2. DEFINITIONS
Inventory-A physical resource that a
firm holds in stock with the intent of
selling it or transforming it into a more
valuable state.
A physical resource that a firm holds in
stock with the intent of selling it or
transforming it into a more valuable
state.
3. TYPES OF INVENTORIES
Raw Materials & purchased parts
Partially completed goods called work in
progress
Finished Goods (manufacturing firms)
or merchandise
(retail stores)
Maintenance, Repair and Operating
(MRO)
Goods in transit to warehouse or to
customers
4. INVENTORY
Inventory System- A set of policies and
controls that monitors levels of
inventory and determines what levels
should be maintained, when stock
should be replenished, and how large
orders should be
5. EXPENSIVE STUFF
The average carrying cost of inventory across all mfg..
is 30-35% of its value.
A typical firm probably has about 30 % of its current
assets invested in inventory.
Savings from reduced inventory result in increased
profit.
If Managerial performance is measured by ROI (return
on investment ) = profit after taxes/ total asset, a
reduction in inventory can increase ROI significantly
6. ZERO INVENTORY?
Reducing amounts of raw materials and
purchased parts and subassemblies by
having suppliers deliver them directly.
Reducing the amount of works-in
process by using just-in-time
production.
Reducing the amount of finished goods
by shipping to markets as soon as
possible.
7. FUNCTIONS OF INVENTORY
To meet anticipated demand
To smooth production requirements
Firms that experience seasonal patterns in demand often
build up inventories during pre-season periods. These are
called seasonal inventories
To decouple operations
Inventories as buffer between successive operations to
maintain continuity in production
To protect against stock-outs
Delayed deliveries and unexpected increase in demand
increase the risk of shortage. Delayed delivery can happen
due to weather condition, supplier stock-outs, quality
problems etc. this risk can be reduced by holding safety
stocks
8. FUNCTIONS OF INVENTORY
To take advantage of order cycles : economic lot
sizes
To help hedge against price increases
To permit operations
To take advantage of quantity discounts
9. OBJECTIVE OF INVENTORY CONTROL
To achieve satisfactory levels of customer service
while keeping inventory costs within reasonable
bounds
Level of customer service : to have right goods, in sufficient
quantities, in right place and at the right time
Costs of ordering and carrying inventory
Inadequate control of inventories can result in
both overstocking / under-stocking
Under-stocking results in missed deliveries, lost
sales dissatisfied customers
Overstocking ties up fund
10. OBJECTIVE OF INVENTORY
CONTROL
Must take into account :
Timing and size of orders
Managers have a number of measures of performance
they can use to judge the effectiveness of inventory
management
no. and quantity of backorders / customer complaints
Inventory turnover is the ratio of annual cost of goods sold to
average inventory investment
11. EFFECTIVE INVENTORY MANAGEMENT
A system to keep track of inventory on
hand and on order
A reliable forecast of demand
Knowledge of lead times
Reasonable estimates of
Holding costs
Ordering costs
Shortage costs
A classification system
12. INVENTORY COUNTING SYSTEMS
Periodic System
Physical count of items made at periodic intervals
Perpetual Inventory System
System that keeps track
of removals from inventory
continuously, thus
monitoring
current levels of
each item
13. INVENTORY COUNTING SYSTEMS
(CONT’D)
Two-Bin System - Two containers of inventory; reorder when
the first is empty
Universal Bar Code - Bar code
printed on a label that has
information about the item
to which it is attached
0
214800 232087768
14. DEMAND FORE CAST AND
LEAD TIME
Lead time : the time interval between ordering
and receiving the order.
The greater the potential variability in the
greater the need for additional stock to reduce
the risk of shortage between deliveries.
Therefore there is a crucial link between the
demand and the inventory management
15. INVENTORY COSTS
Three basic costs are associated with inventory :
Holding costs
Transaction costs
Shortage costs
16. HOLDING COSTS
Interest, insurance, taxes (in some states), depreciation,
obsolescence, deterioration, spoilage, breakage, and
warehousing (Heat, light, rent, security)
Also includes opportunity costs associated with having
funds that could be used elsewhere tied up in inventory.
