1. Logistics Systems Engineering
SMU
SYS 7340
NTU
SY-521-N
Logistics Systems Engineering
Inventory - Requirements, Planning and Management
Dr. Jerrell T. Stracener, SAE Fellow

2. Inventory Requirements1
Why hold inventory?
Enables firm to achieve economics of scale
Balances supply and demand
Enable specialization in manufacturing
Provides uncertainty in demand and order cycle
Acts as a buffer between critical interfaces within the channel of distribution

3. Inventory Requirements
Economics of scale
Price per unit
LTL movements
Long production runs with few line changes
Cost of lost sales
Balancing supply and demand
Holidays
Raw material availability
Specialization
Manufacturing process
Longer production runs

4. Inventory Requirements
Protection from Uncertainties
Future prices
Shortages
World conflicts
Plant catastrophe
Labor disputes
Improve customer service
Buffering
See following graph

5. Inventory Requirements

6. Inventory Planning2 Cycle Stock In transit Safety Stock
Speculative Stock
Seasonal Stock
Dead Stock

7. Inventory Planning2

8. Inventory Planning2

9. Inventory Mangement3 Economic Order Quantity (EOQ)
Minimizes the inventory carrying cost
Minimizes the ordering cost
Total Cost
Annual Cost
EOQ
Inventory
Carrying
Cost
Ordering
Cost
Size of Order

10. Inventory Management EOQ formula: where
P = the ordering cost (dollars/order)
D = Annual demand (number of units)
C = Annual inventory carrying cost (percent of product cost or value)
V = Average cost per unit inventory

11. Inventory Management
Note, if the number is 124 units and there are 20 units per order, then the order quantity becomes 120 units
Adjustments to the EOQ
Includes volume transportation discounts
Considers quantity discounts

12. Inventory Management Adjustments to the EOQ (continue) where
Q1 = the maximum quantity that can be economically ordered
r = the percentage of price reduction if a larger quantity is ordered
D = the annual demand in units
C = the inventory carrying cost percentage
Q0 = the EOQ based on current price

13. Safety Stock Requirements4
Formula for calculating the safety stock requirements:
where
sc = units of safety stock needed to satisfy 68% of all probabilities
R = average replenishment cycle
sR = STD of replenishment cycle
S = average daily sales
sS = STD of daily sales

14. Calculating Fill Rate Formula for calculating the fill rate: where
FR = Fill rate
sc = combined safety stock required to consider both variability in lead time and demand
EOQ = order quantity
I(K) = service function magnitude factor based on desired number of STD

15. Calculating Fill Rate
I(K) Table

16. References
Douglas M. Lambert and James R. Stock, “Strategic Logistics Management”, third edition, (Boston, MA: Irwin, 1993), pp
2 Ibid, pp
3 Ibid, pp
4 Ibid, pp. 415
5 Ibid, pp. 420

17. Logistics Systems Engineering
SMU
SYS 7340
NTU
SY-521-N
Logistics Systems Engineering
Mathematical Computations of Inventory
Dr. Jerrell T. Stracener, SAE Fellow

18. Mathematical Computations
Problems with ordering too much
Items affecting ordering cost
Cost Trade-Offs Chart
Economic Order Quantity (EOQ)
EOQ considering discounts
Uncertainties
Basic Statistics
Safety Stock Requirements
Calculating Fill Rate

19. Problems with ordering too much
Financial Statements
Quick Ratio
Inventory Turnover
Debt Ratio
Basic Earning Power (BEP)
Return on Total Assets (ROA)
Inventorying
Warehousing

20. Problems with ordering too much
Obsolescence
Pricing
Obligation to Shareholders
Demotion
Market Share

21. Items affecting ordering cost
Transmitting the order
Receiving the order
Placing in storage
Processing invoice
Restocking Cost
Transmitting & processing inventory transfers
Handling the product
Receiving at field location
Cost associated with documentation

22. Cost Trade-Offs: Most Economical OQ
Total Cost
Lowest Total Cost
(EOQ)
Inventory
Carry Cost
Ordering Cost

23. Inventory Management EOQ formula: where
P = the ordering cost (dollars/order)
D = Annual demand (number of units)
C = Annual inventory carrying cost (percent of product cost or value)
V = Average cost per unit inventory

24. Inventory Management Example
A company purchased a line of relay for use in its air conditioners from a manufacturer in the Midwest. It ordered approximately 300 cases of 24 units each 54 times per year. The annual volume was about 16,000 cases. The purchase price was $8.00 per case, the ordering cost were $10.00 per order, and the inventory carrying cost was 25 percent. The delivered cost of a case of product would be $9.00 ($8.00 plus $1.00 transportation). What is the EOQ?

