LESSON 3 The EOQ Model MultiPeriod 06 January

LESSON 3 The EOQ Model – Multi-Period 06 January 2014

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 Module 6 Lesson 3: The EOQ Model – Multi-Period 2

Lesson Topics This lesson will cover the following topics: § § The EOQ Model – Multi-Period Total Cost of Inventory Reorder Point Quantity Discounts Module 6 Lesson 3: The EOQ Model – Multi-Period 3

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 Module 6 Lesson 3: The EOQ Model – Multi-Period 4

Lesson Introduction When you are able to place multiple orders, how do you determine what quantity and when to place each order? Module 6 Lesson 3: The EOQ Model – Multi-Period 5

THE EOQ MODEL – MULTI-PERIOD Lesson Topics: 1) The EOQ Model – Multi-Period 2) Total Cost of Inventory 3) Reorder Point 4) Quantity Discounts Module 6 Lesson 3: The EOQ Model – Multi-Period 6

The EOQ Model – Multi-Period What is a multi-period model? Inventory Level Small Batch Large Batch Average Inventory Level for Small Batch Order Size Time Module 6 Lesson 3: The EOQ Model – Multi-Period 7

What is EOQ Model? Cost $ Total Cost Holding Costs Ordering Costs Optimal Order Quantity (Q*) Module 6 Lesson 3: The EOQ Model – Multi-Period Order Quantity 8

Basics of EOQ Model Cost $ Total Cost Holding Costs Ordering Costs Optimal Order Quantity (Q*) Based on Perpetual/ Continuous review Module 6 Lesson 3: The EOQ Model – Multi-Period Order Quantity Two parameters: • Q* - Optimal order quantity • R - Reorder point 9

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 R Q* Time Module 6 Lesson 3: The EOQ Model – Multi-Period 10

EOQ Assumptions § § § § Lead time… Demand… Price per unit… Item cost … Ordering and holding costs… Replenishment batch… Module 6 Lesson 3: The EOQ Model – Multi-Period 11

Basic EOQ Formula Q = Order quantity D = Annual demand S = Cost of placing order H = Holding cost/unit H=i*C Module 6 Lesson 3: The EOQ Model – Multi-Period Q= 2*D*S H √ i = Carrying cost rate C = Cost per unit 12

Example: Determining the EOQ Class Activity § Refer to Module 6, Lesson 3, Scenario 1 CMM 100_M 6_L 3_S 1_Scenario_FINAL. docx § Read directions on Determining the EOQ § Read Question 1 and 2 § Complete this activity as a class on the following slides Module 6 Lesson 3: The EOQ Model – Multi-Period 13

Scenario Solution (1 of 3) § § § Wellness Pharmaceuticals Provides medications to military hospitals and Military Treatment Facilities (MTF) Find the EOQ for ibuprofen Module 6 Lesson 3: The EOQ Model – Multi-Period 14

Scenario Solution (2 of 3) Question 1: “Does the product in the scenario fit a multiperiod situation? ” § § § Demand… Item cost… Ordering and holding costs… Price per unit… Replenishment batch… § § § Constant Fixed Constant Instantaneous Delivered all at once Answer: Yes Module 6 Lesson 3: The EOQ Model – Multi-Period 15

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 Module 6 Lesson 3: The EOQ Model – Multi-Period 16

Job Aid: EOQ Calculator Refer to Module 6, Lesson 3, Job Aid 1 CMM 100_M 6_L 3_JA 1_EOQ Calculator. xlsx Module 6 Lesson 3: The EOQ Model – Multi-Period 17

Scenario Review Cost $ Total Cost Holding Costs Ordering Costs Optimal Order Quantity (Q*) Module 6 Lesson 3: The EOQ Model – Multi-Period Order Quantity 18

Question and Answer When is it appropriate to use the EOQ Model? A. Multiple purchasing occasions B. One-time purchasing occasions C. Occasions do not matter as long as a reorder point is determined D. When demand is uncertain Module 6 Lesson 3: The EOQ Model – Multi-Period 19

Question and Answer The EOQ model is used to monitor and control inventory for this type of inventory system: A. Periodic/Scheduled inventory system B. Perpetual/Continuous review system C. Procedural/Renewal system D. Programmed/Automated system Module 6 Lesson 3: The EOQ Model – Multi-Period 20

Question and Answer The EOQ is suitable to use when demand is constant, and when item cost and ordering/ holding cost are both____. A. B. C. D. Flexible Fixed Fluctuating Costs are never a consideration Module 6 Lesson 3: The EOQ Model – Multi-Period 21

TOTAL COST OF INVENTORY Lesson Topics: 1) The EOQ Model – Multi-Period 2) Total Cost of Inventory 3) Reorder Point 4) Quantity Discounts Module 6 Lesson 3: The EOQ Model – Multi-Period 22