Various components of the holding cost depends upon
the type of the item involved:
Pocket cameras, transistor radios, calculators: prone to theft
Fresh seafood, baked goods etc. : rapid deterioration
Dairy products, medicines, batteries : limited shelf lives
Holding costs are stated in two ways :
Percentage of unit price or Rs. / unit
Holding costs ranges from 20 to 40 percent of the value of
an item
17. TRANSACTION COSTS /
ORDERING COSTS
Ordering costs are the costs of ordering and
receiving inventories
Costs includes : calculation of how much is needed,
preparing invoices, shipping costs, inspecting
goods upon arrival for quality and quantity, moving
of the goods to temporary storage
Generally expressed as a fixed rupee amount per
order regardless of the orders size
When a firm produces its own inventories instead of
ordering from suppliers the cost of machine set up
are analogous to the ordering costs , fixed charge
regardless of the order size
18. SHORTAGE COSTS
Shortage costs result when the demand
exceeds the supply of inventory on hand
This includes the opportunity cost of not
making sale, lose of customer good will etc.
If the shortage occurs in an item carried for
internal use the cost of lost production /
downtime is considered as a shortage cost
19. INVENTORY CLASSIFICATION
SYSTEM
All the inventories has not got equal importance
So inventories are to be classified according to some
measure of importance like annual rupee value
A-B-C approach :
A ( very important) :
generally account for 10-20% of the number of items in the
inventory
60-70% of the annual rupees value
B (moderately important) :
C (least important) :
generally account for 50-60% of the number of items in the
inventory
10-15% of the annual rupees value
20. A-B-C APPROACH
A item
B item
C item
High
Moderate
Low
Low High
Moderate
Annual
rupee
value
of
items
Percentage of items
21. EXAMPLE 1
Item Annual
demand
Unit cost
(Rs.)
Annual Rs
value
Classification
1 2500 330 825000 B
2 1000 70 70000 C
3 1900 500 950000 B
4 1500 100 150000 C
5 3900 700 2730000 A
6 1000 915 915000 B
7 200 210 42000 C
8 1000 4000 4000000 A
9 8000 10 80000 C
10 9000 2 18000 C
11 500 200 100000 C
12 400 300 120000 C
22. EXAMPLE 2
Item Usage Unit cost (in Rs.)
4021 50 1400
9402 300 12
4066 40 700
6500 150 20
9280 10 1020
4050 80 140
6850 2000 15
3010 400 20
4400 7000 5
Given the monthly usage in the following table classify the items in A, B and C categories
24. EOQ
EOQ models identify the optimal order quantity
by minimizing the sum of certain annual costs
that vary with order size.
Order size models are :
Basic economic order quantity model
The economic production quantity model
Quantity discount model
25. BASIC EOQ MODEL
This method is used to identify a fixed order size that will
minimize the annual cost of holding inventory and ordering
inventory
The unit purchase price of the inventory items are not
included in the total cost because the unit cost is unaffected
by the order size unless there is quantity discounts
Assumptions :
Only one product is involved
Annual demand requirements are known
Demand is spread evenly throughout the year ,i.e.,
demand rate is reasonably constant
Lead time does not vary
Each order is received in a single delivery
There are no quantity discounts
26. 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
27. CARRYING COST
Annual carrying cost = average amount of inventory
on hand x cost to carry one unit for one year
Average inventory = half of the order quantity = (Q + 0)/2
Therefore ,
Annual carrying cost =
Carrying cost is a linear function of Q
Q
____
2
H
Annual
cost
Order quantity
____
2
H
Q
28. ORDERING COST
Annual ordering cost will decrease as the
quantity ordered increases, because now fewer
number of orders need as the annual demand
is given
Number of orders per year = D/ Q
Annual ordering cost =
D
__
Q
S
Annual
cost
Order quantity
____
Q
S
D
30. COST MINIMIZATION GOAL
The Total-Cost Curve is U-Shaped
Ordering Costs
QO Order
Quantity (Q)
Annual
Cost
(optimal order quantity)
TC
Q
H
D
Q
S
2
31. DERIVING THE EOQ
We can find the minimum point on the TC curve
by differentiating TC with respect to Q, setting
the result equal to zero and solving for Q.
Q =
2DS
H
=
2(Annual Demand )(Order or Setup Cost )
Annual Holding Cost
OPT
32. MINIMUM TOTAL COST
The total cost curve reaches its minimum where the
carrying and ordering costs are equal.
Length of an order cycle =
Q =
2DS
H
=
2(Annual Demand )(Order or Setup Cost )
Annual Holding Cost
OPT
Q
D
__
33. EXAMPLE 1
A local distributor for a national tire company expects to sell
approximately 9600 steel-belted radial tires of a certain size and
tread design next year. Annual carrying costs are Rs.16 per tire, and
ordering costs are Rs.75. This distributor operate 288 days a year.
a. What is the EOQ?
b. How many times per year does the store reorder?
c. What is the length or an order cycle?
d. What is the total ordering and inventory cost?
