Inventory Management

1. Inventory Management

2. Lecture Outline • Elements of Inventory Management • Inventory Control Systems • Economic Order Quantity Models • Quantity Discounts • Reorder Point • Order Quantity for a Periodic Inventory System

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

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

5. Inventory and Supply Chain Management • Bullwhip effect • demand information is distorted as it moves away from the end-use customer • higher safety stock inventories to 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 stop-pages

6. 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

7. 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

8. Inventory Costs • Carrying cost • cost of holding an item in inventory • Ordering cost • cost of replenishing inventory • Shortage cost • temporary or permanent loss of sales when demand cannot be met

9. 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

10. 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

11. PART UNIT COST ANNUAL USAGE 1 $ 60 90 2 350 40 3 30 130 4 80 60 5 30 100 6 20 180 7 10 170 8 320 50 9 510 60 10 20 120 ABC Classification: Example

12. TOTAL % OF TOTAL % OF TOTAL PART VALUE VALUE QUANTITY % CUMMULATIVE PART UNIT COST ANNUAL USAGE 9 8 2 1 6.3 9.0 24.0 4 4,800 5.6 6.0 30.0 3 3,900 4.6 10.0 40.0 6 3,600 4.2 18.0 58.0 5 3,000 3.5 13.0 71.0 10 2,400 2.8 12.0 83.0 7 1,700 2.0 17.0 100.0 $85,400 1 $ 60 90 2 350 40 3 30 130 4 80 60 5 30 100 6 20 180 7 10 170 8 320 50 9 510 60 10 20 120 ABC Classification: Example (cont.) Example 10.1

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

14. 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

15. 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

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

17. 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 = + Q2 = Qopt = Qopt = EOQ Cost Model

18. Annual cost ($) Slope = 0 Minimum total cost Optimal order Qopt Order Quantity, Q EOQ Cost Model (cont.)

19. Cc = $0.75 per yard Co = $150 D = 10,000 yards CoD Q CcQ 2 TCmin = + Qopt = Qopt = TCmin = + 2CoD Cc Qopt = yards TCmin = = EOQ Example Orders per year = D/Qopt = = orders/year Order cycle time = days/(D/Qopt) = = store days

20. 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

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

22. 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.)

23. 2CoD Cc1 - Qopt = = = yards d p Q p CoD Q CcQ 2 d p TC = + 1 - = Production run = = = days per order Production Quantity Model: Example Cc = $0.75 per yard Co = $150 D = 10,000 yards d = 10,000/311 = 32.2 yards per day p = 150 yards per day

24. D Q Number of production runs = = = runs/year d p Maximum inventory level = Q 1 - = = yards Production Quantity Model: Example (cont.)

25. 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

26. 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.)

27. QUANTITY PRICE 1 - 49 $1,400 50 - 89 1,100 90+ 900 2CoD Cc Qopt = = = PCs For Q = 72.5 CoD Qopt CcQopt 2 For Q = 90 CcQ 2 CoD Q TC = + + PD = TC = + + PD = Quantity Discount: Example Co = $2,500 Cc = $190 per computer D = 200

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

29. Reorder Point: Example Demand = 10,000 yards/year Store open 311 days/year Daily demand = 10,000 / 311 = 32.154 yards/day Lead time = L = 10 days R = dL = = yards

30. 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

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

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

33. 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

34. 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

35. d = 30 yards per day L = 10 days d = 5 yards per day R = dL + zd L = = yards Safety stock = zd L = = yards Reorder Point for Variable Demand The carpet store wants a reorder point with a 95% service level and a 5% stockout probability For a 95% service level, z =

36. 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

37. 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 = = bottles Fixed-Period Model with Variable Demand