25. Inventory Management At what rate should the company order skates?
Solution:
P = $10 per shipment
D = 16,000 units per year
C = 0.25
V = $9.00, and

26. Inventory Management Solution:
Note, if the number is 377 units and there are 20 units per order, then the order quantity becomes 380 units

27. Inventory Management Assumptions:
A continuous, constant and known rate of demand
A constant and known replenishment or lead time
A constant purchase price that is independent of the order quantity or time
A constant transportation cost that is independent of the order quantity or time
The satisfaction of all demand (no stock-outs are permitted)

28. Inventory Management Assumptions: No inventory in transit
Only one item in inventory, or at least no interaction
An infinite planning horizon
No limit on capital availability

29. Inventory Management
Adjustments to the EOQ formula must be made to address
Volume transportation discounts
Quantity discounts
Thus, the formula becomes:

30. Inventory Management where,
Q1 = the maximum quantity that can be economically ordered
r = the percentage of price reduction if a larger quantity is ordered
D = the annual demand in units
C = the inventory carrying cost percentage
Q0 = the EOQ based on current price

31. Inventory Management Example
Using the same example as previous, assume that the relays weighed 25 pounds per case. The freight rate was $4.00 per 100 lbs. on shipments of less than 15,000 lbs., and $3.90 per 100 lbs on shipments of 15,000 to 39,000 lbs. Lastly, on shipments of more than 39,000 lbs, the cost is $3.64 per 100 lbs. The relays were shipped on pallets of 20 cases. What is the cost if the company shipped in quantities of 40,000 pounds or more?

32. Inventory Management Solution:
Cost per case: $3.64/100 lbs x25 lbs= $0.91.
r = [($ $8.91) / $9.00] x 100 = 1.0%
And Q1 is:

33. Uncertainties
What drives managers to consider safety stocks of the product?
Economic conditions
Competitive actions
Change in government regulation
Market shifts
Consumer buying patterns
Transit times
Supplier lead times

34. Uncertainties
What drives managers to consider safety stocks of the product?
Raw material
Suppliers not responding
Work stoppage

35. Basic Statistics Properties of a Normal Distribution
Resembles a bell shape curve
Measures central tendency
Probabilities are determined by its mean, u and standard deviation, s, where
and the theoretically infinite range is

36. Basic Statistics
Normal Curve

37. Safety Stock Requirements
Example: Given

38. Safety Stock Requirements
Formula for calculating the safety stock requirements:
where
sc = units of safety stock needed to satisfy 68% of all probabilities
R = average replenishment cycle
sR = STD of replenishment cycle
S = average daily sales
sS = STD of daily sales

39. Safety Stock Requirements
And where:
Example
Calculate the Safety Stock Requirements based on the two following tables:

40. Safety Stock Requirements
Given: Sales History for Market Area

41. Safety Stock Requirements
Solution: Calculation of STD of Sales
Where S= 100, and n= 25, and Sfd2 = 10,000

42. Safety Stock Requirements
Solution: Given - Replenishment Cycle
Where R = 10, and n = 16, and Sfd2 = 40

43. Safety Stock Requirements
Solution:

44. Safety Stock Requirements
Solution(continue):
Finally, we have

45. Calculating Fill Rate Formula for calculating the fill rate: where
FR = Fill rate
sc = combined safety stock required to consider both variability in lead time and demand
EOQ = order quantity
I(K) = service function magnitude factor based on desired number of STD

46. Calculating Fill Rate Example
Using the data from the previous example, what will the fill rate be if a manager wants to hold 280 units as safety stock? Assume EOQ = 1,000.

47. Calculating Fill Rate Solution:
The safety stock determined by the manager is 280 units. Thus, K is equal to 280 / 175 = From the table in the end, we see that I(K) = Hence,

48. Calculating Fill Rate
Insert table 10-8, p 422

49. Calculating Fill Rate Differences
Safety Stock: policy of customer service and inventory availability
Fill Rate: represents the percent of units demanded that are on hand to fill customer orders. The magnitude of stock-out.

50. Calculating Fill Rate Conclusion
K (the safety factor) is the safety stock the manager decides to hold divided by EOQ
Therefore:
The average fill rate is 99.59%. That is, of every 1,000 units of product XYZ demanded, will be on hand to be sold if the manager uses 280 units of safety stock and orders 1,000 units each time.