34. SOLUTION
D = 9600 tires per year, H = Rs. 16 per unit per year, S = Rs. 75
a. Q0 = {2DS/H} = {2(9600)75/16} = 300
b. Number of orders per year = D/ Q = 9600 / 300 = 32
c. The length of one order cycle = Q/ D = 1 / 32 years = 288/32 days = 9 days
d. Total ordering and inventory cost = QH/2 + DS/Q
= 2400 + 2400 = 4800
35. EXAMPLE 2
A manufacturer assembles monitors. It purchases 3600 black and
white cathode ray tubes a year at Rs 65 each. Ordering costs are Rs.
31 and annual carrying costs are 20 percent of the purchase price.
Compute the optimal quantity and the annual cost of ordering and
carrying inventory.
36.
37.
38.
39. EXAMPLE 3
A large bakery buys flour in 25 kg bags. The bakery uses an average
of 4860 bags a year. Preparing an order and receiving a shipment of
flour involves a cost of Rs. 10 per order. Annual carrying costs are Rs.
75 per bag.
1. Determine the economic order quantity
2. What is the average no. of bags on hand?
3. How many orders per year will there be?
4. Compute the total cost of ordering and carrying flour
5. If ordering cost were to increase by Rs. 1 per order, how much
would that affect the total annual cost?
40. ECONOMIC PRODUCTION
QUANTITY
In assembly operation, capacity to produce some parts
exceeds the part’s demand or usage rate. So continuous
production in these cases will grow the inventory of those
parts. Therefore batch production is preferred in such cases.
Instead of orders received in one delivery units are received
incrementally during production
Assumptions :
Only one product is involved
Annual demand requirements are known
Usage rate is constant
Usage occurs continually but production occurs periodically
Production rate is constant
Lead time does not vary
There are no quantity discounts
42. ECONOMIC PRODUCTION
QUANTITY PROCESS
During the production phase inventory builds
at a rate equal to the difference of production
and usage rate
As long as production occurs inventory will
continue to build
When the production ceases the inventory level
will start decreasing
Inventory level is maximum at the point when
production ceases
When the amount of inventory in hand becomes
nil production resumes and the cycle repeats
43. ORDERING COST OF EPQ
As the company makes its own product no
ordering cost
But with every production run (batch) there is
set up costs : the cost to make the equipment
ready for production
Set up costs are analogous to ordering cost as
they are independent of the lot size
The larger the run size the fewer the runs
needed, and lower the annual set up costs.
The number of runs or batches per year is D/ Q
The annual set up cost = (D/Q) * S
44. EPQ
Total cost is
TC = carrying cost + set up cost
= (Imax / 2) H + (D / Q0)S
Where
Imax = maximum inventory
The economic run quantity = √(2DS/H) √p/(p – u)
Where
p= production or delivery rate
u= usage rate
The cycle time = Q0 / u
Run time = Q0 / p
Imax = (Q0 / p) (p-u)
45. EXAMPLE 1
A toy manufacturer uses 48000 rubber wheels per
year for its truck toy. The firm makes its own
wheels which it can produce at a rate of 800 per
day. The toy trucks are assembled uniformly over
the entire year. Carrying cost is Rs. 1 per wheel a
year. Set up cost for production run of wheels is Rs.
45. the firm operates 240 days per year. Determine
optimal run size
Minimum total annual cost for carrying and set up
Cycle time for the optimal run size
Run time
46. EXAMPLE 2
Dine corporation is both a producer and user of
brass couplings. The firm operates 220 days a year
and uses the couplings at a steady rate of 50 per
day. Couplings can be produced at a rate of 200 per
day. Annual storage cost is $2 per coupling and
machine set up cost is $70 per run.
Determine the economic run quantity
Approximately how many runs per year will there
be?
Compute the maximum inventory level
Determine the length of pure consumption portion
of the cycle
47. EOQ WITH QUANTITY
DISCOUNT
This is a variant of the EOQ model.
Quantity discount is a form of economies of scale:
pay less for each unit if you order more.
The essential trade-off is between economies of
scale and carrying cost.
Buyer’s goal to select order quantity that will
minimize TC
Total cost = carrying cost +ordering cost +
Order quantity Price per box
1-44 Rs. 2
45-69 Rs. 1.70
70 or more Rs. 1.40
48. EOQ WITH QUANTITY
DISCOUNT
To tackle the problem, there will be a separate
(TC) curve for each discount quantity price. The
objective is to identify an order quantity that
will represent the lowest total cost for the entire
set of curves in which the solution is feasible.
There are two general cases:
The carrying cost is constant
The carrying cost is a percentage of the purchasing price.
