1. 11-1 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. Managing Economies of Scale in a Supply Chain: Cycle Inventory Role of Cycle Inventory in a Supply Chain Estimating Cycle Inventory Related Costs in Practice Economies of Scale to Exploit Fixed Costs Lot Sizing for a Single Product Lot Size and Ordering Cost Production Lot Sizing Aggregating Multiple Products in a Single Order Lot Sizing with Multiple Products or Customers Multiple Products Ordered and Delivered Independently Lots Ordered and Delivered Jointly Products Ordered and Delivered Jointly Aggregation with Capacity Constraint Lots Ordered and Delivered Jointly for a Selected Subset Ordered and Delivered Jointly – Frequency Varies by Order Economies of Scale to Exploit Quantity Discounts Quantity Discounts Summary

2. PowerPoint presentation to accompany Chopra and Meindl Supply Chain Management, 5e 1-2 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. 1-2 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. 1-2 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. 11-2 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. 11 Managing Economies of Scale in a Supply Chain: Cycle Inventory

3. 11-3 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. Learning Objectives 1.Balance the appropriate costs to choose the optimal lot size and cycle inventory in a supply chain. 2.Understand the impact of quantity discounts on lot size and cycle inventory. 3.Devise appropriate discounting schemes for a supply chain. 4.Understand the impact of trade promotions on lot size and cycle inventory. 5.Identify managerial levers that reduce lot size and cycle inventory in a supply chain without increasing cost.

4. 11-4 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. Example 11.6 Ordered and Delivered Jointly – Frequency Varies by Order Consider the data in example 11.3. Product managers have decided to order jointly but to be selective about which models they include in each order. Evaluate the ordering policy and cost using the procedure discussed previously. Applying Step 1 Thus

5. 11-5 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. Applying Step 2 Applying Step 3

6. 11-6 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. LiteproMedproHeavypro Demand per year ( D )12,0001,200120 Order frequency ( n ∗ ) 11.47/year5.74/year2.29/year Optimal order size ( D / n ∗ ) 1,04620952 Cycle inventory523104.526 Annual holding cost$52,307$10,461$2,615 Average flow time2.27 weeks4.53 weeks11.35 weeks Table 11-3

7. 11-7 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. Applying Step 4 Applying Step 5 Annual order costTotal annual cost $130,767

8. 11-8 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. 11.4 Economies of Scale to Exploit Quantity Discounts Lot size-based discount – discounts based on quantity ordered in a single lot Volume based discount – discount is based on total quantity purchased over a given period Two common schemes –All-unit quantity discounts –Marginal unit quantity discount or multi-block tariffs

9. 11-9 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. Quantity Discounts In order to investigate the impact of such quantity discounts on the supply chain the following questions should be answered. 1.What is the optimal purchasing decision for a buyer seeking to maximize profits? How does this decision affect the supply chain in terms of lot sizes, cycle inventories, and flow times? 2.Under what conditions should a supplier offer quantity discounts? What are appropriate pricing schedules that a supplier seeking to maximize profits should offer? We start by studying the optimal response of a retailer when faced with either of the two lot size-based discount schemes offered by the manufacturer.

10. 11-10 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. All-Unit Quantity Discounts Pricing schedule has specified quantity break points q 0, q 1, …, q r, where q 0 = 0 If an order is placed that is at least as large as q i but smaller than q i +1, then each unit has an average unit cost of C i Unit cost generally decreases as the quantity increases, i.e., C 0 > C 1 > … > C r

11. 11-11 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. Figure 11-3 Objective is to decide on a lot size that will minimize the sum of material, order, and holding costs. The solution procedure evaluates the optimal lot size for each price and picks the lot size that minimizes the overall cost.

12. 11-12 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. All-Unit Quantity Discounts Step 1:Evaluate the optimal lot size for each price C i,0 ≤ i ≤ r as follows

13. 11-13 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. All-Unit Quantity Discounts Step 2:We next select the order quantity Q * i for each price C i 1. 2. 3. Case 3 can be ignored as it is considered for Q i +1 For Case 1 if, then set Q * i = Q i If, then a discount is not possible Set Q * i = q i to qualify for the discounted price of C i

14. 11-14 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. All-Unit Quantity Discounts Step 3:Calculate the total annual cost of ordering Q * i units (this includes order cost, holding cost, and material cost.

