Adeyl Khan, Faculty, BBA, NSU
Pencils, papers, clips, advertisements-flyer, visiting
cards, nuts, bolts, trucks, needles, airplanes
Raw materials, semi-finished goods, finished goods
What is the worth?
Let top management see the money withheld 
Adeyl Khan, Faculty, BBA, NSU
Inventory- a stock or store of goods
Independent Demand
Dependent Demand
A
B(4)
D(2)
C(2)
E(1)
D(3)
F(2)
Independent demand is uncertain.
Dependent demand is certain.
Adeyl Khan, Faculty, BBA, NSU
12-3
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
Adeyl Khan, Faculty, BBA, NSU
12-4
Types of Inventories
 Raw materials & purchased parts
 Partially completed goods called
work in progress
 Finished-goods inventories
 manufacturing firms
 retail stores (merchandise )
 Replacement parts, tools, & supplies
 Goods-in-transit to warehouses or customers
Adeyl Khan, Faculty, BBA, NSU
12-5
Functions of Inventory
 To meet anticipated demand
 Anticipation stock
 To smooth production requirements
 Seasonal demand (e.g. Potato case!)
 To decouple operations
 Buffer for continuous operation
 To protect against stock-outs
 Delayed delivery, abrupt demand
 Safety stocks
Adeyl Khan, Faculty, BBA, NSU
12-6
Functions of Inventory …
 To take advantage of order cycles
 Purchasing, Producing in Batches (Lots)
 Cycle stock for periodic
 To help hedge against price increases
 Oil price
 To permit operations
 Intermediate Stocks (WIP)

Pipeline inventory
 To take advantage of quantity discounts
Adeyl Khan, Faculty, BBA, NSU
12-7
Objective of Inventory Control
 To achieve satisfactory levels of customer service
while keeping inventory costs within reasonable
bounds
 Level of customer service
 Costs of ordering and carrying inventory
 Inventory turnover
 Ratio of average cost of goods sold to average
inventory investment.
 Days of inventory on hand
Adeyl Khan, Faculty, BBA, NSU
12-8
Effective Inventory Management
 A system to keep track of inventory (and S.O.)
 A reliable forecast of demand
 Knowledge of lead times (and variability)
 Reasonable estimates of
 Holding costs
 Ordering costs
 Shortage costs
 A classification system
Adeyl Khan, Faculty, BBA, NSU
12-9
Inventory Counting Systems
 Periodic System
 Physical count of items made at periodic intervals
 Small Retailers- checks and orders replenishment
 Perpetual Inventory System
 Keeps track of removals from inventory continuously,
thus monitoring current levels of each item
 Reorder point Q
 Also requires periodic counting

Errors, pilferage, spoliage
Adeyl Khan, Faculty, BBA, NSU
Cost?
12-10
Inventory Counting Systems …
 Two-Bin System - Two containers of inventory;
reorder when the first is empty
 2nd cart has enough inventory for the lead time
 Order card
 Universal Bar Code - Bar code printed on a label
that has information about the item to which it is
attached
Adeyl Khan, Faculty, BBA, NSU
12-11
Key Inventory Terms
 Lead time: time interval between ordering and
receiving the order
 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
 Shortage costs: costs when demand exceeds supply
Adeyl Khan, Faculty, BBA, NSU
12-12
The Inventory Cycle- Figure 12.2
Profile of Inventory Level Over Time
Q
Quantity
on hand
Usage
rate
Reorder
point
Receive
order
Place Receive
order order
Lead time
Adeyl Khan, Faculty, BBA, NSU
Place Receive
order order
Time
ABC Classification System
 Classifying inventory according to some measure of
importance and allocating control efforts
accordingly.
 A - very important
 B - mod. important
 C - least important
High
A
Annual
$ value
of items
Example 1- P 549
B
C
Low
Low
Adeyl Khan, Faculty, BBA, NSU
High
Percentage of12-14
Items
Cycle Counting
 A physical count of items in inventory
 Cycle counting management
 How much accuracy is needed?
 When should cycle counting be performed?
 Who should do it?
Adeyl Khan, Faculty, BBA, NSU
12-15
Economic Order Quantity Models
 Economic order quantity (EOQ) model
 The order size that minimizes total annual cost
 Economic production model
 Quantity discount model
Adeyl Khan, Faculty, BBA, NSU
12-16
Total Cost*
Annual
Annual
Total cost* = carrying + ordering
cost
cost
TC =
Adeyl Khan, Faculty, BBA, NSU
Q
H
2
+
DS
Q
12-17
Cost Minimization Goal- Figure 12.4C
Annual Cost
The Total-Cost Curve is U-Shaped
Q
D
TC  H  S
2
Q
Ordering Costs
QO (optimal order quantity)
Order Quantity
(Q)
Minimum Total Cost
Adeyl Khan, Faculty, BBA, NSU
12-18
Assumptions of EOQ Model
•
•
•
•
•
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
Adeyl Khan, Faculty, BBA, NSU
12-19
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.
