This document provides details about Dr. Atif Shahzad's educational background and contact information. It then outlines a lecture on inventory models, including reasons for keeping inventories, inventory management techniques, deciding on the appropriate inventory model, the economic order quantity model, reorder points, carrying costs, and extensions to the basic EOQ model for non-zero lead times, quantity discounts, and non-instantaneous replenishment. Quizzes and examples are provided to illustrate inventory calculations. Key terms related to inventory are also defined.

1. _____________________Dr. Atif Shahzad
BE, MECHANICAL ENGINEERING
UNIVERSITY OF ENGINEERING & TECHNOLOGY, TAXILA, PAKISTAN, 2000
MCS, SOFTWARE ENGINEERING
SZABIST,, ISLAMABAD, PAKISTAN, 2003
MS, AUTOMATION & PRODUCTION SYSTEMS
ECOLE CENTRALE DE NANTES, NANTES, FRANCE, 2007
PhD, AUTOMATION & APPLIED INFORMATICS
UNIVERSITE DE NANTES, NANTES, FRANCE, 2011
EMAIL: atifshahzad@Gmail.com
TEL: +92-333-5219846, +92-51-5179755
LINKEDIN: pk.linkedin.com/in/dratifshahzad

2. ENGINEERING
MANAGEMENT
TODAY’S LECTURE
Inventory Models

3. Dr.AtifShahzad
Review
Reasons for Keeping Inventories Inventory Management
Inventory Control
• what to order,
• when to order,
• how much to order and
• how much to stock
Techniques of Inventory Control
• ABC analysis
• HML analysis
• VED analysis
• FSN analysis
• SDE analysis
• GOLF analysis
• SOS analysis

4. Dr.AtifShahzad
17–4
Deciding on the inventory model
Assume an analyst applies an
inventory model that does not
allow for spoilage to a grocery
chain’s ordering policy for lettuce
and formulates the strategy of
ordering lettuce in large amounts
every 14 days.
A little thought will show that this
is obliviously foolish.
This strategy implies that lettuce
will be spoiled.
However it is not a failure of
inventory, it is a failure to apply the
correct model.

5. Dr.AtifShahzad
EOQ & Re-order point
EOQ – gives answer to question
“How much to Order”
Re-order point – gives answer to
question “when to order”

6. Dr.AtifShahzad
17–6
optimum inventory level

7. Dr.AtifShahzad
17–7
optimum inventory level
Ordering cost
• Quotation or tendering Requisitioning
• Order placing
• Transportation
• Receiving, inspecting and storing
• Quality control
• Clerical and staff
Stock-out cost
Carrying costs

8. Dr.AtifShahzad
17–8
optimum inventory level
Ordering cost
Stock-out cost
• Loss of sale
• Failure to meet
delivery commitments
Carrying costs

9. Dr.AtifShahzad
17–9
optimum inventory level
Ordering cost Stock-out cost
Carrying costs
• Warehousing or storage Handling
• Clerical and staff Insurance
• Interest Deterioration,shrinkage,
• evaporation and obsolescence
• Taxes
• Cost of capital

10. Dr.AtifShahzad
Walmart
 WALMART making sure that the shelves
are stocked with tens of thousands of
products is no simple matter for inventory
managers at Walmart, which has
¤ 10,700 Walmart stores and
Sam’s Club locations in 27
countries,
¤ employs more than 2.2 million
associates,
¤ serves245 million customers
per week worldwide,
¤ and uses 100,000 suppliers.

11. Dr.AtifShahzad
17–11
Approaches
Certainty approach
• Uncertain variables and
risk are addressed
separately
Uncertainty
approach
• Uncertain variables and
risk are
addressedsimultaneously
Deterministic
approach
Probabilistic
approach

12. Dr.AtifShahzad
17–12
Basic EOQ Model: Assumptions
Seasonal fluctuation in demand are ruled out
Zero lead time – Time lapsed between purchase order and
inventory usage
Cost of placing an order and receiving are same and
independent of the units ordered
Annual cost of carrying the inventory is constant
Total inventory cost = Ordering cost + carrying cost
ECONOMICORDERQUANTITY

