M 6. Inventory Manag444444444444ement.pptx

OPERATIONS ANALYTICS
By Dr. Rajesh Chouksey
Saturday, December 30, 2023 1

► Amazon.com started as a “virtual” retailer
► No inventory
► No warehouses
► No overhead
– just computers taking orders to be filled by others
► Growth has forced Amazon.com to become a world leader in
warehousing and inventory management
Inventory Management at Amazon.com

1. Each order is assigned by computer to the closest distribution
center that has the product(s)
2. A “flow meister” at each distribution center assigns work crews
3. Technology helps workers pick the correct items from the
shelves with almost no errors
4. Items are placed in crates on a conveyor, bar code scanners
scan each item 15 times to virtually eliminate errors

5. Crates arrive at central point where items are boxed and
labeled with new bar code
6. Gift wrapping is done by hand at 30 packages per hour
7. Completed boxes are packed, taped, weighed and labeled
before leaving warehouse in a truck
8. Order arrives at customer within 1 - 2 days

The objective of inventory management is to strike a balance
between inventory investment and customer service
Inventory Management

• Inventory can be visualized as stacks of money sitting on forklifts, on
shelves, and in trucks and planes while in transit.
• Inventory can be difficult to convert back into cash.
• It is a good idea to try to get your inventory down as far as possible.
Inventory

• For many businesses, inventory is the largest asset on the balance sheet at
any given time.
• A “typical” firm has roughly 30% of its current assets and as much as 90%
of its working capital invested in inventory and as much as 50% of total
invested capital
▶ Less inventory lowers costs but increases chances of running out
▶ More inventory raises costs but always keeps customers happy
Inventory

• Inventory
• A stock or store of goods
• Independent demand items
• Items that are ready to be sold or used
Inventory

▶ Raw material
▶ Purchased but not processed
▶ Work-in-process (WIP)
▶ Undergone some change but not completed
▶ A function of cycle time for a product
▶ Maintenance/repair/operating (MRO)
▶ Necessary to keep machinery and processes productive
▶ Tools and supplies
▶ Finished goods
▶ Completed product awaiting shipment
▶ Pipeline
▶ Goods-in-transit to warehouses or customers
Types of Inventory

• Seasonal Inventory:
• Seasonality in demand is absorbed using inventory
• Decoupling Inventory:
• Complexity of production control is reduced by splitting manufacturing
into stages and maintaining inventory between these stages
• Cyclic Inventory:
• Periodic replenishment causes cyclic inventory
• Pipeline Inventory:
• Exists due to lead time
• Safety Stock:
• Used to absorb fluctuations in demand due to uncertainty
Types of Inventory

Independent versus Dependent Demand
• The source of demand determines its type
• Independent – Customer demand that is not directly influenced by
the actions of the firm (e.g. customer orders)
• Dependent – Demand that is driven by the plans and activities of
the firm (e.g. components, warehouse demand)

Demand Type
Independent demand – the demands for
various items are unrelated to each
other
• For example, a workstation may produce many
parts that are unrelated but meet some external
demand requirement
Dependent demand – the need for any
one item is a direct result of the
need for some other item
•Usually a higher-level item of which it is
part

Demand Management and MPC
Environment
• DM must conform to the strategy of the firm, capabilities of
manufacturing, and needs of customers
• These define the MPC environment
• MPC environment is defined by customer order decoupling point
• The point where demand changes from independent to dependent
• Alternatively, order penetration point

Make-to-Stock
• Customer demand is filled from finished goods inventory (cosmetics,
grocery items)
• Key focus of demand management is maintenance of finished goods
inventories
• Physical distribution is a key concern

Assemble-to-Order
• Customer requirements are met by a combination of standard
options (personal computers, fast food)
• Primary task of demand management is to define the customer’s
order in terms of components and options (configuration
management)

Make-to-Order
• Items built to customer specifications, starting with raw materials
(airplanes)
• Primary task of demand management is gathering information about
customer needs and coordinating with manufacturing