Total Cost of Inventory § § § Cost of the items Holding cost Ordering cost Module 6 Lesson 3: The EOQ Model – Multi-Period The goal of multi-period EOQ is to minimize total cost 23

Total Annual Costs of Inventory Total Annual Cost of Inventory Formula: Total Annual Cost TC = DC + D S + Q H Q 2 DC: Annual demand * cost of each unit purchased = total annual cost of the items based on unit pricing alone Annual Holding Cost (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 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 Module 6 Lesson 3: The EOQ Model – Multi-Period 24

Example: Total Cost of Inventory Class Activity § § § Refer to Module 6, Lesson 3, Scenario 1 CMM 100_M 6_L 3_S 1_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 Module 6 Lesson 3: The EOQ Model – Multi-Period 25

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 Module 6 Lesson 3: The EOQ Model – Multi-Period 26

Job Aid: EOQ Calculator Refer to Module 6, Lesson 3, Job Aid 1 CMM 100_M 6_L 3_JA 1_EOQ Calculator. xlsx Module 6 Lesson 3: The EOQ Model – Multi-Period 27

Question and Answer What is the goal of the multiperiod EOQ model? A. To stockpile inventory in case of emergencies B. To minimize total cost of inventory C. To eliminate unstable demand D. To maximize ordering costs Module 6 Lesson 3: The EOQ Model – Multi-Period 28

Question and Answer Total annual cost of inventory includes: A. Annual demand, demand per lead time period, and reorder point B. Annual purchase cost, annual ordering cost, and annual holding cost C. Carrying cost penalties, costs for volume, and safety stock cost Module 6 Lesson 3: The EOQ Model – Multi-Period 29

REORDER POINT Lesson Topics: 1) The EOQ Model – Multi-Period 2) Total Cost of Inventory 3) Reorder Point 4) Quantity Discounts Module 6 Lesson 3: The EOQ Model – Multi-Period 30

Reorder Point (R) – Inventory level that triggers an order for additional units Inventory Reorder Point Order Quantity Time Lead Time Module 6 Lesson 3: The EOQ Model – Multi-Period Contractors use reorder points to account for order lead time, so that stock is not exhausted before the order arrives 31

Example: Tracking an EOQ Inventory Situation Part for hydraulic steering system M 2/3 Bradley Fighting Vehicle (BFV): 1. Military unit receives an order quantity Q 4. The cycle then repeats Number of units on hand Q Q R 2. The unit uses them up over time Module 6 Lesson 3: The EOQ Model – Multi-Period 3. When the unit reaches a level of inventory of R, they place their next Q-sized order Time 32

Reorder Point Formula R=d*L § § d = D / periods per year Module 6 Lesson 3: The EOQ Model – Multi-Period § R = Reorder Point d = demand per lead time period L = Lead time 33

Reorder Point with Safety Stock R = d * L + SS § § Module 6 Lesson 3: The EOQ Model – Multi-Period R = Reorder Point d = demand per lead time period L = Lead time SS = Safety Stock 34

Example: Determining the Reorder Point Class Activity § § § Refer to Module 6, Lesson 3, Scenario 1 CMM 100_M 6_L 3_S 1_Scenario_FINAL. docx Read Question 4 on determining the reorder point Complete the activity as a class using the following slides Module 6 Lesson 3: The EOQ Model – Multi-Period 35

Scenario Solution § Reorder point for antihistamine product – D = 10, 000 § Product lead time is 14 days – L = 14 § Product ships 200 days per year – Shipments = 200 days a year Q* = 194 d = D/ periods per year d = 10, 000/ 200 d = 50 R=d*L R = 50 *14 R = 700 units Lead Time 2 Weeks R = 100 Module 6 Lesson 3: The EOQ Model – Multi-Period 36

Question and Answer Why do contractors set reorder points for their products? A. Reorder points encourage safety stock B. Reorder points reduce cycle stock C. Reorder points trigger orders for additional units D. All of the above Module 6 Lesson 3: The EOQ Model – Multi-Period 37

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. A. True B. False Module 6 Lesson 3: The EOQ Model – Multi-Period 38

QUANTITY DISCOUNTS Lesson Topics: 1) The EOQ Model – Multi-Period 2) Total Cost of Inventory 3) Reorder Point 4) Quantity Discounts Module 6 Lesson 3: The EOQ Model – Multi-Period 39

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 Module 6 Lesson 3: The EOQ Model – Multi-Period 40

Example: Quantity Discounts Class Activity § § § Refer to Module 6, Lesson 3, Scenario 1 CMM 100_M 6_L 3_S 1_Scenario_FINAL. docx Read Question 5 on determining a quantity discount Complete the activity as a class using the following slides Module 6 Lesson 3: The EOQ Model – Multi-Period 41

Scenario Solution § Wellness offers various quantity discounts if the Department of Defense (Do. D) purchase more product than usual Quantity Price per Ordered Unit (C) 0 -200 $8. 00 201 -300 $7. 00 301 + $6. 00 Module 6 Lesson 3: The EOQ Model – Multi-Period 42