49. QUANTITY DISCOUNT WITH
CONSTANT CARRYING COST
When the carrying costs are constant, there will be a
single minimum point. All curves will have their
minimum points at the same quantity. The TC curves
line up vertically differing only in the lower unit price.
50. TOTAL COST WITH CONSTANT
CARRYING COSTS
OC
EOQ Quantity
Total
Cost
TCa
TCc
TCb
Decreasing
Price
CC a,b,c
51. EXAMPLE
The maintenance department of a large hospital
uses about 816 cases of liquid cleanser annually.
Ordering costs are $12, carrying cost are $4 per case
a year, and the new price schedule indicates that
orders of less than 50 cases will cost $20 per case,
50 to 79 cases will cost $18 per case, 80 to 99 cases
will cost $17 per case, and larger orders will cost
$16 per case. Determine the optimal order quantity
and the total cost.
52. EXAMPLE (SOLUTIONS)
The common EOQ: = {2(816)(12)/4} = 70
70 falls in the range of 50 to 79, at $18 per case.
TC = DS/Q+ciD+hQ/2
= 816(12)/70 + 18(816) + 4(70)/2 = 14,968
Total cost at 80 cases per order
TC = 816(12)/80 + 17(816) + 4(80)/2 = 14,154
Total cost at 100 cases per order
TC = 816(12)/100 + 16(816) + 4(100)/2 =13,354
The minimum occurs at the break point 100. Thus order 100
cases each time
53. QUANTITY DISCOUNT WITH VARYING
CARRYING COST
When the carrying costs are represented as a
percentage of unit price, each curve will have a
different minimum point.
Because carrying costs are percentage of price, lower
pieces will mean lower carrying costs and larger
minimum points.
Thus as the price decreases the curve’s minimum
point will be on the right side of the next higher
curve’s minimum point.
54. TOTAL COST WITH VARYING
CARRYING COSTS
OC
Quantity
Total
Cost
TCa
TCc
TCb
Decreasing
Price
CC b
CC a
CC c
55. QUANTITY DISCOUNT
(CONSTANT HOLDING COST)
Solution steps:
Compute the EOQ.
If the feasible EOQ is on the lowest price
curve, then it is the optimal order quantity.
If the feasible EOQ is on other curve, find the
total cost for this EOQ and the total costs for
the break points of all the lower cost curves.
Compare these total costs. The point (EOQ
point or break point) that yields the lowest
total cost is the optimal order quantity.
56. EXAMPLE
Surge Electric uses 4000 toggle switches a year. Switches are priced
as follows: 1 to 499 at $0.9 each; 500 to 999 at $.85 each; and 1000
or more will be at $0.80 each. It costs approximately $30 to prepare
an order and receive it. Carrying cost is 40% of purchased price per
unit on an annual basis. Determine the optimal order quantity and
the total annual cost.
57. SOLUTION
D = 4000 per year; S = 30 ; h = 0.40 {price}
Step 1. Find the EOQ for each price, starting with the lowest price
EOQ(0.80) = {2(4000)(30)/(0.32)} = 866 (Not feasible for the price range).
EOQ(0.85)= 840 (feasible for the range 500 to 999)
Step 2. Feasible solution is not on the lowest cost curve
Step 3. TC(840) = 840(.34)/2 + 4000(30)/840 + .85(4000) = 3686
TC(1000) = 1000(.32)/2 + 4000(30)/1000 + .80(4000) = 3480
Thus the minimum total cost is 3480 and the minimum cost order size is
1000 units per order.
58.
59.
60.
61.
62. REORDER POINT
when to order
The determinant of when to order in a continuous
inventory system is the reorder point, the inventory level
at which a new order is placed.
The reorder point for our basic EOQ model with constant
demand and a constant lead time to receive an order is
equal to the amount demanded during the lead time,
R = dL
64. SAFETY STOCKS
During the lead time, the remaining inventory in
stock will be depleted at a constant demand rate,
such that the new order quantity will arrive at
exactly the same moment as the inventory level
reaches zero.
Realistically, demand—and, to a lesser extent
lead time—are uncertain. The inventory level
might be depleted at a faster rate during lead
time.
As a hedge against stockouts when demand is
uncertain, a safety stock of inventory is
frequently added to the expected demand during
lead time.
65.
66. SERVICE LEVEL
There are several ways to determine the amount of
the safety stock. One popular method is to
establish a safety stock that will meet a specified
service level.
The service level is the probability that the amount
of inventory on hand during the lead time is
sufficient to meet expected demand— that is, the
probability that a stockout will not occur. The term
service is used, since the higher the probability that
inventory will be on hand, the more likely that
customer demand will be met—that is, that the
customer can be served. A service level of 90%
means that there is a 0.90 probability that demand
will be met during the lead time, and the probability
67.
