1. LESSON 3 The EOQ Model – Multi-Period
17Julyy2014

2. Lesson Objectives
Upon completion of this lesson, you should be able to:
Determine the occasions for using a fixed Economic Order Quantity (EOQ) model
Determine the total cost of inventory for the EOQ from a given scenario
Determine a reorder point
Select price points for determining EOQ quantity discounts

3. Lesson Topics This lesson will cover the following topics:
The EOQ Model – Multi-Period
Total Cost of Inventory
Reorder Point
Quantity Discounts

4. What’s In It For Me?
Understanding how and why contractors optimize order quantities for multiple-order purchasing situations will enable you to assess a contractor’s supply chain management decision effectiveness

5. Lesson Introduction
When you are able to place multiple orders, how do you determine what quantity and when to place each order?

6. The EOQ Model – Multi-Period
Lesson Topics:
The EOQ Model – Multi-Period
Total Cost of Inventory
Reorder Point
Quantity Discounts

7. The EOQ Model – Multi-Period
What is a multi-period model?
Average
Inventory Level
for Small
Batch Order Size
Inventory
Level
Time
Small Batch
Large Batch

8. Optimal Order Quantity (Q*)
What is EOQ Model?
Order Quantity
Cost $
Total Cost
Ordering Costs
Holding Costs
Optimal Order Quantity (Q*)

9. Optimal Order Quantity (Q*)
Basics of EOQ Model
Optimal Order Quantity (Q*)
Total Cost
Holding Costs
Ordering Costs
Order Quantity
Cost $
Based on Perpetual/ Continuous review
Two parameters:
Q* - Optimal order quantity
R - Reorder point

10. When is the EOQ Appropriate?
Demand is constant
Orders of an optimal size (Q*) are placed when inventory reaches a reorder point (R)
Ideally, orders are received as inventory reaches zero
Time R Q*

11. Only one product is involved
EOQ Assumptions
Lead time…
Demand…
Price per unit…
Item cost …
Ordering and holding costs…
Replenishment…
Replenishment batch…
Constant
Constant and uniform
Fixed
Instantaneous
Delivered all at once
Only one product is involved

12. √ Basic EOQ Formula Q = Order quantity D = Annual demand
S = Cost of placing order
H = Holding cost/unit
Q =
2 * D * S H √
H = i * C
i = Carrying cost rate
C = Cost per unit

13. Example: Determining the EOQ
Class Activity
Refer to Module 6, Lesson 3, Scenario 1 CMM100_M6_L3_S1_Scenario_FINAL.docx
Read directions on Determining the EOQ
Read Question 1 and 2
Complete this activity as a class on the following slides

14. Scenario Solution (1 of 3)
Wellness Pharmaceuticals
Provides medications to military hospitals and Military Treatment Facilities (MTF)
Find the EOQ for ibuprofen

15. Scenario Solution (2 of 3)
Question 1: “Does the product in the scenario fit a multi- period situation?”
Demand…
Item cost…
Ordering and holding costs…
Price per unit…
Replenishment…
Replenishment batch…
Constant
Fixed
Instantaneous
Delivered all at once
Answer: Yes

16. Scenario Solution (3 of 3)
Question 2: “What is the optimal order quantity (Q*) for the product?”
Unit Cost = $15.00
Order cost = $30
Demand = 5,000 units per year
Carrying cost rate/unit = 0.40

17. Job Aid: EOQ Calculator
Refer to Module 6, Lesson 3, Job Aid 1 CMM100_M6_L3_JA1_EOQ Calculator.xlsx

18. Optimal Order Quantity (Q*)
Scenario Review
Order Quantity
Cost $
Total Cost
Ordering Costs
Holding Costs
Optimal Order Quantity (Q*)

19. When is it appropriate to use the EOQ Model?
Question and Answer
When is it appropriate to use the EOQ Model?
Multiple purchasing occasions
One-time purchasing occasions
Occasions do not matter as long as a reorder point is determined
When demand is uncertain

