Here are the steps to solve this EPQ problem: 1) Demand per year = 48,000 wheels 2) Production rate per day = 800 wheels 3) Setup cost = $45 4) Carrying cost per wheel = $1 5) Number of working days per year = 240 6) Using the EPQ formula: EPQ = √(2 * Demand * Setup cost / Carrying cost per unit) = √(2 * 48,000 * $45 / $1) = √432,000 = 208 wheels 7) Cycle time = EPQ / Production rate per day = 208 / 800 = 0.26 days = 6.

1. 2-1
Inventory Management

2. INVENTORYINVENTORY
 An inventory is a stock or store of goods.
 The amounts and dollar values of inventories carried by
different types of firms vary widely. A typical firm probably has
30% of its current asset and 90% of its working capital invested
in inventory.
Different kinds of inventories -
 Raw materials and purchased parts (Clay used in tiles production firms)
 Work in Progress - WIP (Tiles under production)
 Finished good inventories (Ready tiles)
 Replacement parts, tools and supplies (Replacing defective tiles)
 Goods in transit to warehouses or customers - Pipeline inventory
(Tiles for sale)
Return On Investment (ROI) = Profit After Tax / Total
Asset

3.  To meet anticipated customer demand - A customer can be a person
who walks in off the street to buy a new product (Rangs Showrooms)
 To smooth production requirements – Firms that experience
seasonal patterns in demand often build up inventories during pre-season
periods to meet overly high requirements during seasonal periods (IGLOO
and other ice cream companies)
 To decouple operations – Manufacturing firms keep buffer stock to
tackle any disruption in the operation. The buffers permit other operations
to continue temporarily while the problem is resolved (Cement factories)
 To protect against stockout – Unexpected increases in demand
increase the risk of shortages. Delays can occur because of weather
condition, delayed deliveries, quality problem etc. The risk of shortage can
be reduced by holding safety stock.
FUNCTIONS OF INVENTORYFUNCTIONS OF INVENTORY (WHY WE(WHY WE
NEED IT …)NEED IT …)

4. FUNCTIONS OF INVENTORY (CONTD.)FUNCTIONS OF INVENTORY (CONTD.)
 To take advantage of order cycles – To minimize purchasing cost,
firms often buy more than current requirement. They use this additional
quantity for later production. This enables the firms to buy or produce in
economic lot sizes without trying to match purchases or production with
demand requirements in the short run. This results in order cycle
 To hedge against price increase – When firms sense any possibility of
price increase they purchase larger than normal amounts to beat the
increase. The ability to store extra goods allow the firms to take the
advantage of discount for larger orders (Agreement between DIPON and
Paradise Cables to supply cable for Haripur Compressor Station work)
 To permit operations – Inventory of raw material, semi-finished goods
and finished goods as well as goods stored in warehouses allow the
operation to continue at different stages.
 To take advantage of quantity discount – Suppliers give discount on
large orders.

5. INVENTORY COUNTING SYSTEMINVENTORY COUNTING SYSTEM
 Periodic System – Under this system a physical count of the items in
inventory is made at periodic intervals (e.g. – weekly, monthly) to
determine how much to order.
 Many small retailers use this approach.
 An advantage of this system is that orders for many items occur at the
same time and helps to save ordering and shipping cost.
 One of the major disadvantage is the shortages between review
periods.
 Perpetual Inventory System – This system keeps track of removals
from inventory on a continuous basis, so the system can provide
information on the current level of inventory for each item.
 An obvious advantage is continuous monitoring of inventory
withdrawals. Also helps to order optimum quantity.
 One disadvantage of this system is added cost of record keeping.

6. INVENTORY COUNTING SYSTEMINVENTORY COUNTING SYSTEM
(CONTD.)(CONTD.) Universal Product Code or Bar Code – Universal product code or bar
code printed on a label that has information about the item to which it is
attached.
0
214800 232087768
Identifies this
product as a
grocery item
Identifies the
manufacturer
Indicates the
specific item
Radio Frequency
Identification
System will
replace UPC in
near future

7. INVENTORY COSTSINVENTORY COSTS
 Three basic costs are associated with inventories –
 Holding or Carrying Cost – The cost to carry an item in inventory for a
length of time.
 Holding or carrying cost is a variable cost. Costs include warehousing
cost (heat, light, rent, security), insurance, spoilage, breakage cost etc.
 Typically annual holding costs range from 20% to 40% of the value of
an item.
 Ordering Cost – Ordering costs are the costs of ordering and receiving
inventory.
 Ordering cost is a fixed type cost. Costs include invoice cost, shipping
cost, inspection cost etc.
 Shortage Cost – Costs resulting when demand exceeds the supply
of inventory (Result – Not making a sale, loss of customer goodwill etc.).
Lead Time - timeinterval betweenordering andreceiving the order

8. ABC CLASSIFICATION AND INVENTORYABC CLASSIFICATION AND INVENTORY
ANALYSISANALYSIS
◦ ABC classification, based on Pareto’s principle or the 80/20 rule,
assumes that 20% of the items in a list will account for 80% of the
significant measurement.
◦ For example, in a shopping list, 80% of the cost will be due to only
a few high-cost purchases such as oil, milk. Other items such as
bread, vegetable, pasta etc. will be relatively low in cost.
A Category Items Comprise 20% of SKU & Contribute to 70% of $ spend.
B Category Items Comprise 30% of SKU & Contribute to 25% of $ spend.
C Category Items Comprise 50% of SKU & Contribute to 5% of $ spend.

