Inventory Management

1. Inventory Management Chapter 12 Operations Management - 5th Edition Roberta Russell & Bernard W. Taylor, III

2. What Is Inventory? • Stock of items kept to meet future demand • Purpose of inventory management • how many units to order? • when to order?

3. Types of Inventory • Raw materials • Purchased parts and supplies • Work-in-process/partially completed products (WIP) • Items being transported • Tools and equipment

4. Inventory and Supply Chain Management • Bullwhip effect • demand information is distorted as it moves away from the end-use customer • higher safety stock inventories are stored to compensate • Seasonal or cyclical demand • Inventory provides independence from vendors • Take advantage of price discounts • Inventory provides independence between stages and avoids work stoppages

5. Two Forms of Demand • Dependent • Demand for items used to produce final products • Tires stored at a Goodyear plant are an example of a dependent demand item • Independent • Demand for items used by external customers • Cars, appliances, computers, and houses are examples of independent demand inventory

6. Inventory and Quality Management • Customers usually perceive quality service as availability of goods they want when they want them • Inventory must be sufficient to provide high-quality customer service in TQM

7. Inventory Costs • Carrying cost • Cost of holding an item in inventory • Also called “holding cost” • Ordering cost • Cost of replenishing inventory • Shortage cost • Temporary or permanent loss of sales when demand cannot be met

8. Inventory Control Systems • Continuous system (fixed-order-quantity) • constant amount ordered when inventory declines to predetermined level • Periodic system (fixed-time-period) • order placed for variable amount after fixed passage of time

9. ABC Classification • Class A • 5 – 15 % of units • 70 – 80 % of value • Class B • 30 % of units • 15 % of value • Class C • 50 – 60 % of units • 5 – 10 % of value

10. Economic Order Quantity (EOQ) Models • EOQ • optimal order quantity that will minimize total inventory costs • Basic EOQ model • Production quantity model

11. Assumptions of Basic EOQ Model Demand is known with certainty and is constant over time No shortages are allowed Lead time for the receipt of orders is constant Order quantity is received all at once

12. Order quantity, Q Demand rate Inventory Level Reorder point, R 0 Time Lead time Lead time Order placed Order receipt Order placed Order receipt Inventory Order Cycle

13. Co - cost of placing order D - annual demand Cc - annual per-unit carrying cost Q - order quantity Annual ordering cost = CoD Q CoD Q Annual carrying cost = CcQ 2 CcQ 2 Total cost = + EOQ Cost Model

14. Annual cost ($) Total Cost Slope = 0 Carrying Cost = Minimum total cost CcQ 2 CoD Q Ordering Cost = Optimal order Qopt Order Quantity, Q EOQ Cost Model (cont.)

15. Deriving Qopt Proving equality of costs at optimal point CoD Q CcQ 2 TC = + CoD Q2 Cc 2 TC Q = + = C0D Q2 Cc 2 0 = + 2CoD Cc CoD Q CcQ 2 Q2 = 2CoD Cc Qopt = 2CoD Cc Qopt = EOQ Cost Model

16. Cc = $0.75 per gallon Co = $150 D = 10,000 gallons CoD Q CcQ 2 TCmin = + Qopt = 2(150)(10,000) (0.75) (150)(10,000) 2,000 (0.75)(2,000) 2 Qopt = TCmin = + 2CoD Cc Qopt = 2,000 gallons TCmin = $750 + $750 = $1,500 EOQ Example Orders per year = D/Qopt = 10,000/2,000 = 5 orders/year Order cycle time = 311 days/(D/Qopt) = 311/5 = 62.2 store days

17. Production QuantityModel • An inventory system in which an order is received gradually, as inventory is simultaneously being depleted • AKA non-instantaneous receipt model • assumption that Q is received all at once is relaxed • p - daily rate at which an order is received over time, a.k.a. production rate • d - daily rate at which inventory is demanded

18. Inventory level Maximum inventory level Q(1-d/p) Average inventory level Q 2 (1-d/p) 0 Begin order receipt End order receipt Time Order receipt period Production Quantity Model (cont.)