68. MODELS OF WHEN TO ORDER
If an estimate of expected demand during lead time and its
standard deviation are available
Assumption is that any variability in demand rate or lead time can be
adequately described by a normal distribution.
However, this is not a strict requirement; the models provide
approximate reorder points even where actual distributions depart
from normal.
70. MODELS OF WHEN TO ORDER
When data on lead time demand are not readily available, the
previous formula cannot be used.
Nevertheless, data are generally available on daily or weekly demand,
and on the length of lead time.
Using those data, a manager can determine whether demand and/or
lead time is variable, if variability exists in one or both, and the related
standard deviation(s).
For those situations, one of the following formulas can be used:
72. EXPLANATION OF THE
FORMULAS
The first part of each formula is the expected demand, which is the
product of daily (or weekly) demand and the number of days (or weeks) of
lead time.
The second part of the formula is z times the standard deviation of lead
time demand.
The daily or weekly demand is assumed to be normally
distributed and has the same mean and standard deviation.
The standard deviation of demand for entire lead time is
found by summing the variances of daily or weekly demands
and then finding the square root of that number because
unlike variance standard deviations are not additive.
if the daily standard deviation is σd , the variance is σd
2 , and if lead time
is four days, the variance of lead time demand will equal the sum of the
four variances, which is 4σd
2.
The standard deviation of lead time demand will be the square root of this,
which is equal to 2σd. In general, this becomes √LT σd and, hence, the
last part of Formula
76. EXAMPLE
Housekeeping department of a motel uses approximately 400
washcloths per day. The actual number tends to vary with the number
of guests on any given night. Usage can be approximated by a normal
distribution that has a mean of 400 and a standard deviation of nine
washcloths per day. A linen supply company delivers towels and
washcloths with a lead time of three days. If the motel policy is to
maintain a stockout risk of 2 percent, what is the minimum number of
washcloths that must be on hand at reorder time, and how much of
that amount can be considered safety stock?
78. EXAMPLE
The motel in the preceding example uses approximately 600 bars of
soap each day, and this tends to be fairly constant. Lead time for soap
delivery isnormally distributed with a mean of six days and a standard
deviation of two days. A service level of 90 percent is desired.
a. Find the ROP.
b. How many days of supply are on hand at the ROP?
80. EXAMPLE
The motel replaces broken glasses at a rate of 25 per day. In the past,
this quantity has tended to vary normally and have a standard
deviation of three glasses per day. Glasses are ordered from a
Cleveland supplier. Lead time is normally distributed with an average
of 10 days and a standard deviation of 2 days. What ROP should be
used to achieve a service level of 95 percent?
81. PERIODIC INVENTORY
SYSTEM
We defined a continuous, or fixed-order-quantity, inventory
system as one in which the order quantity was constant and
the time between orders varied.
The less common periodic, or fixed-time-period, inventory
system is one in which the time between orders is constant
and the order size varies. Small retailers often use this
system. Drugstores are one example of a business that
sometimes uses a fixed-period inventory system. Drugstores
stock a number of personal hygiene- and health-related
products such as shampoo, toothpaste, soap, bandages,
cough medicine, and aspirin. Normally, the vendors who
provide these items to the store will make periodic visits—
every few weeks or every month—and count the stock of
inventory on hand for their product. If the inventory is
exhausted or at some predetermined reorder point, a new
order will be placed for an amount that will bring the
inventory level back up to the desired level. The drugstore
managers will generally not monitor the inventory level
between vendor visits but instead will rely on the vendor to
83. PERIODIC INVENTORY
SYSTEM
The first term in this formula, , is the average
demand during the order cycle time plus the
lead time. It reflects the amount of inventory
that will be needed to protect against the entire
time from this order to the next and the lead
time until the order is received.
The second term, is the safety stock for a
specific service level, determined in much the
same way as previously described for a reorder
point. These first two terms combined are a
“target” level of inventory to maintain.
The final term, I, is the amount of inventory on
hand when the inventory level is checked and
an order is made.
85. EXAMPLE
The KVS Pharmacy stocks a popular brand of over-the-
counter flu and cold medicine. The average demand for
the medicine is 6 packages per day, with a standard
deviation of 1.2 packages. A vendor for the
pharmaceutical company checks KVS’s stock every 60
days.
During one visit the store had 8 packages in stock. The
lead time to receive an order is 5 days. Determine the
order size for this order period that will enable KVS to
maintain a 95% service level.
