Inventory Management

1. Inventory Management

2. Learning Objectives • Define the term inventory and list the major reasons for holding inventories; and list the main requirements for effective inventory management. • Discuss the nature and importance of service inventories • Discuss periodic and perpetual review systems. • Discuss the objectives of inventory management. • Describe the A-B-C approach and explain how it is useful.

3. Learning Objectives • Describe the basic EOQ model and its assumptions and solve typical problems. • Describe the economic production quantity model and solve typical problems. • Describe the quantity discount model and solve typical problems. • Describe reorder point models and solve typical problems. • Describe situations in which the single-period model would be appropriate, and solve typical problems.

4. Inventory Independent Demand Dependent Demand A C(2) B(4) D(2) E(1) D(3) F(2) Independent demand is uncertain. Dependent demand is certain. Inventory: a stock or store of goods

5. Inventory Models • Independent demand – finished goods, items that are ready to be sold • E.g. a computer • Dependent demand – components of finished products • E.g. parts that make up the computer

6. Types of Inventories • Raw materials & purchased parts • Partially completed goods called work in progress • Finished-goods inventories • (manufacturingfirms) or merchandise (retail stores)

7. Types of Inventories (Cont’d) • Replacement parts, tools, & supplies • Goods-in-transit to warehouses or customers

8. Functions of Inventory • To meet anticipated demand • To smooth production requirements • To decouple operations • To protect against stock-outs

9. Functions of Inventory (Cont’d) • To take advantage of order cycles • To help hedge against price increases • To permit operations • To take advantage of quantity discounts

10. Objective of Inventory Control • To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds • Level of customer service • Costs of ordering and carrying inventory Inventory turnover is the ratio ofaverage annual cost of goods sold toaverage inventory investment.

11. Effective Inventory Management • A system to keep track of inventory • A reliable forecastof demand • Knowledge of lead times • Reasonable estimates of • Holding costs • Ordering costs • Shortage costs • A classification system

12. Inventory Counting Systems • Periodic System Physical count of items made at periodic intervals • Perpetual Inventory SystemSystem that keeps track of removals from inventory continuously, thus monitoringcurrent levels of each item

13. Perpetual Inventory System 0 214800 232087768 • Two-Bin System - Two containers of inventory; reorder when the first is empty • Universal Bar Code - Bar code printed on a label that hasinformation about the item to which it is attached

14. Key Inventory Terms • Lead time: time interval between ordering and receiving the order • Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year • Ordering costs: costs of ordering and receiving inventory • Shortage costs: costs when demand exceeds supply

15. ABC Classification System High A Annual Value of items B C Low Low High Percentage of Items Classifying inventory according to some measure of importance and allocating control efforts accordingly. A–10-20% items, 60-70% value B– 30-40% items, 20-30% value C– 50-60% items, 10-15% value

16. Cycle Counting • A physical count of items in inventory • Cycle counting management • How much accuracy is needed? • When should cycle counting be performed? • Who should do it?

17. Cycle Counting Example 5,000 items in inventory, 500 A items, 1,750 B items, 2,750 C items Policy is to count A items every month (20 working days), B items every quarter (60 days), and C items every six months (120 days)

18. Economic Order Quantity Models • Economic order quantity (EOQ) model • The order size that minimizes total annual cost • Economic production model • Quantity discount model

19. Assumptions of EOQ Model • Only one product is involved • Annual demand requirements known • Demand is even throughout the year • Lead time does not vary • Each order is received in a single delivery • There are no quantity discounts

20. The Inventory Cycle Profile of Inventory Level Over Time Q Usage rate Quantity on hand Reorder point Time Place order Receive order Receive order Receive order Place order Lead time

21. Total Cost Q D S H + 2 Q Annual carrying cost Annual ordering cost Total cost = + TC = Q = Order quantity H = Holding cost D = Annual demand S = Ordering cost or Setup cost

22. Cost Minimization Goal The Total-Cost Curve is U-Shaped Annual Cost Ordering Costs Order Quantity (Q) QO (optimal order quantity)

23. Deriving the EOQ Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.

24. Minimum Total Cost Q D S H = 2 Q The total cost curve reaches its minimum where the carrying and ordering costs are equal.