2DS
2(Annual Demand)(Or der or Setup Cost)
Q OPT =
=
H
Annual Holding Cost
 Minimum Total Cost
 The total cost curve reaches its minimum where the
carrying and ordering costs are equal.
Q
H
2
Adeyl Khan, Faculty, BBA, NSU
=
DS
Q
12-20
Economic Production Quantity (EPQ)
 Production done in batches or lots
 Capacity to produce a part exceeds the part’s usage
or demand rate
Assumptions
 Similar to EOQ
 Orders are received
incrementally during
production
Adeyl Khan, Faculty, BBA, NSU
•
•
•
•
•
•
•
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
12-21
Economic Run Size
Q0 
2DS
p
H p u
We do not buy the product.
We produce it.
Total demand / year is D
Demand / day or consumption rate is u
Production rate is p / day
Adeyl Khan, Faculty, BBA, NSU
12-22
Instantaneous Replenishment
Incremental Replenishment
Adeyl Khan, Faculty, BBA, NSU
EPQ: Incremental Replenishment
(Production and Consumption)
Demand / day or consumption rate is u
Production rate is p / day
p-u
p
u
u × ( number of working days ) = D = Total demand per year
Adeyl Khan, Faculty, BBA, NSU
EPQ: Ordering Cost and Carrying Cost
D
I max
S 
TC 
H
Q
2
State Imax in terms of Q!
Adeyl Khan, Faculty, BBA, NSU
EPQ : Production & Consumption; rate & time
How much do we produce each time? Q
How long does it take to produce Q? d1
What is our production rate per day? p
Q  pd1
How long does it take to consume Q? d1 +d2
What is our consumption rate per day ? u
I max  ud 2
Q  u(d1  d 2 )
I max  ( p  u )d1
Adeyl Khan, Faculty, BBA, NSU
I max
p-u
d1
d2
u
Example- What is the optimal
production size?
 A toy manufacturer
 Uses 48000 parts for one of its products.
 Consumption rate is uniform throughout the year.
 Working days are 240 / year.
 The firm can produce at a rate of 800 parts / day
 Carrying cost is $1 / part / year
 Setup cost for production run is $45 / setup
Adeyl Khan, Faculty, BBA, NSU
What is Run Time, What is Cycle Time
Q0 
2DS
H
p
p u
Q  u(d1  d 2 )
Q0 using formula = 2400
u = 48000 /240 = 200 units/day
2400  200(d1  d2 )
Q  pd1
(d1  d2 )  12
2400  800d1
d1  3
I max
p-u
d1
Adeyl Khan, Faculty, BBA, NSU
u
d2
What is the Optimal Total Cost
I max  ( p  u )d1
I max  (800  200)3
I max  1800
I Max
D
TC  S  H
Q
2
48000 1800
TC  45
1
2400
2
TC  900  900  1800
Adeyl Khan, Faculty, BBA, NSU
EPQ : Optimal Q
EPQ 
2 SDp
H ( p  u)
2 SD
EPQ 
H
Adeyl Khan, Faculty, BBA, NSU
p
p u
Reorder Point- ROP
 Reorder Point
 When the quantity on hand of an item drops to this
amount, the item is reordered
 If setup time takes 2 days, at which level of inventory we
should start setup?
 2(200) = 400
 200 ?
Adeyl Khan, Faculty, BBA, NSU
Yet Another Example
 A company has a yearly demand of 120,000 boxes of its
product. The product can be produced at a rate of 2000
boxes per day. The shop operates 240 days per year.
Assume that demand is uniform throughout the year.
Setup cost is $8000 for a run, and holding cost is $10 per
box per year.