13. Dr.AtifShahzad
EOQ – Three Approaches
Trial and Error method
Order-formula approach
Graphical approach

14. Dr.AtifShahzad
Trial and Error
method
Trial and Error method
Order-formula approach
Graphical approach
Order size Q 1200 600 400 300 240 200 150 120 100
Average inventory Q/2 600 300 200 150 120 100 75 60 50
No. of orders C/Q 1 2 3 4 5 6 8 10 12
Annual carrying cost
I* Q/2
600 300 200 150 120 100 75 60 50
Annual ordering cost
O*C/Q
37.5 75 112.5 150 187.5 225 300 375 450
Total annual cost 637.5 375 312.5 300 307.5 325 375 435 500
Assumptions:-
Annual requirement (C)=1200 units Carrying cost
(I) = Rs.1
Ordering cost (O) =Rs.37.5

15. Dr.AtifShahzad
Order-formula
approach
EOQ =(2*1200*37.5/1) =
300 units
Trial and Error method
Order-formula approach
Graphical approach
Assumptions:-
Annual requirement (C)=1200 units Carrying cost
(I) = Rs.1
Ordering cost (O) =Rs.37.5
EOQ
=(2CO/I)
C = Annual
demand
O = Ordering
cost per order
I = Carrying
cost per unit

16. Dr.AtifShahzad
Graphical
approach
Trial and Error method
Order-formula approach
Graphical approach
Assumptions:-
Annual requirement (C)=1200 units Carrying cost
(I) = Rs.1
Ordering cost (O) =Rs.37.5
CostinRS.
Order quantity
EOQ0

17. Dr.AtifShahzad
Graphical
approach
Trial and Error method
Order-formula approach
Graphical approach

18. Dr.AtifShahzad
QUIZ
 A plant makes monthly shipments of electric drills
to a wholesaler in average lot sizes of 280 drills.
 The wholesaler’s average demand is 70 drills a
week, and the lead time from the plant is 3
weeks.
 The wholesaler must pay for the inventory from
the moment the plant makes a shipment.
 If the wholesaler is willing to increase its purchase
quantity to 350 units, the plant will give priority
to the wholesaler and guarantee a lead time of
only2 weeks.
 What is the effect on the
wholesaler’s cycle and pipeline
inventories?
Intellectualssolveproblems; geniusesprevent them.

19. Dr.AtifShahzad
QUIZ
 A museum of natural history opened a gift shop two years
ago. Managing inventories has become a problem. Low
inventory turnover is squeezing profit margins and causing
cash-flow problems.
 One of the top-selling SKUs in the container group at the
museum’s gift shop is a bird feeder.
 Sales are 18 units per week, and the supplier charges $60
per unit.
 The cost of placing an order with the supplier is $45.
 Annual holding cost is 25 percent of a feeder’s value, and the
museum operates 52 weeks per year.
 Management chose a 390-unit lot size so that new orders
could be placed less frequently.
 What is the annual cycle-inventory cost of the
current policy of using a 390-unit lot size?
 Would a lot size of 468 be better?

20. Dr.AtifShahzad
QUIZ
 What is the annual cycle-inventory cost of the
current policy of using a 390-unit lot size?
 Would a lot size of 468 be better?

21. Dr.AtifShahzad
QUIZ
 What is the annual cycle-inventory cost of the
current policy of using a 390-unit lot size?
 Would a lot size of 468 be better?

22. Dr.AtifShahzad
EOQ
 We use calculus to obtain the EOQ formula from the total annual cycle-
inventory cost function.
 We take the first derivative of the total annual cycle-inventory cost function
with respect to Q, set it equal to 0, and solve for Q.

23. Dr.AtifShahzad
EOQ

24. Dr.AtifShahzad
Activity
 A distribution center experiences an average weekly demand of
50 units for one of its items.
 The product is valued at $650 per unit.
 Inbound shipments from the factory warehouse average 350
units.
 Average lead time (including ordering delays and transit time) is
2 weeks.
 The distribution center operates 52 weeks per year; it carries a
1-week supply of inventory as safety stock and no anticipation
inventory.
 What is the value of the average aggregate inventory being
held by the distribution center?

