3. 3
3
Learning Objectives
You should be able to:
1. Define the term inventory, list the major reasons for holding inventories,
and list the main requirements for effective inventory management
2. Discuss the nature and importance of service inventories
3. Explain periodic and perpetual review systems
4. Explain the objectives of inventory management
5. Describe the A-B-C approach and explain how it is useful
6. Describe the basic EOQ model and its assumptions and solve typical
problems
7. Describe reorder point models
4. 4
4
• Inventory
• A stock or store of goods
• Independent demand items
• Items that are ready to be sold or used
Inventory
Inventories are a vital part of business: (1) necessary for
operations and (2) contribute to customer satisfaction
A “typical” firm has roughly 30% of its current assets
and as much as 90% of its working capital invested in
inventory
5. 5
Inventory Management
• Management has two basic functions concerning inventory:
1. Establish a system for tracking items in inventory
2. Make decisions about
• When to order
• How much to order
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6
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
7. 7
Purchase cost
The amount paid to buy the inventory
Holding (carrying) costs
Cost to carry an item in inventory for a length of time, usually a
year
Ordering costs
Costs of ordering and receiving inventory
Setup costs
The costs involved in preparing equipment for a job
Analogous to ordering costs
Shortage costs
Costs resulting when demand exceeds the supply of inventory;
often unrealized profit per unit
Inventory Costs
8. 8
An inventory classification system based on some
measure of importance, usually the annual dollar
(monetary) value
Typically three classes of items are used:
A (very important): 10 to 20% of inventory items but 60 to 70%
of annual dollar value
B (moderately important)
C (least important): 50 to 60% of inventory items but only about
10 to 15% of annual dollar value
Actual number of categories may vary from organization
to organization
A-B-C Approach
9. 9
Basic Economic Order Quantity (EOQ) Model
Assumptions
1. Only one product is involved.
2. Annual demand requirements are known.
3. Demand is spread evenly throughout the
year so that the demand rate is reasonably
constant.
4. Lead time is known and constant.
5. Each order is received in a single delivery.
6. There are no quantity discounts.
10. 10
Derivation of EOQ Model
Fig 1: Carrying costs are linearly related to order size Fig 2: Ordering costs are inversely and nonlinearly
related to order size
Fig 3: Total cost curve is U-shaped
11. 11
Derivation of EOQ Model contd.
Annual carrying cost =
𝑄
2
𝐻
Where, Q = Order quantity in Units
H = Holding (carrying) cost per unit per year
Annual ordering cost =
𝐷
𝑄
𝑆
Where, D = Demand in units per year
S = Ordering cost per order
Total cost = Annual carrying cost + Annual ordering cost
=
𝑄
2
𝐻 +
𝐷
𝑄
𝑆
Optimal order quantity occurs when, Annual carrying cost = Annual ordering cost
Or,
𝑄
2
𝐻 =
𝐷
𝑄
𝑆
cost
holding
unit
per
annual
cost)
der
demand)(or
annual
(
2
2
O
H
DS
Q
12. 12
Example
A local distributor for a national tire company expects to sell approximately 9,600 steel-
belted radial tires of a certain size and tread design next year. Annual carrying cost is $16
per tire, and ordering cost is $75. The distributor operates 288 days a year.
a. What is the EOQ?
b. How many times per year does the store reorder?
c. What is the length of an order cycle?
d. What is the total annual cost if the EOQ quantity is ordered?
Solution:
D = 9600 units
H = $16 per unit per year
S = $75
a) 𝑄0 =
2𝐷𝑆
𝐻
=
2∗9600∗75
16
= 300 tires
b) No. of orders per year = D/Q0 = 9600/300 = 32
c) Length of order cycle = Q0/D = (1/32)*288 = 9 days
d) Total Cost (TC) =
𝑄
2
𝐻 +
𝐷
𝑄
𝑆 = (300/2)*16 + (9600/300)*75 = $4800
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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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• 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
Reorder Point: Under Uncertainty
Stock
Safety
time
lead
during
demand
Expected
ROP
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16
• 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
How Much Safety Stock?
demand
time
lead
of
deviation
standard
The
deviations
standard
of
Number
where
time
lead
during
demand
Expected
ROP
LT
LT
d
d
z
z
17. 17
Reorder Point: Demand Uncertainty
)
as
units
time
(same
time
Lead
LT
)
as
units
time
(same
period
per
demand
of
stdev.
The
per week)
day,
(per
period
per
demand
Average
deviations
standard
of
Number
where
LT
ROP
d
d
d
z
z
LT
d
d
d
LT
LT d
d
Note: If only demand is variable, then
18. 18
18
• Fixed-order-interval (FOI) model
• Orders are placed at fixed time intervals
• Reasons for using the FOI model
• Supplier’s policy may encourage its use
• Grouping orders from the same supplier can produce savings in shipping costs
• Some circumstances do not lend themselves to continuously monitoring inventory position
How Much to Order: FOI
20. 20
Technology in Inventory Management
• Real-time data capture
• RFID tags
• GPS navigation
• ERP system
https://www.youtube.com/watch?v=BnQG4NGyyAU
22. 22
Operations Strategy
• Improving inventory processes can offer significant cost reduction and customer
satisfaction benefits
• Areas that may lead to improvement:
• Record keeping
• Records and data must be accurate and up-to-date
• Variation reduction
• Lead variation
• Forecast errors
• Lean operations
• Supply chain management
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Summary
• Discussed need for inventory management and inventory
costs
• The EOQ model and numerical problems related to that
• Discussed the terms reorder point, safety stock – under
demand certainty and uncertainty
24. 24
24
References
Essential Reading
• Stevenson, William J. (2015) Operations Management, 11th Edition, Mc
Graw Hill Education
Recommended Reading
• Kumar, S. A., & Suresh, N. (2008) Operations Management, 2nd edition.
New Age International Publishers
Magazines and Journals
• Operations Research/Management Science Today
• International Journal of Operational Research, Inderscience Publishers
Websites
• https://harvardmagazine.com/tags/quantitative-methods
• https://sloanreview.mit.edu/
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Disclaimer
• All data and content provided in this presentation are
taken from the reference books, internet – websites
and links, for informational purposes only.