15. 11-15 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. All-Unit Quantity Discounts Step 4:Select Q * i with the lowest total cost TC i Cutoff price

16. 11-16 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. Example 11-7 All-Unit Quantity Discount Example Order QuantityUnit Price 0–4,999$3.00 5,000–9,999$2.96 10,000 or more$2.92 q 0 = 0, q 1 = 5,000, q 2 = 10,000 C 0 = $3.00, C 1 = $2.96, C 2 = $2.92 D = 120,000/year, S = $100/lot, h = 0.2 Drugs online (DO) is an online retailer of prescription drugs and health supplements. Vitamins represent a significant percentage of its sales. Demand for vitamins is 10,000 bottles per month. DO incurs a fixed order placement, transportation, and receiving cost of $100 each time an order is placed for vitamins with the manufacturer. DO incurs a holding cost of 20 percent. The manufacturer uses the following all unit discount pricing schedule. Evaluate the number of bottles that the DO manager should order in each lot.

17. 11-17 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. All-Unit Quantity Discount Example Step 1 Step 2 Ignore i = 0 because Q 0 = 6,324 > q 1 = 5,000 For i = 1, 2

18. 11-18 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. All-Unit Quantity Discount Example Step 3 Lowest total cost is for i = 2 Order bottles per lot at $2.92 per bottle

19. 11-19 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. Marginal Unit Quantity Discounts Pricing schedules with all quantity discounts encourages retailers to order a larger lot to take advantage of price discounts. This effects the inventory flow time and average inventory. ??? The value of quantity discounts. Multi-block tariffs – the marginal cost of a unit that decreases at a breakpoint For each value of i, 0 ≤ i ≤ r, let V i be the cost of ordering q i units

20. 11-20 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. Marginal Unit Quantity Discounts Figure 11-4

21. 11-21 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. Marginal Unit Quantity Discounts Material cost of each order Q is V i + ( Q – q i ) C i Total annual cost

22. 11-22 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. Marginal Unit Quantity Discounts Step 1:Evaluate the optimal lot size for each price C i

23. 11-23 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. Marginal Unit Quantity Discounts Step 2:Select the order quantity Q i * for each price C i 1. 2. 3.

24. 11-24 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. Marginal Unit Quantity Discounts Step 3:Calculate the total annual cost of ordering Q i * Step 4:Select the order size Q i * with the lowest total cost TC i

25. 11-25 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. Marginal Unit Quantity Discount Example Original data now a marginal discount Order QuantityUnit Price 0–4,999$3.00 5,000–9,999$2.96 10,000 or more$2.92 q 0 = 0, q 1 = 5,000, q 2 = 10,000 C 0 = $3.00, C 1 = $2.96, C 2 = $2.92 D = 120,000/year, S = $100/lot, h = 0.2

26. 11-26 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. Marginal Unit Quantity Discount Example Step 1

27. 11-27 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. Marginal Unit Quantity Discount Example Step 2 Step 3

28. 11-28 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. Why Quantity Discounts? Quantity discounts can increase the supply chain surplus for the following two main reasons 1.Improved coordination to increase total supply chain profits 2.Extraction of surplus through price discrimination

29. 11-29 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. Quantity Discounts for Commodity Products D = 120,000 bottles/year, S R = $100, h R = 0.2, C R = $3 S M = $250, h M = 0.2, C M = $2 Annual supply chain cost (manufacturer + DO) = $6,009 + $3,795 = $9,804

30. 11-30 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. Locally Optimal Lot Sizes Annual cost for DO and manufacturer Annual supply chain cost (manufacturer + DO) = $5,106 + $4,059 = $9,165

31. 11-31 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall. Designing a Suitable Lot Size-Based Quantity Discount Design a suitable quantity discount that gets DO to order in lots of 9,165 units when its aims to minimize only its own total costs Manufacturer needs to offer an incentive of at least $264 per year to DO in terms of decreased material cost if DO orders in lots of 9,165 units Appropriate quantity discount is $3 if DO orders in lots smaller than 9,165 units and $2.9978 for orders of 9,165 or more