9. ABC CLASSIFICATION - MATHABC CLASSIFICATION - MATH
Item
Annual unit
usage
Unit cost ($) Usage in dollar
Percentage of total
dollar usage
PA 01 5,000 1.50 7,500 2.94
PA 02 1,500 8.00 12,000 4.71
PA 03 10,000 10.50 105,000 41.22
PA 04 6,000 2.00 12,000 4.71
PA 05 7,500 0.50 3,750 1.47
PA 06 6,000 13.60 81,600 32.03
PA 07 5,000 0.75 3,750 1.47
PA 08 4,500 1.25 5,625 2.21
PA 09 7,000 2.50 17,500 6.87
PA 10 3,000 2.00 6,000 2.36
Total 254,725 100

10. Class A Class B Class C
ABC CLASSIFICATION – MATH (CONTD.)ABC CLASSIFICATION – MATH (CONTD.)

11. BENEFITS OF ABC CLASSIFICATION SYSTEMBENEFITS OF ABC CLASSIFICATION SYSTEM
Area of use Benefit of ABC classification system
Cycle Counting
Frequency
Using ABC classification in cycle counting, A class items will be counted more
frequently than B or C class items.
Customer Service
Order quantity and safety stock levels are established according to the criticality
and cost of each item. Generally this is approached from a dollar accuracy
perspective.
Engineering
Priorities
The engineering department may use ABC classification to identify items of high
cost or high usage and concentrate their efforts accordingly. There is little point re-
engineering products of little value or low usage.
Replenishment
Systems
Inventory replenishment systems will vary according to the importance of the
inventory items. For example, C class items may be controlled with a simple two-
bin system if they are not particularly bulky. This minimizes the cost of control and
replenishment and does not significantly increase inventory carrying costs.
Investment
Decisions
As A class items form a larger investment in inventory, these items are closely
analyzed to ensure appropriate order quantities and safety stocks are used. A class
items are always the focus of attempts to improve inventory turns as changes in
the way A class items are procured and managed will have the most significant
effect on the overall inventory investment level

12. Item Usage Unit Cost($) Usage in dollar Percentage of total dollar usage
K34 50 1200
K35 20 400
K36 72 300
M10 160 400
M20 40 600
Z45 60 1600
F14 40 160
ABC CLASSIFICATION - MATHABC CLASSIFICATION - MATH
Do it at home

13. 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
INVENTORY CYCLEINVENTORY CYCLE

14. ECONOMIC ORDER QUANTITY (EOQ) MODELECONOMIC ORDER QUANTITY (EOQ) MODEL
 Economic Order Quantity (EOQ) Model - A EOQ Model helps to
identify a fixed order size that will minimize the sum of the annual costs of
holding inventory and ordering inventory.
Annual Holding Cost =
Q
2
H Where,
Q = Order quantity in units
H = Holding (or carrying) cost per unit
Order Quantity
AnnualCost
Q
2
H
Holding costs
are linearly
related to
order size

15. ECONOMIC ORDER QUANTITY (EOQ) MODELECONOMIC ORDER QUANTITY (EOQ) MODEL
(CONTD.)(CONTD.)
Annual Ordering Cost =
D
Q
S
Where,
Q = Order quantity in units
D = Demand, in units per year
S = Ordering cost
Order Quantity
(Q)
AnnualCost
D
Q
S
Ordering costs
are inversely
and nonlinearly
related to order
size

16. ECONOMIC ORDER QUANTITY (EOQ) MODELECONOMIC ORDER QUANTITY (EOQ) MODEL
(CONTD.)(CONTD.)
Annual holding cost Annual ordering costTotal cost = +
Q
2 H
D
Q
STC = +
Order Quantity (Q)
Ordering Costs
QO
AnnualCost
(optimal order quantity)
Holding Costs
TC

17. DERIVING THE EOQDERIVING 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.
Q
2 H
D
Q
STC = +
CostHoldingAnnual
Cost)SetuporderDemand)(Or2(Annual
=
H
2DS
=QOPT
The total cost curve reaches its
minimum where the carrying and
ordering costs are equal.

18. TOTAL COST WITH PURCHASING COSTTOTAL COST WITH PURCHASING COST
Total cost = Annual holding cost + Annual ordering cost + Purchasing cost
Q
2 H
D
Q
STC = + + PD
Cost
EOQ
TC with PD
TC without PD
PD
0 Quantity
Adding Purchasing cost
doesn’t change EOQ

19. MATH ON EOQMATH ON EOQ
A local distridutor of National Tire company expects to
sell 9600 tires next year. Annual carrying cost is $16 per
tire and ordering cost is $75. The distributor operates
288 days a year.
Calculate the EOQ.
How many times per year does the store reorder?
What is the length of the order cycle.
Calculate the total annual cost.

20. MATH ON EPQMATH ON EPQ
A toy manufacturer uses 48,000 rubber wheels for their
popular dump truck series. 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 $1 per wheel and setup cost is $45.
The firm operates 240 days a year.
Calculate the EPQ.
Find out maximum inventory level.
Calculate cycle time and run time.
Calculate the total annual cost.