25. Reorder Points Lead time for a new order in days ROP = Demand per day D Number of working days in a year d = • EOQ answers the “how much” question • The reorder point (ROP) tells when to order = d x L

26. Reorder Point Curve Q* Slope = units/day = d Inventory level (units) ROP (units) Time (days) Lead time = L

27. Economic Production Quantity (EPQ) • Production done in batches or lots • Capacity to produce a part exceeds the part’s usage or demand rate • Assumptions of EPQ are similar to EOQ except orders are received incrementally during production

28. Economic Production Quantity Assumptions • Only one item is involved • Annual demand is known • Usage rate is constant • Usage occurs continually • Production rate is constant • Lead time does not vary • No quantity discounts

29. Production Order Quantity Model Part of inventory cycle during which production (and usage) is taking place Maximum inventory t Inventory level Demand part of cycle with no production Time

30. Economic Run Size Q = Order quantity H = Holding cost D = Annual demand S = Ordering cost or Setup cost p = Production rate or Delivery rate u = Usage rate

31. Quantity discount model Annual carrying cost Annual ordering cost Purchasing cost + TC = + Q D PD S H TC = + + 2 Q

32. Quantity discount model Cost TC1 TC2 TC3 Unit price 1 Unit price 2 Unit price 3 Quantity

33. When to Reorder with EOQ Ordering • Reorder Point- When the quantity on hand of an item drops to this amount, the item is reordered • Safety Stock- Stock that is held in excess of expected demand due to variable demand rate and/or lead time. • Service Level- Probability that demand will not exceed supply during lead time.

34. Determinants of the Reorder Point • The rate of demand • The lead time • Demand and/or lead time variability • Stockout risk (safety stock)

35. Stock-out Cost can be determined • Used when demand is not constant or certain • Use safety stock to achieve a desired service level and avoid stockouts ROP = d x L + ss Annual stockout costs = the sum of the {units short x the probability x the stockout cost/unitx the number of orders per year}

36. Safety Stock Example ROP = 50 units Stockout cost = $40 per units Orders per year = 6 Carrying cost = $5 per units per year

37. Safety Stock Example ROP = 50 units Stockout cost = $40 per frame Orders per year = 6 Carrying cost = $5 per frame per year A safety stock of 20 frames gives the lowest total cost ROP = 50 + 20 = 70 frames

38. Probabilistic Demand Minimum demand during lead time Mean demand during lead time ROP ROP  Normal distribution probability of demand during lead time Lead time Receive order Maximum demand during lead time Inventory level Expected demand during lead time Safety stock 0 Time Risk Place order

39. Probabilistic Demand Risk of a stockout (5% of area of normal curve) Probability ofno stockout95% of the time ROP = ? units Mean demand Quantity Safety stock z 0 Number of standard deviations Z=1.65

40. Probabilistic Demand Use prescribed service levels to set safety stock when the cost of stockouts cannot be determined ROP = demand during lead time + Zsdlt where Z = number of standard deviations sdlt = standard deviation of demand during lead time

41. Other Probabilistic Models When data on demand during lead time is not available, there are other models available When demand is variable and lead time is constant When lead time is variable and demand is constant When both demand and lead time are variable

42. Other Probabilistic Models where sd = standard deviation of demand per day sdlt = sdlead time Demand is variable and lead time is constant ROP = (average daily demand x lead time in days) + Zsdlt

43. Probabilistic Example ROP = (15 units x 2 days) + Zsdlt = 30 + 1.28(5)( 2) = 30 + 8.96 = 38.96 ≈ 39 Average daily demand (normally distributed) = 15 Standard deviation = 5 Lead time is constant at 2 days 90% service level desired Z for 90%= 1.28 Safety stock is about 9 units

44. Other Probabilistic Models Lead time is variable and demand is constant ROP = (daily demand x average lead time) + Zsdlt Zsdlt =Z x (daily demand) xσlt where slt = standard deviation of lead time in days

45. Probabilistic Example Daily demand (constant) = 10 Average lead time = 6 days Standard deviation of lead time = slt = 3 98% service level desired Z for 98%= 2.055 ROP = (10 units x 6 days) + 2.055(10 units)(3) = 60 + 61.55 = 121.65 Reorder point is about 122 units

46. Other Probabilistic Models Both demand and lead time are variable ROP = (average daily demand x average lead time) + Zsdlt where sd = standard deviation of demand per day slt = standard deviation of lead time in days sdlt = (average lead time x sd2) + (average daily demand) 2slt2

47. Probabilistic Example ROP = (150 packs x 5 days) + 1.65sdlt = (150 x 5) + 1.65 (5 days x 162) + (1502 x 12) = 750 + 1.65(154) = 1,004 packs Average daily demand (normally distributed) = 150 Standard deviation = sd = 16 Average lead time 5 days (normally distributed) Standard deviation = slt = 1 days 95% service level desired Z for 95%= 1.65

48. Fixed-Order-Interval Model • Orders are placed at fixed time intervals • Order quantity for next interval? • Suppliers might encourage fixed intervals • May require only periodic checks of inventory levels • Risk of stockout

49. Fixed-Order-Interval Model Target maximum (T) Q4 Q2 P Q1 Q3 On-hand inventory P P Time

50. Fixed-Interval Benefits • Tight control of inventory items • Items from same supplier may yield savings in: • Ordering • Packing • Shipping costs • May be practical when inventories cannot be closely monitored