

• Dependent demand – components of finished products– E.g. parts that make up the computer

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Independent Demand Items

A

B(4) C(2)

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

Dependent Demand Items

Inventory Models

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• Economic order quantity (EOQ) model

– The order size that minimizes total annual cost

• Economic production model

• Quantity discount model

Economic Order Quantity Models

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• Only one product is involved

• Annual demand requirements known

• Demand is even throughout the year

• Lead time does not vary

• Each order is received in a single delivery

• There are no quantity discounts

Assumptions of EOQ Model

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The Inventory Cycle

Profile of Inventory Level Over Time

Quantityon hand

Q

Receive order

Placeorder

Receive order

Placeorder

Receive order

Lead time

Reorderpoint

Usage rate

Time

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The Inventory Cycle

Large Q

Time

Small Q

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Total Cost

Annualcarryingcost

Annualorderingcost

Total cost = +

TC = Q2

H DQ

S+

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Cost Minimization Goal

Order Quantity (Q)

The Total-Cost Curve is U-Shaped

Ordering Costs

QO

An

nu

al C

os

t

(optimal order quantity)

TCQH

D

QS

2

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Deriving the EOQ

Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.

Q = 2DS

H =

2(Annual Demand)(Order or Setup Cost)

Annual Holding CostOPT

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Minimum Total Cost

The total cost curve reaches its minimum where the carrying and ordering costs are equal.

Q2

H DQ

S=

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• Production done in batches or lots

• Capacity to produce a part exceeds the part’s usage or demand rate

• Assumptions of EPQ are similar to EOQ except orders are received incrementally during production

Economic Production Quantity (EPQ)

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• Only one item is involved

• Annual demand is known

• Usage rate is constant

• Usage occurs continually

• Production rate is constant

• Lead time does not vary

• No quantity discounts

Economic Production Quantity Assumptions

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EPQ: Inventory Profile

Q

Q*

Imax

Productionand usage

Productionand usage

Productionand usage

Usageonly

Usageonly

Cumulativeproduction

Amounton hand

Time

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EPQ – Total Cost

rate Usage

ratedelivery or Production

inventory Maximum

where

2

Cost SetupCost CarryingTC

max

max

u

p

upp

Q

I

SQ

DH

I

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Economic Run Size

QDS

H

p

p u0

2

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Total Costs with Purchasing Cost

Annualcarryingcost

PurchasingcostTC = +

Q2

H DQ

STC = +

+Annualorderingcost

PD +

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Total Costs with PDC

ost

EOQ

TC with PD

TC without PD

PD

0 Quantity

Adding Purchasing costdoesn’t change EOQ

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Total Cost with Constant Carrying Costs

OC

EOQ Quantity

To

tal C

os

t

TCa

TCc

TCbDecreasing Price

CC a,b,c

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Quantity Discounts

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Quantity Discounts

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When to Reorder

• Reorder point– When the quantity on hand of an item drops to this

amount, the item is reordered.– Determinants of the reorder point

1. The rate of demand

2. The lead time

3. The extent of demand and/or lead time variability

4. The degree of stockout risk acceptable to management

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Reorder Point: Under Certainty

) as units timesame(in timeLeadLT

per week) day,per period,per (units rate Demand

where

LTROP

d

d

d

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Reorder Point: Under Uncertainty

• Demand or lead time uncertainty creates the possibility that demand will be greater than available supply

• To reduce the likelihood of a stockout, it becomes necessary to carry safety stock– Safety stock

• Stock that is held in excess of expected demand due to variable demand and/or lead time

StockSafety timelead during

demand Expected ROP

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Safety Stock

LT Time

Expected demandduring lead time

Maximum probable demandduring lead time

ROP

Qu

an

tity

Safety stock

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Safety stock reduces risk ofstockout during lead time

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Safety Stock?

• As the amount of safety stock carried increases, the risk of stockout decreases.– This improves customer service level

• Service level– The probability that demand will not exceed supply

during lead time– Service level = 100% - Stockout risk

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How Much Safety Stock?

• The amount of safety stock that is appropriate for a given situation depends upon:

1. The average demand rate and average lead time

2. Demand and lead time variability

3. The desired service level

demand timelead ofdeviation standard The

deviations standard ofNumber

where

timelead duringdemand Expected

ROP

dLT

dLT

z

z

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Distribution of Lead Time Demand

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Reorder Point

ROP

Risk ofa stockout

Service level

Probability ofno stockout

Expecteddemand Safety

stock0 z

Quantity

z-scale

The ROP based on a normalDistribution of lead time demand

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Reorder Point: Demand Uncertainty

) as units time(same timeLead LT

) as units time(same periodper demand of stddev. The

per week) day,(per periodper demand Average

deviations standard ofNumber

where

LTLT ROP

d

d

d

z

zd

d

d

LT :Note ddLT

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Reorder Point: Lead Time Uncertainty

) as units time(same timelead Average LT

) as units time(same timelead of stddev. The

per week) day,(per periodper Demand

deviations standard ofNumber

where

LT ROP

LT

LT

d

d

d

z

zdd

LTdLT d :Note

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Reorder Point: both Demand and Lead Time are uncertain (variable)

2

LT

22

LT

LT

LT

where

LT ROP

d

zd

dd

d

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ROP equations of different cases

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• Orders are placed at fixed time intervals• Order quantity for next interval?• Suppliers might encourage fixed intervals• May require only periodic checks of

inventory levels• Risk of stockout• Fill rate – the percentage of demand filled

by the stock on hand

Fixed-Order-Interval Model

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• Tight control of inventory items• Items from same supplier may yield

savings in:– Ordering– Packing– Shipping costs

• May be practical when inventories cannot be closely monitored

Fixed-Interval Benefits

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• Requires a larger safety stock

• Increases carrying cost

• Costs of periodic reviews

Fixed-Interval Disadvantages

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Fixed-Quantity vs. Fixed-Interval Ordering

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When to order How much to order

Fixed-quantity (orders are triggered by a quantity)

Fixed-quantity (orders are triggered by a quantity)

Fixed-interval (orders are triggered by time)

Fixed-interval (orders are triggered by time)

Amount for order = Expected demand during production interval + SS – Amount on hand at reorder time =

LT ROP dzLTd

H

2DS = EOQ

OI isit DH

2S =

Period)Order (Economic EOP

ALTOIzLTOId d )(

demand safety stock

excel

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ริวม 63

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ริวม 50