10 OM- Invent

Slack, Chambers and Johnston, Operations Management 5th Edition © Nigel Slack, Stuart Chambers, and Robert Johnston 2007

Inventory planning and control



Operations strategy

Design Improvement

Planning and control

Operations management


The operation supplies ... the delivery of a quantity of products and services when

required

The market requires … a quantity of products

and services at a particular time


Inventory is created to compensate for the differences in timing between supply and demand

Input process

Inventory

Output process

Rate of supply from input process

Rate of demand from output processInventory

Source: Alamy/Van Hilversum

Functions of Inventory

1. To meet anticipated demand: Anticipation stock – average demand

2. To smooth production requirements: Seasonal inventories

3. To decouple operations: Buffer inventories

4. To protect against stock-outs: Safety stock – uncertainty

5. To take advantage of order cycles: Cycle stock - batch

6. To help hedge against price increases

7. To permit operations: Work-in-process, pipeline inventories

8. To take advantage of quantity discounts


The Material Flow CycleThe Material Flow Cycle

InputInput Wait forWait for Wait toWait to MoveMove Wait in queueWait in queue SetupSetup RunRun OutputOutputinspectioninspection be movedbe moved timetime for operatorfor operator timetime timetime

Cycle timeCycle time

95%95% 5%5%


e.g. Automotive parts distributor

e.g. Local retail store

Single-stage inventory system

Suppliers Suppliers

Stock Sales operation

Central depot

Distribution Local distribution

point

Sales operation

Two-stageinventory system

Single-stage and two-stage inventory systems


e.g. Television manufacturer

Suppliers

Input stock

Stage 1

A multi-stage inventory system

WIP Stage 2

WIP Stage 3

Finished goods stock


A multi-echelon inventory system

Yarn producers

Cloth manufacturers

Garment manufacturers

Regional warehouses

Retail stores


A paper merchant must get its inventory planning and control right

11-10 Inventory Management

Economic order quantity model

Economic production model

Quantity discount model

Economic Order Quantity ModelsEconomic Order Quantity Models


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 ModelAssumptions of EOQ Model


The Inventory CycleThe Inventory CycleFigure 11.2

Profile of Inventory Level Over Time

Quantityon hand

Q

Receive order

Placeorder

Receive order

Placeorder

Receive order

Lead time

Reorderpoint

Usage rate

Time

11-13 Inventory ManagementThe EOQ The EOQ ModelModel

QQ = Number of pieces per order= Number of pieces per order Q*Q* = Optimal number of pieces per order (EOQ)= Optimal number of pieces per order (EOQ)

DD = Annual demand in units for the Inventory item= Annual demand in units for the Inventory itemSS = Setup or ordering cost for each order= Setup or ordering cost for each orderHH = Holding or carrying cost per unit per year= Holding or carrying cost per unit per year

Optimal order quantity is found when annual setup cost Optimal order quantity is found when annual setup cost equals annual holding costequals annual holding cost

Annual setup cost = SDQ

Annual holding cost = HQ2

DDQQ

S = HS = HQQ22

Solving for Q*Solving for Q*2DS = Q2DS = Q22HHQQ22 = 2DS/H = 2DS/H

Q* = 2DS/HQ* = 2DS/H


Total CostTotal Cost

Annualcarryingcost

Annualorderingcost

Total cost = +

Q2

H DQ

STC = +


Cost Minimization GoalCost Minimization Goal

Order Quantity (Q)

The Total-Cost Curve is U-Shaped

Ordering Costs

QO

An

nu

al C

os

t

(optimal order quantity)

TCQ

HD

QS

2

Figure 11.4C


Deriving the EOQDeriving 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


Minimum Total CostMinimum Total Cost

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

Q = 2DS

H =

2(Annual Demand)(Order or Setup Cost)

Annual Holding CostOPT

© 2006 Prentice Hall, Inc. 12 – 18

An EOQ ExampleAn EOQ Example

Determine optimal number of needles to orderDetermine optimal number of needles to orderD = 1,000 unitsD = 1,000 unitsS = $10 per orderS = $10 per orderH = $.50 per unit per yearH = $.50 per unit per year

Q* =Q* =2DS2DS

HH

Q* =Q* =2(1,000)(10)2(1,000)(10)

0.500.50= 40,000 = 200 units= 40,000 = 200 units


If the true costs of stock holding are taken into account,and if the cost of ordering (or changeover) is reduced,the economic order quantity (EOQ) is much smaller

Original holding costs

Original total costs

Revised holding costs

Order quantity

Co

st s

Original EOQ

Revised EOQ

Revised order costs

Revised total costs

Original order costs


100

90

80

70

60

50

40

30

20

10

100908070605040302010

Class C items

Class B items

Class A items

Pareto curve for stocked items

Percentage of types of items

Pe

rce

nta

ge

of v

alu

e o

f ite

ms

Source: Howard Smith Paper Group


Inventory classifications and measures

Class A items – the 20% or so of high-value items which account for around 80% of the total stock value

Class B items – the next 30% or so of medium-value items which account for around 10% of the total stock value

Class C items – the remaining 50% or so of low-value items which account for around the last 10% of the total stock value

ABC Classification ABC Classification SystemSystem

Demand volume and value of items varyDemand volume and value of items vary Classify inventory into 3 categories, Classify inventory into 3 categories,

typically on the basis of the dollar value typically on the basis of the dollar value to the firmto the firm

