LESSON 3 The EOQ Model – Multi-Period 17Julyy2014

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

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

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

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

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

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

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

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

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*

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

√ 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 $8.00 201-300 $7.00 301 + $6.00

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

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

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

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

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

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

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

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

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

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

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

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: http://www.dau.mil/pubscats/PubsCats/PM/articles02/BOGSE-0C2.pdf

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

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

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

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

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.