20. Question and Answer
The EOQ model is used to monitor and control inventory for this type of inventory system:
Periodic/Scheduled inventory system
Perpetual/Continuous review system
Procedural/Renewal system
Programmed/Automated system

21. Question and Answer
The EOQ is suitable to use when demand is constant, and when item cost and ordering/ holding cost are both________.
Flexible
Fixed
Fluctuating
Costs are never a consideration

22. Total Cost of Inventory
Lesson Topics:
The EOQ Model – Multi-Period
Total Cost of Inventory
Reorder Point
Quantity Discounts

23. Total Cost of Inventory
Cost of the items
Holding cost
Ordering cost
The goal of multi-period EOQ is to minimize total cost

24. Total Annual Costs of Inventory
TC = DC +
S + H
Total Annual Cost
DC: Annual demand * cost of each unit purchased = total annual cost of the items based on unit pricing alone
(D/Q)S: the number of times you make a purchase during the year * how much it costs to order the items = total ordering costs for the year
Annual HoldingCost
Total Annual Cost of Inventory Formula: D Q Q 2
D/Q: Annual demand / quantity purchased = how many times you must purchase items during the year
Q = Quantity purchased D = Annual demand S = Ordering cost per order H = Holding cost per unit

25. Example: Total Cost of Inventory
Class Activity
Refer to Module 6, Lesson 3, Scenario 1 CMM100_M6_L3_S1_Scenario_FINAL.docx
Read Question 3 (a-e) on determining the Total Cost of Inventory
Complete the activity as a class using the following slides

26. Example: Total Cost of Inventory (cont.)
Antihistamine is the most ordered product from the MTFs
Determine:
EOQ and item cost
Annual holding cost
Annual ordering cost
Total cost of inventory

27. Job Aid: EOQ Calculator
Refer to Module 6, Lesson 3, Job Aid 1 CMM100_M6_L3_JA1_EOQ Calculator.xlsx

28. What is the goal of the multi-period EOQ model?
Question and Answer
What is the goal of the multi-period EOQ model?
To stockpile inventory in case of emergencies
To minimize total cost of inventory
To eliminate unstable demand
To maximize ordering costs

29. Total annual cost of inventory includes:
Question and Answer
Total annual cost of inventory includes:
Annual demand, demand per lead time period, and reorder point
Annual purchase cost, annual ordering cost, and annual holding cost
Carrying cost penalties, costs for volume, and safety stock cost

30. Reorder Point Lesson Topics: The EOQ Model – Multi-Period
Total Cost of Inventory
Reorder Point
Quantity Discounts

31. Reorder Point
Reorder Point (R) – Inventory level that triggers an order for additional units
Reorder
Point
Order Quantity
Lead
Time
Inventory
Contractors use reorder points to account for order lead time, so that stock is not exhausted before the order arrives

32. Example: Tracking an EOQ Inventory Situation
Part for hydraulic steering system M2/3 Bradley Fighting Vehicle (BFV):
Military unit receives an order quantity Q
The cycle then repeats
Time R
Number of units on hand Q Q Q Q
When the unit reaches a level of inventory of R, they place their next Q-sized order
The unit uses them up over time

33. Reorder Point Formula R = d * L d = D / periods per year
R = Reorder Point
d = demand per lead time period
L = Lead time
d = D / periods per year

34. Reorder Point with Safety Stock
R = d * L + SS
R = Reorder Point
d = demand per lead time period
L = Lead time
SS = Safety Stock

35. Example: Determining the Reorder Point
Class Activity
Refer to Module 6, Lesson 3, Scenario 1 CMM100_M6_L3_S1_Scenario_FINAL.docx
Read Question 4 on determining the reorder point
Complete the activity as a class using the following slides

36. Scenario Solution Reorder point for antihistamine product
Product lead time is 14 days
L = 14
Product ships 200 days per year
Shipments = 200 days a year
d = D/ periods per year
d = 10,000/ 200
d = 50
R = d * L
R = 50 *14
R = 700 units
Lead Time
2 Weeks
Q* = 194
R = 100