Engineer-to-Order
• Firm works with the customer to design the product, then produces
the product, starting with raw materials (ships, bridges)
• Primary task of demand management is gathering information about
customer needs and coordinating with engineering and
manufacturing

MPC Environments
Suppliers Raw
materials
Work-in-
process
Finished
goods
Make-
to-Stock
Assemble-
to-Order
Make-
to-Order
Engineer-
to-Order
Independent Dependent
Decoupling
Points
MPC
Environment
Inventory Location

Independent Demand
• Finished goods and spare parts typically belong to independent demand items in
manufacturing organizations
• Two attributes characterize and distinguish independent demand items:
• Timing of demand: Independent demand items have a continuous demand
• Uncertainty of demand: There is considerable element of uncertainty in the demand
in the case of independent demand items
• Inventory planning of independent demand items must address the following two key
questions:
• How much?
• When?

• Periodic System
• Physical count of items in inventory made at periodic intervals
• Perpetual Inventory System
• System that keeps track of removals from inventory continuously,
thus monitoring current levels of each item
• An order is placed when inventory drops to a predetermined minimum
level
• Two-bin system
• Two containers of inventory; reorder
when the first is empty
Inventory Counting Systems

• Universal product code (UPC)
• Bar code printed on a label that has information about the item to which it is
attached
• Radio frequency identification (RFID) tags
• A technology that uses radio waves to identify objects, such as goods, in
supply chains
Inventory Counting Technologies

Selective
Control of
Inventories
Alternative
Classification
Schemes
• ABC Classification (on the basis of consumption value)
• XYZ Classification (on the basis of unit cost of the item)
• High Unit cost (X Class item)
• Medium Unit cost (Y Class item)
• Low unit cost (Z Class item)
• FSN Classification (on the basis of movement of inventory)
• Fast Moving
• Slow Moving
• Non-moving
• VED Classification (on the basis of criticality of items)
• Vital
• Essential
• Desirable
• On the basis of sources of supply
• Imported
• Indigenous (National Suppliers)
• Indigenous (Local Suppliers)

ABC Classification
• A-B-C approach
• Classifying inventory according to some measure of importance, and
allocating control efforts accordingly
• A items (very important)
• 10 to 20 percent of the number of items in inventory and about 60 to 70
percent of the annual dollar value
• B items (moderately important)
• C items (least important)
• 50 to 60 percent of the number
of items in inventory but only
about 10 to 15 percent of the
annual dollar value

Classifying inventory according to some measure of importance, and
allocating control efforts accordingly
• A items (very important)
• 10 to 20 percent of the number of items in inventory and about 60
to 70 percent of the annual value
• B items (moderately important)
• C items (least important)
• 50 to 60 percent of the number of items in inventory but only about
10 to 15 percent of the annual value
ABC Classification System

ABC ANALYSIS
A Items
B Items
| | | | | | | | | |
10 20 30 40 50 60 70 80 90 100
Percentage
of
annual
dollar
usage
80 –
70 –
60 –
50 –
40 –
30 –
20 –
10 –
0 –
Percentage of inventory items
C Items

ABC Classification
A graphical illustration

• DAT, Inc., produces
digital audiotapes to be
used in the consumer
audio division. DAT
lacks sufficient
personnel in its
inventory supply section
to closely control each
item stocked, so it has
asked you to determine
an ABC classification.
Here is a sample from
the inventory records:
Develop an ABC
classification for these
10 items.
Problem Item
Average Monthly
Demand
Price per Unit
Item
1 700 6
2 200 4
3 2,000 12
4 1,100 20
5 4,000 21
6 100 10
7 3,000 2
8 2,500 1
9 500 10
10 1,000 2

• Classify the items as
A, B, or C.
Problem Item Annual Demand Unit Price
H4-010 20,000 2.5
H5-201 60,200 4
P6-400 9,800 28.5
P6-401 14,500 12
P7-100 6,250 9
P9-103 7,500 22
TS-300 21,000 45
TS-400 45,000 40
TS-041 800 20
V1-001 33,100 4

Boreki Enterprises has the following 10 items in inventory. Theodore
Boreki asks you, a recent OM graduate, to divide these items into ABC
classifications.
a) Develop an ABC classification system for the 10 items.
b) How can Boreki use this information?
c) Boreki reviews the classification and then places item A2 into the A
category. Why might he do so?

