1. Inventory Management

2. Amazon.com
Amazon.com started as a “virtual” retailer – no inventory, no warehouses, no overhead; just computers taking orders to be filled by others
Growth has forced Amazon.com to become a world leader in warehousing and inventory management

3. What Is Inventory? Stock of items kept to meet future demand
Working Capital
Def. - A physical resource that a firm holds in stock with the intent of selling it or transforming it into a more valuable state.

4. Inventory by Nature of Material
Raw Materials
Works-in-Process
Finished Goods
Maintenance, Repair and Operating (MRO)

5. Inventory by Uses of Material
Transaction Inventory
Speculative Inventory
Precautionary Inventory

6. Functional Classification Of Inventory
Based on utility, all inventory can be in one or more of the following categories
Working stock
Safety stock
Anticipation stock
Pipeline stock
Decoupling stock
Psychic stock

7. Cost of Inventory

8. Cost of replenishing inventory
1.Ordering /Procurement cost
Cost of replenishing inventory
Order processing
Shipping
Handling

9. 2.Carrying Costs Cost of holding an item in inventory
Working Capital (opportunity) costs
Inventory risk costs( spoilage, breakage, detoriation ,obsolescence)
Space costs
Inventory service costs
Insurance & Taxes

10. 3.Out-of-Stock Costs/Shortage Cost
Lost sales cost
Back-order cost

11. Inventory Management If company holds too little Inventory
too frequent ordering
loss of quantity discount
higher transportation charges
likely shortage in future
If company holds too much Inventory
carrying/holding charges
storage
obsolescence, depreciation
Involvement of working capital

12. Objectives of Inventory Management
1) Maximize the level of customer service by avoiding under stocking.(How much to order?)
2) Promote efficiency in production and purchasing by minimizing the cost of providing an adequate level of customer service.(When to order?)

13. Design of Inventory Mgmt. Systems: Micro Issues
Order Quantity
Economic Order Quantity
Order Timing
Reorder Point

14. Inventory Systems Single-Period Inventory Model
One time purchasing decision (Example: vendor selling t-shirts at a football game)
Seeks to balance the costs of inventory overstock and under stock
Multi-Period Inventory Models
Fixed-Order Quantity Models
Event triggered (Example: running out of stock) 7

15. Single-Period Inventory Model
This model states that we should continue to increase the size of the inventory so long as the probability of selling the last unit added is equal to or greater than the ratio of: Cu/Co+Cu 8

16. Single Period Model Example
Our college basketball team is playing in a tournament game this weekend. Based on our past experience we sell on average 2,400 shirts with a standard deviation of We make Rs100 on every shirt we sell at the game, but lose Rs50 on every shirt not sold. How many shirts should we make for the game?
Cu = Rs100 and Co = Rs50; P ≤ 100 / ( ) = .667
Z.667 = .432 (use NORMSDIST(.667) or Appendix E)
therefore we need 2, (350) = 2,551 shirts

17. Multi-Period Inventory Models Fixed Order Quantity Systems
Economic Order Quantity (EOQ) Systems

18. Behavior of EOQ Systems
As demand for the inventoried item occurs, the inventory level drops
When the inventory level drops to a critical point, the order point, the ordering process is triggered
The amount ordered each time an order is placed is fixed or constant
When the ordered quantity is received, the inventory level increases

19. Basic Fixed-Order Quantity Model and Reorder Point Behavior
4. The cycle then repeats.
1. You receive an order quantity Q.
R = Reorder point
Q = Economic order quantity
L = Lead time L Q R
Time
Number
of units
on hand
2. Your start using them up over time.
3. When you reach down to a level of inventory of R, you place your next Q sized order.