37. Why do contractors set reorder points for their products?
Question and Answer
Why do contractors set reorder points for their products?
Reorder points encourage safety stock
Reorder points reduce cycle stock
Reorder points trigger orders for additional units
All of the above

38. Question and Answer
If a contractor wants to maintain safety stock to protect the company from stockouts, the firm would add the amount of safety stock to their reorder point calculation.
True
False

39. Quantity Discounts Lesson Topics: The EOQ Model – Multi-Period
Total Cost of Inventory
Reorder Point
Quantity Discounts

40. Quantity Discounts Quantity Discount Models Similar to EOQ model
Determines optimal quantity to order
Analyzes different price points and how they reduce total cost
Unit price depends upon quantity ordered

41. Example: Quantity Discounts
Class Activity
Refer to Module 6, Lesson 3, Scenario 1 CMM100_M6_L3_S1_Scenario_FINAL.docx
Read Question 5 on determining a quantity discount
Complete the activity as a class using the following slides

42. Scenario Solution
Wellness offers various quantity discounts if the Department of Defense (DoD) purchase more product than usual
Quantity Ordered
Price per Unit (C)
0-200
$8.00
$7.00
301 +
$6.00

43. Evaluating Quantity Discounts
Two step process:
Find the lowest price point with a feasible EOQ
Compare total annual cost of price point with lowest feasible EOQ and all lower price points
Quantity Ordered
Price Per Unit
0 – 200
$8.00
201 – 300
$7.00
301 +
$6.00

44. Step 1: Evaluating Quantity Discounts (1 of 4)
Determine lowest price point with a feasible EOQ:
Compute EOQ for lowest price first
Continue with next higher price
Move to step 2 once a feasible EOQ value is found
Quantity Ordered
Price Per Unit
EOQ
0 – 200
$8.00
201 – 300
$7.00
301 +
$6.00
224
Quantity Ordered
Price Per Unit
EOQ
0 – 200
$8.00
201 – 300
$7.00
301 +
$6.00

45. Step 1: Evaluating Quantity Discounts (2 of 4)
Determine lowest price point with a feasible EOQ:
Compute EOQ for lowest price first
Continue with next higher price
Move to step 2 once a feasible EOQ value is found
EOQ is not feasible.
224 is not within Order Quantity range (301+).
Quantity Ordered
Price Per Unit
EOQ
0 – 200
$8.00
201 – 300
$7.00
301 +
$6.00
Quantity Ordered
Price Per Unit
EOQ
0 – 200
$8.00
201 – 300
$7.00
301 +
$6.00
224

46. Step 1: Evaluating Quantity Discounts (3 of 4)
Determine lowest price point with a feasible EOQ:
Compute EOQ for lowest price first
Continue with next higher price
Move to step 2 once a feasible EOQ value is found
Quantity Ordered
Price Per Unit
EOQ
0 – 200
$8.00
201 – 300
$7.00
207
301 +
$6.00
224
Quantity Ordered
Price Per Unit
EOQ
0 – 200
$8.00
201 – 300
$7.00
301 +
$6.00
Quantity Ordered
Price Per Unit
EOQ
0 – 200
$8.00
201 – 300
$7.00
301 +
$6.00
224

47. Step 1: Evaluating Quantity Discounts (4 of 4)
Determine lowest price point with a feasible EOQ:
Compute EOQ for lowest price first
Continue with next higher price
Move to step 2 once a feasible EOQ value is found
Quantity Ordered
Price Per Unit
EOQ
0 – 200
$8.00
201– 300
$7.00
207
301 +
$6.00
224

48. Step 2: Evaluating Quantity Discounts (1 of 4)
Determine the valid quantity
EOQ is not within Order Quantity range (301 +).
Use the minimum Order Quantity for price point (301).
Quantity Ordered
Price Per Unit (C)
EOQ
Valid Qty (Q) TC
0 – 200
$8.00
201 – 300
$7.00
207
301 +
$6.00
224
Quantity Ordered
Price Per Unit (C)
EOQ
Valid Qty (Q)
Total Cost
(TC)
0 – 200
$8.00
201 – 300
$7.00
207
301 +
$6.00
224
301