ITEM ANNUAL DEMAND COST/UNIT
A2 3000 50
B8 4000 12
C7 1500 45
D1 6000 10
E9 1000 20
F3 500 500
G2 300 1500
H2 600 20
I5 1750 10
J8 2500 5
DATA

• L. Houts Plastics is a large manufacturer of injection-molded plastics
in North Carolina. An investigation of the company’s manufacturing
facility in Charlotte yields the information presented in the table
below. How would the plant classify these items according to an ABC
classification system?

ITEM CODE # AVERAGE INVENTORY
(UNITS)
V7ALUE
($/UNIT)
A 400 3.75
B 300 4.00
C 120 2.50
D 75 1.50
E 60 1.75
F 30 2.00
G 20 1.15
H 12 2.05
I 8 1.80
J 7 2.00
K 6 3.00
L. Houts
Plastics’
Charlotte
Inventory
Levels

Inventory MODEL
IDEPENDENT DEMAND - EOQ Model

Inventory Models for Independent
Demand
1. Basic economic order quantity (EOQ) model
2. Production order quantity model
3. Quantity discount model

Basic EOQ Model
1. Demand is known, constant, and independent
2. Lead time is known and constant
3. Receipt of inventory is instantaneous and complete
4. Quantity discounts are not possible
5. Only variable costs are setup (or ordering) and holding
6. Stockouts can be completely avoided
Important assumptions

• Economic order quantity models identify the optimal order quantity
by minimizing the sum of annual costs that vary with order size and
frequency
1. The basic economic order quantity model
2. The economic production quantity model
3. The quantity discount model
How Much to Order: EOQ Models

Robust Model
▶The EOQ model is robust
▶It works even if all parameters and assumptions are
not met
▶The total cost curve is relatively flat in the area of the
EOQ

Total Annual Cost
Annual setup cost = (Number of orders placed per year) x (Setup or order cost per order)
Annual demand
Number of units in each order
Setup or order
cost per order
=
=
D
Q
æ
è
ç
ö
ø
÷S

Inventory Usage Over Time
Order quantity
= Q (maximum
inventory level)
Usage rate
Average
inventory on
hand
Q
2
Minimum
inventory
Inventory
level
Time
0
Total order received

Total Annual Cost
Annual holding cost = (Average inventory level) x (Holding cost per unit per year)
Order quantity
2
(Holding cost per unit per year)
=
=
Q
2
æ
è
ç
ö
ø
÷H

Total Annual Cost
Total Cost = Annual Holding Cost + Annual Ordering Cost
=
𝑄
2
𝐻 +
𝐷
𝑄
𝑆
where
𝑄 = Order quantity in units
𝐻 = Holding (carrying) cost per unit, usually per year
𝐷 = Demand, usually in units per year
𝑆 = Ordering cost per order
Q* = Optimal number of units per order (EOQ)
Annual setup cost = (Number of orders placed per year) x (Setup or order cost per order)

Minimizing Cost :
Total cost of carrying
Total cost of ordering
Sum of the two costs
Minimum Cost
Economic
Order Qty.
Level of Inventory
Cost
of
Inventory
Objective is to minimize total costs

Goal: Total Cost Minimization
Order Quantity (Q)
The Total-Cost Curve is U-Shaped
Ordering Costs
QO
Annual
Cost
(optimal order quantity)
Holding Costs
S
Q
D
H
Q
TC 

