2. Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Operations Management Contemporary Concepts and Cases Chapter Fifteen Independent Demand Inventory

3. 15-2 Chapter 15 Outline Purpose of Inventories Costs of Inventories 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 Definitions Inventory: a stock of materials used to facilitate production or satisfy customer demand Types of inventory –Raw materials, purchased parts (RM) –Work in process (WIP) –Finished goods (FG) –Maintenance, repair & operating supplies (MRO)

5. 15-4 Inventory Management Technologies Bar coding Point of sale (data) (POS) Radio-frequency Identification (RFID)

6. 15-5 Materials-Flow Process (Fig. 15.1) Work in process Work in process Work in process Finished goods Raw Materials Vendors Customer Productive Process

7. 15-6 Water Tank Analogy for Inventory Supply Rate Inventory Level Demand Rate Inventory Level

8. 15-7 Purpose of Inventories (1) To protect against uncertainties (safety stock) –demand (FG, MRO) –supply (RM, MRO) –lead times (RM, WIP) –schedule changes (WIP) To allow economic production and purchase (discounts for buying RM in bulk)

9. 15-8 Purpose of Inventories (2) To cover anticipated changes in demand (as in a level strategy) or supply –FG –RM To provide for transit (pipeline inventories) –RM –FG –WIP (independence of operations)

10. 15-9 Inventory Cost Structures ( 1 ) Item cost –Expressed as cost per unit or SKU. Gets into LIFO and FIFO issues. –Problem can be compounded by quantity discounts. 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 (2) 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. Estimated U.S. average is 35% per year. Businesses often use only cost of capital (understatement).

12. 15-11 Inventory Cost Structures (3) How the 35% 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 (4) Shrinkage –“… ‘shrinkage’…costs U.S. retailers about $41.6 billion last year.” This is more than the combined total from other crimes such as robberies, auto theft and larceny. Source: Wall Street Journal, 11 July 2007, p. B4.

14. 15-13 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.

15. 15-14 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.

16. 15-15 Two Forms of Demand (2) Dependent demand (Chapter 16) –Parts that go into the finished products, RM or WIP –Demand is a known function of independent demand –Calculate instead of forecast –Managed using a ‘requirements philosophy’, i.e., only produced or ordered as needed for higher level components or products (‘parents’).

17. 15-16 Figure 15.4: Demand Patterns A pattern plus random influences‘Lumpy’ because of production lots

18. 15-17 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 variety of situations, even when its assumptions don’t hold exactly).

19. 15-18 Economic Order Quantity (EOQ) Basic Model Assumptions 1. Demand rate is constant, recurring, and known. 2. Lead time is constant and known. 3. No stockouts allowed. 4. Material is ordered or produced in a lot or batch and the lot is received all at once. 5. Costs are constant: 1.Unit cost is constant (no quantity discounts) 2.Carrying cost is constant per unit (SKU) 3.Ordering (setup) cost per order is fixed 6. Item is a single product or SKU; demand not influenced by other items.

20. 15-19 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 sizes) lead to lower average inventory level, i.e., higher total ordering costs and lower total holding costs. –Fewer orders (large lot sizes) lead to higher average inventory level, i.e., lower total ordering costs and higher total holding costs.

21. 15-20 Figure 15.5: EOQ Inventory Levels (‘sawtooth model’) Time Lot size = Q Order Interval Average Inventory Level = Q/2 On Hand

22. 15-21 Notation in EOQ Calculation 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

23. 15-22 Cost Equations in EOQ Ordering cost per year = (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

24. 15-23 Total Cost of Inventory (Fig. 15.6)

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

26. 15-25 EOQ Example Sales = 10 cases/weekS = $12/order i = 30% per yearC = $80/case _________ EOQ =  SD)/iC =  *12*10*52) / (.3*80) = 22.8 cases/order TC = ordering cost + holding cost = S*(D/Q) + iC*(Q/2) = 12*(520/22.8) +.3*80(22.8/2) = 273.68 + 273.60 = $547.28/year If order 22 cases instead, TC = $547.64; if 23, TC = $547.30

27. 15-26 EOQ Example

28. 15-27 Relevant Supply Chain Costs for Personal Computer Inventories Component devaluation costs Price protection costs Product return costs Obsolescence costs (end-of-life)

29. 15-28 Continuous Review System Relax assumption of constant demand. Demand is assumed to be random. Check inventory position each time there is 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).

30. 15-29 Continuous Review (Q) System (Fig. 15.7) R = Reorder Point Q = Order Quantity L = Lead time

31. 15-30 Continuous Review (Q) System Amount to order = EOQ Order when inventory position = Reorder point Reorder point (R) = 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.

32. 15-31 Service Level When demand is random, the reorder point must take into account the desired 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.

33. 15-32 Probability Distribution of Demand over Lead Time (Fig. 15.8) m = mean demandR = Reorder points = Safety stock

34. 15-33 Reorder Point The Reorder point is defined as: R = m + s where:R = reorder point m = mean demand during lead time m = mean demand during lead time s = safety or buffer stock s = safety or buffer stock Using the normal distribution: s = zσ where: z = safety factor (from normal table) σ = standard deviation of lead time demand σ = standard deviation of lead time demandThus: R = m + zσ

35. 15-34 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. Inventory brought up to a ‘target’ level. Also known as “P system,” “Fixed-order- interval system” or “Fixed-order-period system”

36. 15-35 Periodic Review System (2) Has a target inventory level rather than a reorder point. Does not use EOQ (directly) since order quantity varies according to demand. The order interval is fixed, the order quantity varies.

37. 15-36 Periodic Review (P) System (Fig. 15.9)

38. 15-37 Time Between Orders (P) and Target Level (T) Calculation Where:T = target inventory level m’ = average demand over P+L s’ = safety stock

39. 15-38 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.

40. 15-39 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 quickly to increases in demand. Either may be more costly: P in safety stock, Q in monitoring cost.

41. 15-40 P and Q Systems at Home P system: You go to the grocery store on the same day every week. You ask: “What will we need for the next week?” –P is more likely to run out since cannot respond quickly to increases in demand –P will carry more inventory (enough to last until the next trip) Q system: You go to the grocery store each time you need something. You ask: “What do we need?” –Q may require more ordering and unplanned order (trips to the store)

42. 15-41 Service Level versus Inventory Level (Fig. 15.10)

43. 15-42 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.

44. 15-43 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! Some low value, but critical items may be classified as ‘A.’

45. 15-44 Annual Usage of Items by Dollar Value (Table 15.4)

46. 15-45 ABC Chart for Table 15.4 A BC

47. 15-46 Summary Purpose of Inventories Costs of Inventories Independent versus Dependent Demand Economic Order Quantity Continuous Review System Periodic Review System Using P and Q System in Practice ABC Inventory Management

48. 15-47 End of Chapter Fifteen