20. Inventory Order Cycle Demand rate Time Lead time Order placed
Order receipt
Inventory Level
Reorder point, R
Order quantity, Q 20

21. Determining Order Quantities
Basic EOQ
EOQ for Production Lots
EOQ with Quantity Discounts

22. Assumptions of Basic EOQ Model
Demand is known with certainty and is constant over time
No shortages are allowed
Lead time for the receipt of orders is constant
Order quantity is received all at once
Quantity Discount does not exist
Average Invenory is half of total inventory 22

23. EOQ Cost Model Co - cost of placing order D - annual demand
Cc - annual per-unit carrying cost Q - order quantity
Annual ordering cost =
CoD Q
Annual carrying cost =
CcQ 2
Total cost = 23

24. EOQ Cost Model Proving equality of costs at optimal point = CoD Q CcQ2
Q2 =
2CoD Cc
Qopt = 24

25. Cost Minimization Goal
By adding the item, holding, and ordering costs together, we determine the total cost curve, which in turn is used to find the Qopt inventory order point that minimizes total costs
Total Cost C O S T
Holding
Costs
QOPT
Annual Cost of
Items (DC)
Ordering Costs
Order Quantity (Q)

26. Example:Electronic Village stocks and sells a particular brand of personal computer. It costs the store Rs450 each time it places an order with the manufacturer for the personal computers. The annual cost of carrying the PCs in inventory is Rs170. The store manager estimates that annual demand for the PCs will be 1200 units.
Determine the optimal order quantity and the total minimum inventory cost.

27. Example: Basic EOQ
Zartex Co. produces fertilizer to sell to wholesalers. One raw material – calcium nitrate – is purchased from a nearby supplier at $ per ton. Zartex estimates it will need 5,750,000 tons of calcium nitrate next year.
The annual carrying cost for this material is 40% of the acquisition cost, and the ordering cost is $595.
a) What is the most economical order quantity?
b) How many orders will be placed per year?
c) How much time will elapse between orders?

28. Example 10.2
Electronic Village stocks and sells a particular brand of personal computer. It costs the store Rs450 each time it places an order with the manufacturer for the personal computers. The annual cost of carrying the PCs in inventory is Rs170. The store
manager estimates that annual demand for the PCs will be 1200 units. Determine the optimal order quantity and the total minimum inventory cost.

29. Reorder Point ROP = D X LT D = Demand rate per period
Quantity to which inventory is allowed to drop before replenishment order is made
Need to order EOQ at the Reorder Point:
ROP = D X LT
D = Demand rate per period
LT = lead time in periods

30. Example
The I-75 Discount Carpet Store is open 311 days per year. If annual demand is 10,000 yards of Super Shag Carpet and the lead time to receive an order is 10 days, determine the reorder point for carpet.

31. Example (a) Whenever item X is ordered, what should the order size be?
Item X is a standard item stocked in a company’s inventory of component parts. Each year the firm, on a random basis, uses about 2000 of item X, which costs Rs25 each. Storage costs, which include insurance and cost of capital, amount to Rs5 per unit of average inventory. Every time an order is placed for more item X, it costs Rs10.
(a) Whenever item X is ordered, what should the order size be?
(b) What is the annual cost for ordering item X?
(c) What is the annual cost for storing item X?

32. Production Quantity Model(EOQ for lot)
An inventory system in which an order is received gradually, as inventory is simultaneously being depleted
Non-instantaneous receipt model
assumption that Q is received all at once is relaxed
p - daily rate at which an order is received over time, production rate
d - daily rate at which inventory is demanded

33. Assumptions of Production Quantity Model
Demand is known with certainty and is constant over time
No safety stock
No shortages are allowed
Lead time for the receipt of orders is constant
Goods are supplied (p)at and consumed (d)at uniform rate,
Supply rate is greater than usage rate.
Quantity Discount does not exist 33

34. Production Quantity Model (cont.)
p = supply rate d = consumption rate
Maximum inventory level = ( p- d)
= Q 1 - Q p d
Average inventory level = 2 Q 2 d p
Annual carrying cost= Cc 34

35. Production Quantity Model (cont.)
p = supply rate d = consumption rate
Annual ordering cost=
TC = d p
CoD Q
CcQ 2
Qopt =
2CoD
Cc 1 -
CoD Q 35

36. Production Quantity Model (cont.)
Q(1-d/p)
Inventory
level
(1-d/p) Q 2
Time
Order
receipt period
Begin
order
receipt
End
Maximum
inventory level
Average
(p-d) 36

37. Production Quantity Model: Example
Cc = $0.75 per yard Co = $150 D = 10,000 yards
d = 10,000/311 = 32.2 yards per day p = 150 yards per day
Qopt = = = 2,256.8 yards
2CoD
Cc 1 - d p
2(150)(10,000)
32.2
150
TC = = $1,329 d p
CoD Q
CcQ 2
Production run = = = days per order Q p
2,256.8
150 37