2

Minimizing Costs
D
Q
æ
è
ç
ö
ø
÷S =
Q
2
æ
è
ç
ö
ø
÷H
Optimal order quantity is found when annual
setup cost equals annual holding cost
Solving for Q*
2DS = Q2
H
Q2
=
2DS
H
Q*
=
2DS
H
Q = Number of pieces per order
Q* = Optimal number of pieces per order (EOQ)
D = Annual demand in units for the inventory item
S = Setup or ordering cost for each order
H = Holding or carrying cost per unit per year

• The basic EOQ model is used to find a fixed order quantity that will minimize total
annual inventory costs
• Assumptions:
1. Only one product is involved
2. Annual demand requirements are known
3. Demand is even throughout the year
4. Lead time does not vary
5. Each order is received in a single delivery
6. There are no quantity discounts
Basic EOQ Model

Quantity
Time
Safety stock
Cyclic Stock
Pipeline inventory
L
Cyclic inventory, pipeline inventory and safety stocks are critically linked to “how much” and “when”
decisions in inventory planning
The Inventory Cycle

The Inventory Cycle
Profile of Inventory Level Over Time
Quantity
on hand
Q
Receive
order
Place
order
Receive
order
Place
order
Receive
order
Lead time
Reorder
point
Usage
rate
Time

• Using calculus, we take the derivative of the total cost function and set the
derivative (slope) equal to zero and solve for Q.
• The total cost curve reaches its minimum where the carrying and ordering costs
are equal.
Deriving EOQ
𝑄∗
=
2𝐷𝑆
𝐻
=
2(annual demand)(order cost)
annual per unit holding cost

An EOQ Example
= N = =
Expected number of
orders
Demand
Order quantity
*
Q
D
Total annual cost = Setup cost + Holding cost
= T =
Expected time
between orders
Number of working days per year
Expected number of orders
Annual setup cost =
D
Q
S Annual holding cost =
Q
2
H
ROP = Demand per day * Lead time for a new order in days
ROP = d * L
The demand per day, d, is found by dividing the annual demand, D, by the number of
working days in a year:
d = D / Number of working days in a year

Illustration
A toy manufacturer uses approximately 32,000 silicon chips annually.
The chips are used at a steady rate during the 240 days a year that the
plant operates. Annual holding cost is $3 per chip, and ordering cost is
$120. Determine
a. The optimal order quantity.
b. The number of workdays in an order cycle.
Given Data
D = 32,000 chips per year
S = $120
H = $3 per unit per year

Illustration
Given Data
D = 32,000 chips per year, S = $120, H = $3 per unit per year
a.
𝑄∗ =
2𝐷𝑆
𝐻
=
𝑄∗
=
2(32000)(120)
3
𝑄∗
= 1600 chips

Illustration
Given Data
b.
Q*/ D = 1600 chips / 32,000 chips/yrs
= 1/20 year
= 1/20*240 days
= 12 days
𝑇ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑜𝑟𝑘𝑑𝑎𝑦𝑠 𝑖𝑛 𝑎𝑛 𝑜𝑟𝑑𝑒𝑟 𝑐𝑦𝑐𝑙𝑒 = 12 days

Illustration
William Beville’s computer training school, in Richmond, stock
workbooks with the following characteristics:
Demand D = 19,500 units / year
Ordering cost S = $ 25 /order
Holding cost H = $ 4 /unit/year
a) Calculate the EOQ for the workbooks.
b) What are the annual holding costs for the workbooks?
c) What are the annual ordering costs?

Illustration
If D-5 8,000 per month, S-5 $45 per order, and H-5 $2 per unit per
month,
a) What is the economic order quantity?
b) How does your answer change if the holding cost doubles?
c) What if the holding cost drops in half?

Illustration
The Warren W. Fisher Computer Corporation purchases 8,000
transistors each year as components in minicomputers. The unit cost of
each transistor is $10, and the cost of carrying one transistor in
inventory for a year is $3. Ordering cost is $30 per order.
What are
(a) the optimal order quantity,
(b) the expected number of orders placed each year, and
(c) the expected time between orders?
Assume that Fisher operates on a 200-day working year.