25. Dr.AtifShahzad
Activity
 A distribution center experiences an average weekly demand of
50 units for one of its items.
 The product is valued at $650 per unit.
 Inbound shipments from the factory warehouse average 350
units.
 Average lead time (including ordering delays and transit time) is
2 weeks.
 The distribution center operates 52 weeks per year; it carries a
1-week supply of inventory as safety stock and no anticipation
inventory.
 What is the value of the average aggregate inventory being
held by the distribution center?

26. Dr.AtifShahzad
Certainty case of the inventory
cycle
T1,T2,T3,T4
represents the
replenishment points
Q
0 T1 T2 T3 T4
Average inventory = Q/2
Inventorylevel
orderquantity

27. Dr.AtifShahzad
Extension of basic EOQ model
quantity discounts
27
T hewholeofscienceisnothingmore
thana refinementofeverydaythinking.
–Albert Einstein

28. Dr.AtifShahzad
Extension of basic EOQ model
Non-zero lead time
If the lead time is‘n’ then procurement must be done prior to‘n’ days, i.e.T-n
T1 - n T1 T2 - n T2 T3 - n T3 T4 - n T4
Q
0
Reorder point
Time
Placement of a order

29. Dr.AtifShahzad
Extension of basic EOQ model
Quantity discounts
Quantity discounts are price incentives to purchase large quantities
 For example, a supplier may offer a price of $4.00 per unit for orders
between 1 and 99 units, a price of $3.50 per unit for orders between 100 and
199 units, and a price of $3.00 per unit for orders of 200 or more units.
 The item’s price is no longer fixed, as assumed in the EOQ derivation;
instead, if the order quantity is increased enough, the price is discounted.
For any per-unit price level, P, the total cost is

30. Dr.AtifShahzad
Extension of basic EOQ model
Non- instantaneous
Replenishment
 If an item is being produced internally rather than
purchased, finished units may be used or sold as soon as
they are completed, without waiting until a full lot is
completed.
 For example, a restaurant that bakes its own dinner rolls
begins to use some of the rolls from the first pan even
before the baker finishes a five-pan batch.
 The inventory of rolls never reaches the full five-pan
level, the way it would if the rolls all arrived at once on a
truck sent by a supplier.

31. Dr.AtifShahzad
Extension of basic EOQ model
 Figure depicts the usual case, in which the production rate, p, exceeds the
demand rate, d. If demand and production were equal, manufacturing
would be continuous with no buildup of cycle inventory.
 If the production rate is lower than the demand rate, sales opportunities are
being missed on an ongoing basis.We assume that p > d here.
Economic production lot size
(ELS)
Non- instantaneous
Replenishment

32. Dr.AtifShahzad
Some terminology
 cycle inventory: The portion of total inventory that varies directly with lot
size.
 lot sizing: The determination of how frequently and in what quantity to
order inventory.
 safety stock inventory: Surplus inventory that a company holds to protect
against uncertainties in demand, lead time, and supply changes
 anticipation inventory: Inventory used to absorb uneven rates of demand
or supply.
 Pipeline Inventory: Inventory that is created when an order for an item is
issued but not yet received is called

33. Dr.AtifShahzad
17–33
Objectives of Inventory Control
To ensure adequate supply of products to customer and avoid shortages as far as possible.
To make sure that the financial investment in inventories is minimum (i.e., to see that the working capital is blocked to
the minimum possible extent).
Efficient purchasing, storing, consumption and accounting for materials is an important objective.
To maintain timely record of inventories of all the items and to maintain the stock within the desired limits.
To ensure timely action for replenishment.
To provide a reserve stock for variations in lead times of delivery of materials.
To provide a scientific base for both short-term and long-term planning of materials.

34. Dr.AtifShahzad
17–34
Benefits of Inventory Control
Improvement in customer’s relationship because of the timely delivery of goods and
service.
Smooth and uninterrupted production and, hence, no stock out.
Efficient utilisation of working capital. Helps in minimising loss due to deterioration,
obsolescence damage and pilferage.
Economy in purchasing.
Eliminates the possibility of duplicate ordering.

35. QUESTIONS

36. THANK YOU FOR YOUR INTEREST