2. McGraw-Hill/Irwin  The McGraw-Hill Companies, Inc. 2007, All Rights Reserved Independent-Demand Inventory Chapter 15

3. 15-2 Chapter 15 Outline Introduction Purpose of Inventories Inventory Cost Structures Independent versus Dependent Demand Economic Order Quantity Continuous Review System Periodic Review System Using P and Q System in Practice ABC Inventory Management

4. 15-3 Introduction Inventory: a stock of materials used to facilitate production or to satisfy customer demand. Types of inventory –Raw materials (RM) –Work in process (WIP) –Finished goods (FG) –Maintenance, repair & operating supplies (MRO)

5. 15-4 A Material-Flow Process Work in process Work in process Work in process Finished goods Raw Materials Vendors Customer Productive Process

6. 15-5 A Water Tank Analogy for Inventory Supply Rate Inventory Level Demand Rate Inventory Level

7. 15-6 Purpose of Inventories (1) To protect against uncertainties –in demand (finished goods, MRO) –supply (RM, MRO) –lead times (RM/PP or WIP) –schedule changes (WIP) To allow economic production and purchase (as in discounts for buying RM/PP in bulk)

8. 15-7 Purpose of Inventories (2) To cover anticipated changes in demand (as in a level strategy) or supply –finished goods –RM/PP To provide for transit (pipeline inventories) –RM/PP –finished goods –WIP (independence of operations)

9. 15-8 Inventory Cost Structures ( 1 ) Item or SKU cost –Expressed as cost per unit or SKU. Gets into LIFO and FIFO issues. –Problem can be compounded by quantity discounts.

10. 15-9 Inventory Cost Structures ( 2 ) Ordering (or setup) cost –Paperwork, worker time (ordering) –worker time, downtime (setup) –Typically expressed as a fixed cost per order or setup.

11. 15-10 Inventory Cost Structures (3) Carrying (or holding) cost: –Cost of capital (market rate or internal rate of return) –Cost of storage (building, utilities, insurance, handling) –Cost of obsolescence, deterioration, and loss (shrinkage) –Management cost (record keeping, counting) Typically expressed as a percentage of SKU cost. Average in U.S. is estimated to be 35 percent per year. Businesses often use only cost of capital (understatement).

12. 15-11 Inventory Cost Structures (4) How the 35 percent carrying cost is distributed Cost of Capital—9-20 percent Obsolescence—2-5 percent Storage—2-5 percent Material Handling—1-3 percent Shrinkage—1-3 percent Taxes & Insurance—1-3 percent Source: Mark Williams, APICS Instructor Listserv, 22 January 2001

13. 15-12 Inventory Cost Structures (5) Stock out cost (back order or lost sales) –record maintenance –lost income –customer dissatisfaction –Typically expressed as a fixed cost per backorder or as a function of aging of backorders.

14. 15-13 Two Forms of Demand (1) Independent demand (this chapter) –finished goods, spare parts, MRO –based on market demand –requires forecasting –managed using ‘replenishment philosophy’, i.e. reorder when reach a pre-specified level.

15. 15-14 Two Forms of Demand (2) Dependent demand (next two chapters) –parts that go into the finished products, RM/PP or WIP –dependent demand is a known function of independent demand –calculate instead of forecast –Managed using a ‘requirements philosophy’, i.e. only ordered as needed for higher level components or products.

16. 15-15 Independent versus Dependent Demand A pattern plus random influences‘Lumpy’ because of production lots

17. 15-16 Economic Order Quantity (EOQ) Developed in 1915 by F.W. Harris Answers the question ‘How much do I order?’ Used for independent demand items. Objective is to find order quantity (Q) that minimizes the total cost (TC) of managing inventory. Must be calculated separately for each SKU. Widely used and very robust (i.e. works well in a lot of situations, even when its assumptions don’t hold exactly).

18. 15-17 Economic Order Quantity (EOQ) Basic Model Assumptions Demand rate is constant, recurring, and known. Lead time is constant and known. No stockouts allowed. Material is ordered or produced in a lot or batch and the lot is received all at once Costs are constant –Unit cost is constant (no quantity discounts) –Carrying cost is a constant per unit (SKU) –Ordering (setup) cost per order is fixed The item is a single product or SKU.

19. 15-18 EOQ Lot Size Choice There is a trade-off between frequency of ordering (or the size of the order) and the inventory level. –Frequent orders (small lot size) lead to a lower average inventory size, i.e. higher ordering cost and lower holding cost. –Fewer orders (large lot size) lead to a larger average inventory size, i.e. lower ordering cost and higher holding cost.