38. Production Quantity Model: Example (cont.)
Number of production runs = = = 4.43 runs/year D Q
10,000
2,256.8
Maximum inventory level = Q = 2,
= 1,772 yards d p
32.2
150 38

39. Example
I-75 Outlet Store has its own manufacturing facility in which it produces Super Shag carpet. The ordering cost is the cost of setting up the production process to make Super Shag carpet. Estimated annual demand is 10,000 meters of carpet, and annual carrying cost is Rs0.75 per meter. The manufacturing facility operates the same days the store is open (i.e., 311 days) and produces 150 meters of the carpet per day. Determine the optimal order size, total inventory cost, the length of time to receive an order, the number of orders per year, and the maximum inventory level.

40. Example: EOQ for Production Lots
Highland Electric Co. buys coal from Cedar Creek Coal Co. to generate electricity. CCCC can supply coal at the rate of 3,500 tons per day for $10.50 per ton. HEC uses the coal at a rate of 800 tons per day and operates 365 days per year.HEC’s annual carrying cost for coal is 20% of the acquisition cost, and the ordering cost is $5,000.
a) What is the economical production lot size?
b) What is HEC’s maximum inventory level for coal?

41. Quantity Discounts
Price per unit decreases as order quantity increases
TC = PiD
CoD Q
CcQ 2
PO= if Q<q1
P1= if q1<Q<q2
P2= if q2<Q<q3 .
P n-1= if Q>=qn
where
P i= 41

42. Quantity Discounts Cc= I *Pi Qoptm=
Price per unit decreases as order quantity increases
Where
Cc= I *Pi
I =carrying cost %
2CoD Cc
Qoptm=
PO= if Q<q1
P1= if q1<Q<q2
P2= if q2<Q<q3 .
P n-1= if Q>=qn
where
P i= 42

43. Quantity Discount Model (cont.)
Qopt
Carrying cost
Ordering cost
Inventory cost ($)
Q(d1 ) = 100
Q(d2 ) = 200
TC (d2 = $6 )
TC (d1 = $8 )
TC = ($10 )
ORDER SIZE PRICE
$10
100 – (d1)
(d2) 43

44. Price-Break Example Problem Data (Part 1)
A company has a chance to reduce their inventory ordering costs by placing larger quantity orders using the price-break order quantity schedule below. What should their optimal order quantity be if this company purchases this single inventory item with an ordering cost of Rs4, a carrying cost rate of 2% of the inventory cost of the item, and an annual demand of 10,000 units?
Order Quantity(units) Price/unit(Rs)
0 to 2,499 Rs1.20
2,500 to 3,
4,000 or more 14 44

45. Price-Break Example Solution (Part 2)
First, plug data into formula for each price-break value of “C”
Annual Demand (D)= 10,000 units
Cost to place an order (S)= Rs4
Carrying cost % of total cost (i)= 2%
Cost per unit (C) = $1.20, $1.00, $0.98
Next, determine if the computed Qopt values are feasible or not
Interval from 0 to 2499, the Qopt value is feasible
Interval from , the Qopt value is not feasible
Interval from 4000 & more, the Qopt value is not feasible 15 45

46. Price-Break Example Solution (Part 4)
Next, we plug the true Qopt values into the total cost annual cost function to determine the total cost under each price- break
TC(0-2499)=(10000*1.20)+(10000/1826)*4+(1826/2)(0.02*1.20)
= Rs12,043.82
TC( )= Rs10,041
TC(4000&more)= Rs9,949.20
Finally, we select the least costly Qopt, which is this problem occurs in the 4000 & more interval. In summary, our optimal order quantity is 4000 units 15 46

47. Quantity Discount: Example
A hardware store procures and sells hardware items.Information on a item s give here:
Expected annual sales=8,000 units
Ordering cost=Rs.180 per order
Holding cost=10% of the average inventory value.
Items can be purchased to the following schedule:
LOT SIZE UNIT PRICE(In Rs.)
Rs 22.00
1,000-1,499 Rs.20.00
1, Rs.19.00
2,000 and above Rs
We are require to determine the best order size. 47