 a) What is the demand rate per day
 b) What is the Economic Production Quantity (EPQ)
 c) What is the run time
 d) What is the maximum inventory
 e) What is the total cost of the system
Adeyl Khan, Faculty, BBA, NSU
Yet Another Example …
a)
What is the demand rate per day




Demand per year is 120,000 there are 240 days per year
Demand per day = 120000/240 = 500
u = D/240 = 500
b) What is the Economic Production Quantity (EPQ)
2 SD
EPQ 
H
p
p u
2(8000)(120000)
2000
EPQ 
10
2000  500
Adeyl Khan, Faculty, BBA, NSU
=16000
Yet Another Example …
 c) What is the run time
 We produce 16000 units
 Our production rate is 2000 per day
 It takes 16000/2000 = 8 days
 d1 = EPQ/p = 8 days
 d) What is the maximum inventory
 We produce for 8 days. Each day we produce 2000 units and we
consume 500 units of it. Therefore we add to our inventory at rate of
1500 per day for 8 days. That is
 Imax = 8(1500) = 12000
 Imax = pd1 = 8(1500) = 12000
Adeyl Khan, Faculty, BBA, NSU
Yet Another Example …
 e) What is the total cost of the system
I Max
D
TC  S  H
Q
2
120000
12000
TC  8000
 10
16000
2
TC  60000  60000  120000
Adeyl Khan, Faculty, BBA, NSU
Annual
Annual
Purchasing
+
TC = carrying + ordering cost
cost
cost
Q
H
TC =
2
+
DS
Q
+
PD
Including the Purchasing Cost
Adeyl Khan, Faculty, BBA, NSU
12-36
Cost
Total Costs with Vs. Quantity Ordered
Adding Purchasing cost
doesn’t change EOQ
TC with PD
TC without PD
PD
0
Adeyl Khan, Faculty, BBA, NSU
EOQ
Quantity
12-37
Total Cost with Constant Carrying Costs
Total Cost
TCa
TCb
Decreasing
Price
TCc
CC a,b,c
OC
EOQ
Adeyl Khan, Faculty, BBA, NSU
Quantity
12-38
Do the Math
Ex 5, 6
Total Cost with Variable Carrying Costs
Adeyl Khan, Faculty, BBA, NSU
12-39
ROP with EOQ Ordering
When to Reorder
 Safety Stock
 Stock that is held in excess of expected demand due
to variable demand rate and/or lead time.
 Service Level
 Probability that demand will not exceed supply
during lead time.
Adeyl Khan, Faculty, BBA, NSU
12-40
Determinants of the Reorder Point
 The rate of demand
 The lead time
 Demand and/or lead time variability
 Stockout risk (safety stock)
Adeyl Khan, Faculty, BBA, NSU
12-41
Quantity
Safety Stock- Figure 12.12
Maximum probable demand
during lead time
Expected demand
during lead time
ROP
Safety stock
Safety stock reduces risk of
stockout during lead time
Adeyl Khan, Faculty, BBA, NSU
LT
Time
12-42
Reorder Point- Figure 12.13
See also: Fig 11.14
The ROP based on a normal
Distribution of lead time demand
Service level
Risk of
a stockout
Probability of
no stockout
Expected
demand
0
ROP
Quantity
Safety
stock
z
z-scale
ROPs = Exp. Demand + z. σdLT
Adeyl Khan, Faculty, BBA, NSU
12-43
Shortage and Service Level
 Service level determines ROP
 E(n) = E(z) z σdLT
 E(n) = Expected number of short/cycle
 E(z) = Standardized number of units-short from table
11.3
 σdLT = Standard deviation of lead time
 Example 10 @ Page 568
Adeyl Khan, Faculty, BBA, NSU
44
Fixed-Order-Interval Model
 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
Adeyl Khan, Faculty, BBA, NSU
12-45
Calculations
Ex 13
Adeyl Khan, Faculty, BBA, NSU
46
Fixed-Interval tradeoffs
Benefits
• 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
Adeyl Khan, Faculty, BBA, NSU
Disadvantages
• Requires a larger safety
stock
• Increases carrying cost
• Costs of periodic reviews
12-47
Single Period Model
 Model for ordering items
with limited useful lives
 Perishables
 Shortage cost is generally
the unrealized profits per
unit
 Excess cost is the
difference between
purchase cost and salvage
value of items left over at
the end of a period
Adeyl Khan, Faculty, BBA, NSU
Continuous stocking
levels
• Identifies optimal stocking
levels
• Optimal stocking level balances
unit shortage and excess cost
Discrete stocking levels
• Service levels are discrete rather
than continuous
• Desired service level is equaled
or exceeded
12-48
Optimal Stocking Level
Service level =
Cs
Cs + Ce
Cs = Shortage cost per unit
Ce = Excess cost per unit
Ce
Cs
Service Level
Quantity
So
Balance point
Adeyl Khan, Faculty, BBA, NSU
12-49
Example 15
 Ce = $0.20 per unit
 Cs = $0.60 per unit
 Service level = Cs/(Cs+Ce) = .6/(.6+.2)
 Service level = .75
Ce
Cs
Service Level = 75%
Quantity
Stockout risk = 1.00 – 0.75 = 0.25
Adeyl Khan, Faculty, BBA, NSU
12-50
Operations Strategy
 Too much inventory
 Tends to hide problems
 Easier to live with problems than to eliminate them
 Costly to maintain
 Wise strategy
 Reduce lot sizes
 Reduce safety stock
Adeyl Khan, Faculty, BBA, NSU
12-51
Adeyl Khan, Faculty, BBA, NSU
52
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 periodic and perpetual review systems.
 Discuss the objectives of inventory management.
 Describe the A-B-C approach and explain how it is
useful.
Adeyl Khan, Faculty, BBA, NSU
12-53
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 the quantity discount model and solve
typical problems.
 Describe reorder point models and solve typical
problems.
 Describe situations in which the single-period
model would be appropriate, and solve typical
problems.
Adeyl Khan, Faculty, BBA, NSU
12-54