20. 15-19 EOQ Inventory Levels (‘sawtooth model’) Time Lot size = Q Order Interval Average Inventory Level = Q/2 On Hand

21. 15-20 Notations and measurement units in EOQ D =Demand rate, units per year S =Cost per order placed, or setup cost, dollars per order C =Unit cost, dollars per unit i =Carrying rate, percent of value per year Q =Lot size, units TC=total of ordering cost plus carrying cost

22. 15-21 Cost Equations in EOQ Ordering cost = (cost per order) x orders per year) = SD/Q Carrying cost per year = (annual carrying rate) x (unit cost) x average inventory = iCQ/2 Total annual cost (TC) = ordering cost per year + carrying cost per year = SD/Q + iCQ/2

23. 15-22 Total Cost of Inventory

24. 15-23 TC and EOQ TC = ordering cost + holding cost = S*(D/Q) + iC*(Q/2) EOQ = note: Although we have used annual costs, any time period is all right. Just be consistent! The same is true for currency designations.

25. 15-24 EOQ Example Sales = 10 cases/weekS = $12/order i = 30 pct/yearC = $80/case _________ EOQ =  SD)/iC = SQRT[(2*12*10*52)/(80*.3)] = SQRT[12,480/24] = 22.8 cases/order TC = ordering cost + holding cost = S*(D/Q) + iC*(Q/2) = 10(520/22.8) + 24 * 11.4 = 228.70 + 273.60 = $547.28/year If order 22 cases instead, TC = $547.64; if 23, TC = $547.30

26. 15-25 EOQ Example

27. 15-26 Continuous Review System Relax assumption of constant demand. Demand is assumed to be random. Check inventory position each time there is a demand (i.e continuously). If inventory position drops below the reorder point, place an order for the EOQ. Also called fixed-order-quantity or Q system (the fixed order size is EOQ).

28. 15-27 A Continuous Review (Q) System R = Reorder Point Q = Order Quantity L = Lead time

29. 15-28 A Continuous Review (Q) System Amount to order = EOQ Order when inventory position = reorder point. Reorder point = lead time * demand/period = R= lead time demand (when demand is constant) Reorder point is independent of EOQ! EOQ tells how much to order. Reorder point tells when to order.

30. 15-29 Service Level When demand is random, the reorder point must take into account the service level or fill rate. Service level has many definitions: –Probability that all orders will be refilled while waiting for an order to arrive. –Percentage of demand filled from stock in a time period. –Percentage of time the system has stock on hand.

31. 15-30 Probability Distribution of Demand over Lead Time m = mean demandR = Reorder points = Safety stock

32. 15-31 Periodic Review System (1) Instead of reviewing continuously, we review the inventory position at fixed intervals. For example, the bread truck visits the grocery store on the same days every week. Also known as “P system”, “Fixed-order- interval system” or “Fixed-order-period system”

33. 15-32 Periodic Review System (2) Each time we review the inventory, we either order or don’t. The decision depends upon our reorder point. The amount we order may be fixed, or may be the amount needed to bring us up to a target (T).

34. 15-33 A Periodic Review (P) System

35. 15-34 Time Between Orders (P) and Target Level (T) Calculation Where: T = target inventory level m’ = average demand over P+L s’ = safety stock

36. 15-35 Using P and Q System in Practice Use P system when orders must be placed at specified intervals. Use P systems when multiple items are ordered from the same supplier (joint- replenishment). Use P system for inexpensive items.

37. 15-36 Using P and Q Systems in Practice P may be easier to use since levels are reviewed less often. P requires more safety stock since may only order at fixed points. P is more likely to run out since cannot respond to increases in demand immediately Either may be more costly: P in safety stock, Q in monitoring cost.

38. 15-37 Service Level versus Inventory Level (Figure 15.10)

39. 15-38 ABC Inventory Management (1) Based on “Pareto” concept (80/20 rule) and total usage in dollars of each item. Classification of items as A, B, or C based on usage. Purpose is to set priorities on effort used to manage different SKUs, i.e. to allocate scarce management resources.

40. 15-39 ABC Inventory Management (2) ‘A’ items: 20% of SKUs, 80% of dollars ‘B’ items: 30 % of SKUs, 15% of dollars ‘C’ items: 50 % of SKUs, 5% of dollars Three classes is arbitrary; could be any number. Percents are approximate. Danger: dollar use may not reflect importance of any given SKU!

41. 15-40 Annual Usage of Items by Dollar Value (Table 15.4)

42. 15-41 ABC Chart for Table 15.4 A BC

43. 15-42 Managing A items: Diamonds

44. 15-43 Summary Introduction Purpose of Inventories Inventory Cost Structures Independent versus Dependent Demand Economic Order Quantity Continuous Review System Periodic Review System Using P and Q System in Practice ABC Inventory Management

45. 15-44 End of Chapter Fifteen