49. Step 2: Evaluating Quantity Discounts (2 of 4)
Determine the valid quantity
EOQ is within Order Quantity range (201 – 300).
Use EOQ for price point (207).
Quantity Ordered
Price Per Unit (C)
EOQ
Valid Qty (Q)
Total Cost
(TC)
0 – 200
$8.00
201 – 300
$7.00
207
301 +
$6.00
224
301
Quantity Ordered
Price Per Unit (C)
EOQ
Valid Qty (Q) TC
0 – 200
$8.00
201 – 300
$7.00
207
301 +
$6.00
224
Quantity Ordered
Price Per Unit (C)
EOQ
Valid Qty (Q)
Total Cost
0 – 200
$8.00
201 – 300
$7.00
207
301 +
$6.00
224
301

50. Step 2: Evaluating Quantity Discounts (3 of 4)
Next, find the lowest Total Cost
Quantity Ordered
Price Per Unit (C)
EOQ
Valid Qty (Q)
Total Cost
(TC)
0 – 200
$8.00
---
201 – 300
$7.00
207
301 +
$6.00
224
301
Use the EOQ Calculator Job Aid
CMM100_M6_L3_JA1_EOQ Calculator.xlsx

51. Total Annual Cost of Inventory
Quantity Ordered
Price Per Unit (C)
Valid Qty (Q)
201 – 300
$7.00
207
Change the cost of item to $7.00
EOQ displays “207”
TC computes to $70,289.83

52. Total Annual Cost of Inventory (cont.)
Quantity Ordered
Price Per Unit (C)
Valid Qty (Q)
301 +
$6.00
301
Change the cost of item to $6.00
Change the EOQ to 301
TC computes to $60,280.27

53. Step 2: Evaluating Quantity Discounts (4 of 4)
Compare total annual cost of price point with lowest feasible EOQ and all lower price points
Quantity Ordered
Price Per Unit (C)
Valid Qty (Q)
Total Cost
(TC)
0 – 200
$8.00
---
201 – 300
$7.00
250
$70,289.83
301 +
$6.00
301
$60,280.27
Quantity discount of 301 achieves the minimum total cost

54. Self-Directed Learning Activity
Individual Activity
Read: “Total Ownership Cost” article as homework or during class breaks
Discusses the value of quantity discounts to the DoD
File:
CMM100_M6_L3_Total_Ownership_Cost.pdf
Or can be retrieved from the DAU website:

55. What is the purpose of analyzing price points for quantity discounts?
Question and Answer
What is the purpose of analyzing price points for quantity discounts?
To determine the most effective reorder point for a product
To determine which price points would achieve minimum total costs
To reduce the cost of carrying inventory

56. What is the first step in analyzing quantity discounts?
Question and Answer
What is the first step in analyzing quantity discounts?
Analyze the Total Cost Curve for each price point
Compare the costs
Determine the least expensive feasible EOQ value

57. Exercise: Multi-Period EOQ Inventory Model
Small Group Exercise
Find a partner or work in a trio
Refer to Module 6, Lesson 3, Exercise 1 CMM100_M6_L3_E1_Exercise_FINAL.docx
Read directions on: Determining Economic Order Quantity
Complete the activity; be prepared to share your responses
Time allowed: 20 minutes

58. Summary Having completed this lesson, you should now be able to:
Determine the occasions for using a fixed Economic Order Quantity (EOQ) model
Determine the total cost of inventory for the EOQ from a given scenario
Determine a reorder point
Select price points for determining EOQ quantity discounts

59. Summary (cont.)
Your ability to understand the optimal order quantities for multiple order purchasing decisions helps you to evaluate suppliers’ decisions for managing their supply chain.