19. p = production rate d = demand rate 2CoD Cc1 - Q p Maximum inventory level = Q - d = Q 1 - Qopt = d p d p d p CoD Q CcQ 2 Q 2 d p Average inventory level = 1 - TC = + 1 - Production Quantity Model (cont.)

20. 2CoD Cc1 - Qopt = = = 2,256.8 gallons d p Q p 2,256.8 150 CoD Q CcQ 2 d p 32.2 150 TC = + 1 - = $1,329 2(150)(10,000) 0.75 1 - Production run = = = 15.05 days per order Production Quantity Model: Example Cc = $0.75 per gallon Co = $150 D = 10,000 gallons d = 10,000/311 = 32.2 gallons per day p = 150 gallons per day

21. D Q 10,000 2,256.8 Number of production runs = = = 4.43 runs/year d p 32.2 150 Maximum inventory level = Q 1 - = 2,256.8 1 - = 1,772 gallons Production Quantity Model: Example (cont.)

22. CoD Q CcQ 2 TC = + + PD where P = per unit price of the item D = annual demand Quantity Discounts Price per unit decreases as order quantity increases

23. TC = ($10 ) ORDER SIZE PRICE 0 - 99 $10 100 – 199 8 (d1) 200+ 6 (d2) TC (d1 = $8 ) TC (d2 = $6 ) Inventory cost ($) Carrying cost Ordering cost Q(d1 ) = 100 Qopt Q(d2 ) = 200 Quantity Discount Model (cont.)

24. QUANTITY PRICE 1 - 49 $1,400 50 - 89 1,100 90+ 900 2CoD Cc 2(2500)(200) 190 Qopt = = = 72.5 TVs For Q = 72.5 CoD Qopt CcQopt 2 For Q = 90 CcQ 2 CoD Q TC = + + PD = $233,784 TC = + + PD = $194,105 Quantity Discount: Example Co = $2,500 Cc = $190 per TV D = 200

25. Reorder Point Level of inventory at which a new order is placed R = dL where d = demand rate per period L = lead time

26. Reorder Point: Example Demand = 10,000 gallons/year Store open 311 days/year Daily demand = 10,000 / 311 = 32.154 gallons/day Lead time = L = 10 days R = dL = (32.154)(10) = 321.54 gallons

27. Safety Stocks • Safety stock • buffer added to on-hand inventory during lead time • Stockout • an inventory shortage • Service level • probability that the inventory available during lead time will meet demand

28. Q Inventory level Reorder point, R 0 LT LT Time Variable Demand with a Reorder Point

29. Q Inventory level Reorder point, R Safety Stock 0 LT LT Time Reorder Point with a Safety Stock

30. R = dL + zd L where d = average daily demand L = lead time d = the standard deviation of daily demand z = number of standard deviations corresponding to the service level probability zd L = safety stock Reorder Point With Variable Demand

31. Probability of meeting demand during lead time = service level Probability of a stockout Safety stock zd L dL Demand R Reorder Point for a Service Level

32. d = 30 yards per day L = 10 days d = 5 yards per day R = dL + zd L = 30(10) + (1.65)(5)( 10) = 326.1 yards Safety stock = zd L = (1.65)(5)( 10) = 26.1 yards Reorder Point for Variable Demand A carpet store is open 365 days/year and has an annual demand of 10,950 yards of carpet for a particular brand. The carpet store wants a reorder point with a 95% service level and a 5% stockout probability. For a 95% service level, z = 1.65

33. Q = d(tb + L) + zdtb + L - I where d = average demand rate tb = the fixed time between orders L = lead time sd = standard deviation of demand zdtb + L = safety stock I = inventory level Order Quantity for a Periodic Inventory System

34. d = 6 bottles per day sd = 1.2 bottles tb = 60 days L = 5 days I = 8 bottles z = 1.65 (for a 95% service level) Q = d(tb + L) + zdtb + L - I = (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8 = 397.96 bottles Fixed-Period Model with Variable Demand