Stevenson 13

1. Stevenson13 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 Economic Order Quantity (“EOQ”) model and its assumptions, and solve typical problems. • Describe the Economic Production Quantity (“EPQ”) model and solve typical problems. • Describe the quantity discount model and solve typical problems. • Describe reorder point models and solve typical problems.

4. 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

5. Dependent and Independent Inventory Dependent Demand Independent Demand Note: Independent Demand is uncertain, whereas Dependent Demand is certain

6. Types of Inventories • Raw materials & purchased parts • Partially completed goods called work in progress • Finished-goods inventories • (manufacturingfirms) or merchandise (retail stores) • Replacement parts, tools, & supplies • Goods-in-transit to warehouses or customers (pipeline inventory)

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

8. 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

9. 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 of average cost of goods sold to average inventory investment.

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

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

12. Inventory Counting Systems (Cont’d) 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

13. 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

14. 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-very important B- mod. important C- least important

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

16. 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

17. 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

18. Total Cost Q D S H + 2 Q Annual carrying cost Annual ordering cost Total cost = + TC = Q is Order Quantity (in units) H is Holding (Carrying) cost per unit D is Demand, usually in units per year S is Ordering Cost per order

19. Total Cost Curve and Cost Minimization Goal

20. 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.

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

22. EOQ Example • A local distributor for a national tire company expects to sell approximately 9,600 steel-belted radial tires of a certain size and tread design next year. Annual carrying cost is $16 per tire, and ordering cost is $75. The distributor operates 288 days a year. • What is the EOQ? • How many times per year does the store reorder? • What is the length of an order cycle (time between orders)? • What is the total annual cost if the EOQ quantity is ordered?

23. EOQ Example

24. EOQ Example Piddling Manufacturing assembles security monitors. It purchases 3,600 black-and-white cathode ray tubes a year at $65 each. Ordering costs are $31, and annual carrying costs are 20 percent of the purchase price. Compute the optimal quantity and the total annual cost of ordering and carrying the inventory.

25. 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

26. 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

28. Economic Run Size p is production or delivery rate u is usage rate

29. EPQ Example A toy manufacturer uses 48,000 rubber wheels per year for its popular dump truck series. The firm makes its own wheels, which it can produce at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is $1 per wheel a year. Setup cost for a production run of wheels is $45. The firm operates 240 days per year. Determine the: • Optimal run size • Minimum total annual cost for carrying and setup • Cycle time for the optimal run size • Run time

30. EPQ Example

31. EPQ Example

32. Total Costs with Purchasing Cost Annual carrying cost Annual ordering cost Purchasing cost + TC = + Q D PD S H TC = + + 2 Q

33. Total Costs with PD Cost Adding Purchasing costdoesn’t change EOQ TC with PD TC without PD PD 0 Quantity EOQ

34. Quantity Discount Example The maintenance department of a large hospital uses about 816 cases of liquid cleanser annually. Ordering costs are $12, carrying costs are $4 per case a year, and the new price schedule indicates that orders of less than 50 cases will cost $20 per case, 50 to 79 cases will cost $18 per case, 80 to 99 cases will cost $17 per case, and larger orders will cost $16 per case. Determine the optimal order quantity and the total cost.

35. Quantity Discount Example

36. Quantity Discount Example • The 70 cases can be bought at $18 per case because 70 falls in the range of 50 to 79 cases. The total cost to purchase 816 cases a year, at the rate of 70 cases per order, will be • Because lower cost ranges exist, each must be checked against the minimum cost generated by 70 cases at $18 each. In order to buy at $17 per case, at least 80 cases must be purchased. (Because the TC curve is rising, 80 cases will have the lowest TC for that curve's feasible region.) The total cost at 80 cases will be • To obtain a cost of $16 per case, at least 100 cases per order are required, and the total cost at that price break will be

37. Quantity Discount Example 100 cases per order yields the lowest total cost, 100 cases is the overall optimal order quantity. With Quantity Discounts, purchase quantity will be equal to or greater optimal economic quantity.

38. 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, (i.e., we will not have turn customers back during lead time because we ran out of inventory).

39. Determinants of the Reorder Point • The rate of demand • The lead time • Demand and/or lead time variability • Stockout risk (safety stock) If demand and lead time are both constants, then ROP = dxLT Question: What happens to the EOQ if the lead time or demand rate changes?

40. Safety Stock • Safety stock reduces risk of stock-out during lead time

41. Reorder Point Example Rahim takes Two-a-Day vitamins, which are delivered to his home seven days after an order is called in. At what point should Rahim reorder? Rahim should reorder when 14 vitamin tablets are left, which is equal to a seven-day supply of two vitamins a day.

42. Safety Stock When variability is present in demand or lead time, it creates the possibility that actual demand will exceed expected demand. Consequently, it becomes necessary to carry additional inventory, called safety stock , to reduce the risk of running out of inventory (a stockout) during lead time. The reorder point then increases by the amount of the safety stock: For example, if expected demand during lead time is 100 units, and the desired amount of safety stock is 10 units, the ROP would be 110 units

43. Service Level • Order cycle service level can be defined as the probability that demand will not exceed supply during lead time (i.e., that the amount of stock on hand will be sufficient to meet demand). • A service level of 95 percent implies a probability of 95 percent that demand will not exceed supply during lead time. • The risk of a stockout is the complement of service level; a customer service level of 95 percent implies a stockout risk of 5 percent.

44. 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 • Fill rate – the percentage of demand filled by the stock on hand

45. 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

46. Fixed-Interval Disadvantages • Requires a larger safety stock • Increases carrying cost • Costs of periodic reviews

47. Single Period Model • Single period model: model for ordering of perishables and other items with limited useful lives • Shortage cost: generally the unrealized profits per unit • Excess cost: difference between purchase cost and salvage value of items left over at the end of a period

48. Optimal Stocking Level • Ce • Cs Service Level • Quantity • So • Cs • Balance point • Cs + Ce • Service level = • Cs = Shortage cost per unitCe = Excess cost per unit

49. Example • Ce • Cs Service Level = 75% • Quantity • Ce = $0.20 per unit • Cs = $0.60 per unit • Service level = Cs/(Cs+Ce) = .6/(.6+.2) • Service level = .75 Stockout risk = 1.00 – 0.75 = 0.25

50. Operations Strategy • Too much inventory • Tends to hide problems • Easier to live with problems than to eliminate them • Costly to maintain