Evaluating Quantity Discounts Two step process: 1. Find the lowest price point with a feasible EOQ 2. Compare total annual cost of price point with lowest feasible EOQ and all lower price points Quantity Ordered 0 – 200 201 – 300 301 + Module 6 Lesson 3: The EOQ Model – Multi-Period Price Per Unit $8. 00 $7. 00 $6. 00 43

Step 1: Evaluating Quantity Discounts (1 of 4) Determine lowest price point with a feasible EOQ: a) Compute EOQ for lowest price first b) Continue with next higher price c) Move to step 2 once a feasible EOQ value is found Quantity Ordered 0 – 200 201 – 300 301 + Price Per Unit EOQ $8. 00 $7. 00 $6. 00 224 Module 6 Lesson 3: The EOQ Model – Multi-Period 44

Step 1: Evaluating Quantity Discounts (2 of 4) Determine lowest price point with a feasible EOQ: a) Compute EOQ for lowest price first EOQ not price feasible. b) Continue with nextishigher 224 is not Order Quantity range (301+). c) Move to within step 2 once a feasible EOQ value is found Quantity Ordered 0 – 200 201 – 300 301 + Price Per Unit EOQ $8. 00 $7. 00 $6. 00 224 Module 6 Lesson 3: The EOQ Model – Multi-Period 45

Step 1: Evaluating Quantity Discounts (3 of 4) Determine lowest price point with a feasible EOQ: a) Compute EOQ for lowest price first b) Continue with next higher price c) Move to step 2 once a feasible EOQ value is found Quantity Ordered 0 – 200 201 – 300 301 + Price Per Unit EOQ $8. 00 $7. 00 $6. 00 207 224 Module 6 Lesson 3: The EOQ Model – Multi-Period 46

Step 1: Evaluating Quantity Discounts (4 of 4) Determine lowest price point with a feasible EOQ: a) Compute EOQ for lowest price first b) Continue with next higher price c) Move to step 2 once a feasible EOQ value is found Quantity Ordered 0 – 200 201– 300 301 + Price Per Unit EOQ $8. 00 $7. 00 $6. 00 207 224 Module 6 Lesson 3: The EOQ Model – Multi-Period 47

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 Price Ordered Per Unit (C) 0 – 200 $8. 00 201 – $7. 00 301 + $6. 00 Module 6 Lesson 3: The EOQ Model – Multi-Period EOQ Valid Qty (Q) Total TC Cost (TC) 207 224 301 48

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 Price Ordered Per Unit (C) 0 – 200 $8. 00 201 – $7. 00 301 + $6. 00 Module 6 Lesson 3: The EOQ Model – Multi-Period EOQ Valid Qty (Q) 207 224 301 Total TC Cost (TC) 49

Step 2: Evaluating Quantity Discounts (3 of 4) Next, find the lowest Total Cost Quantity Ordered Price Per Unit (C) EOQ Valid Qty (Q) 0 – 200 $8. 00 --- 201 – 300 $7. 00 207 301 + $6. 00 224 301 Total Cost (TC) Use the EOQ Calculator Job Aid CMM 100_M 6_L 3_JA 1_EOQ Calculator. xlsx Module 6 Lesson 3: The EOQ Model – Multi-Period 50

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 Module 6 Lesson 3: The EOQ Model – Multi-Period 51

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 Module 6 Lesson 3: The EOQ Model – Multi-Period 52

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 Price Ordered 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 Module 6 Lesson 3: The EOQ Model – Multi-Period Quantity discount of 301 achieves the minimum total cost 53

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 Do. D File: – CMM 100_M 6_L 3_Total_Ownership_Cost. pdf – Or can be retrieved from the DAU website: http: //www. dau. mil/pubscats/Pubs. Cats/PM/articles 02/BOGSE-0 C 2. pdf Module 6 Lesson 3: The EOQ Model – Multi-Period 54

Question and Answer What is the purpose of analyzing price points for quantity discounts? A. To determine the most effective reorder point for a product B. To determine which price points would achieve minimum total costs C. To reduce the cost of carrying inventory Module 6 Lesson 3: The EOQ Model – Multi-Period 55

Question and Answer What is the first step in analyzing quantity discounts? A. Analyze the Total Cost Curve for each price point B. Compare the costs C. Determine the least expensive feasible EOQ value Module 6 Lesson 3: The EOQ Model – Multi-Period 56

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 CMM 100_M 6_L 3_E 1_Exercise_FINAL. docx Read directions on: Determining Economic Order Quantity Complete the activity; be prepared to share your responses Time allowed: 20 minutes Module 6 Lesson 3: The EOQ Model – Multi-Period 57

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 Module 6 Lesson 3: The EOQ Model – Multi-Period 58

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. Module 6 Lesson 3: The EOQ Model – Multi-Period 59