PERCENTAGEPERCENTAGE PERCENTAGEPERCENTAGECLASSCLASS OF UNITSOF UNITS OF DOLLARSOF DOLLARS

AA 5 - 155 - 15 70 - 8070 - 80BB 3030 1515CC 50 - 6050 - 60 5 - 105 - 10

ABC ClassificationABC Classification

11 $ 60$ 60 909022 350350 404033 3030 13013044 8080 606055 3030 10010066 2020 18018077 1010 17017088 320320 505099 510510 6060

1010 2020 120120

PARTPART UNIT COSTUNIT COST ANNUAL USAGEANNUAL USAGE


11 $ 60$ 60 909022 350350 404033 3030 13013044 8080 606055 3030 10010066 2020 18018077 1010 17017088 320320 505099 510510 6060

1010 2020 120120

PARTPART UNIT COSTUNIT COST ANNUAL USAGEANNUAL USAGETOTAL % OF TOTAL % OF TOTALPART VALUE VALUE QUANTITY % CUMMULATIVE

9 $30,600 35.9 6.0 6.08 16,000 18.7 5.0 11.02 14,000 16.4 4.0 15.01 5,400 6.3 9.0 24.04 4,800 5.6 6.0 30.03 3,900 4.6 10.0 40.06 3,600 4.2 18.0 58.05 3,000 3.5 13.0 71.0

10 2,400 2.8 12.0 83.07 1,700 2.0 17.0 100.0

$85,400


11 $ 60$ 60 909022 350350 404033 3030 13013044 8080 606055 3030 10010066 2020 18018077 1010 17017088 320320 505099 510510 6060

1010 2020 120120


9 $30,600 35.9 6.0 6.08 16,000 18.7 5.0 11.02 14,000 16.4 4.0 15.01 5,400 6.3 9.0 24.04 4,800 5.6 6.0 30.03 3,900 4.6 10.0 40.06 3,600 4.2 18.0 58.05 3,000 3.5 13.0 71.0

10 2,400 2.8 12.0 83.07 1,700 2.0 17.0 100.0

$85,400

AA

BB

CC


11 $ 60$ 60 909022 350350 404033 3030 13013044 8080 606055 3030 10010066 2020 18018077 1010 17017088 320320 505099 510510 6060

1010 2020 120120


9 $30,600 35.9 6.0 6.08 16,000 18.7 5.0 11.02 14,000 16.4 4.0 15.01 5,400 6.3 9.0 24.04 4,800 5.6 6.0 30.03 3,900 4.6 10.0 40.06 3,600 4.2 18.0 58.05 3,000 3.5 13.0 71.0

10 2,400 2.8 12.0 83.07 1,700 2.0 17.0 100.0

$85,400

AA

BB

CC

% OF TOTAL % OF TOTALCLASS ITEMS VALUE QUANTITY

A 9, 8, 2 71.0 15.0B 1, 4, 3 16.5 25.0C 6, 5, 10, 7 12.5 60.0


100 100 –

80 80 –

60 60 –

40 40 –

20 20 –

0 0 –| | | | | |00 2020 4040 6060 8080 100100

% of Quantity% of Quantity

% o

f V

alu

e%

of

Val

ue

AA

BBCC


Key Terms TestInventory (also known as stock)The stored accumulation of transformed resources in a process;

usually applies to material resources but may also be used for inventories of information; inventories of customers (or customers of customers) are usually called queues.

Buffer inventoryAn inventory that compensates for unexpected fluctuations in

supply and demand; can also be called a safety inventory.

Cycle inventoryInventory that occurs when one stage in a process cannot supply

all the items it produces simultaneously and so has to build up inventory of one item while it processes the others.


Key Terms Test

De-coupling inventoryThe inventory that is used to allow work centres or

processes to operate relatively independently.

Anticipation inventoryInventory that is accumulated to cope with expected

future demand or interruptions in supply.

Pipeline inventoryThe inventory that exists because material cannot be

transported instantaneously.


Key Terms Test

Work-in-process (WIP)The number of units within a process waiting to be processed

further (also called work-in-progress).

Economic order quantity (EOQ)The quantity of items to order that supposedly minimizes the total

cost of inventory management, derived from various formulae.

Economic batch quantity (EBQ)The amount of items to be produced by a machine or process that

supposedly minimizes the costs associated with production and inventory holding.


Key Terms Test

Re-order pointThe point in time at which more items are ordered, usually

calculated to ensure that inventory does not run out before the next batch of inventory arrives.

Re-order levelThe level of inventory at which more items are ordered, usually

calculated to ensure that inventory does not run out before the next batch of inventory arrives.

Lead-time usageThe amount of inventory that will be used between ordering

replenishment and the inventory arriving, usually described by a probability distribution to account for uncertainty in demand and lead time.


Key Terms Test

Continuous reviewAn approach to managing inventory that makes inventory-related

decisions when inventory reaches a particular level, as opposed to periodic review.

Periodic reviewAn approach to making inventory decisions that defines points in

time for examining inventory levels and then makes decisions accordingly, as opposed to continuous review.

Usage valueA term used in inventory control to indicate the quantity of items

used or sold multiplied by their value or price.


Key Terms TestPareto lawA general law found to operate in many situations that indicates

that 20% of something causes 80% of something else, often used in inventory management (20% of products produce 80% of sales value) and improvement activities (20% of types of problems produce 80% of disruption).

ABC inventory controlAn approach to inventory control that classes inventory by its

usage value and varies the approach to managing it accordingly.

Perpetual inventory principleA principle used in inventory control that inventory records should

be automatically updated every time items are received or taken out of stock.

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10 OM- Invent