Illustration
Given Data
a.
𝑄∗ =
2𝐷𝑆
𝐻
=
𝑄∗
=
2(32000)(120)
3
𝑄∗
= 1600 chips

An EOQ Example
Determine optimal number of needles to order
D = 1,000 units
S = Rs 10 per order
H = Rs .50 per unit per year

An EOQ Example
Determine optimal number of needles to order
D = 1,000 units
S = Rs 10 per order
Q*
=
2DS
H
Q*
=
2(1,000)(10)
0.50
= 40,000 = 200 units

An EOQ Example
Determine expected number of orders
D = 1,000 units Q* = 200 units
S = Rs 10 per order
N = = 5 orders per year
1,000
200
= N = =
Expected
number of
orders
Demand
Order quantity *
Q
D

An EOQ Example
Determine optimal time between orders
S = Rs 10 per order N = 5 orders/year
T = = 50 days between orders
250
5
= T =
Expected time
between
orders
Number of working days per year
Expected number of orders

An EOQ Example
Determine the total annual cost
S = Rs 10 per order N = 5 orders/year
H = Rs .50 per unit per year T = 50 days
Total annual cost = Setup cost + Holding cost

Numerical
• William Beville’s computer training school, in Richmond, stocks
workbooks with the following characteristics:
• Demand D = 19,500 units / year
• Ordering cost = S = Rs 25 / order
• Holding Cost = H = Rs 4 per unit per year
a)Calculate the EOQ for the workbooks.
b)What are the annual holding costs for the workbooks?
c)What are the annual ordering costs?

Solution
(b) Annual holdings costs = [Q/2]H
= [494/2](4)
= Rs 988
(c) Annual ordering costs = [D/Q]S
= [19500/494](25)
= Rs 987
(a)
2(19,500)(25)
EOQ = 493.71 494 units
4
Q
  

Numerical
• If D = 8000 per month, S = Rs 45 per order, and H = Rs 2 per unit per
month,
a)What is the economic order quantity?
b)How does your answer change if the holding cost doubled?
c)What if the holding cost drops in half?

Solution
 
2(8,000)(45)
EOQ 600 units
2
  
2 8,000 45
EOQ = = 424.26 units
4
  
2 8,000 45
EOQ 848.53 units
1
 
(a)
(b) If H doubles, from Rs 2 to Rs 4/unit/month,
(c) If H drops in half, from Rs 2 to Rs 1/unit/month,

Numerical
• Henry Crouch’s law office has traditionally ordered ink refills 60 units
at a time. The firm estimates that carrying cost is 40% of the Rs 10
unit cost and that annual demand is about 240 units per year. The
assumptions of the basic EOQ model are thought to apply.
a)For what value of ordering cost would its action be optimal?
b)If the true ordering cost turns out to be much greater than your
answer to (a), what is the impact on the firm’s ordering policy?

Solution
2 240 480
60 ; or 60 , or
.4 10 4
3,600
60 120 , so solving for results in $30.
120
S S
S S S
 
 

  
(a) This problem reverses the unknown of a standard EOQ problem to solve for S.
(a) S = Rs 30
(b)If S were Rs 30, then the EOQ would be 60.
If the true ordering cost turns out to be much
greater than RS 30, then the firm’s order policy is
ordering too little at a time.

Solution
An Apple store has a demand (D) for 8,000 iPhones per year. The firm
operates a 250-day working year. On average, delivery of an order takes 3
working days, but has been known to take as long as 4 days. The store
wants to calculate the reorder point without a safety stock and then with a
one-day safety stock.
d = D / Number of working days in a year
= 8,000 / 250
= 32 units
ROP = Reorder point = d * L
= 32 units per day * 3 days
= 96 units

Thank You!

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