Chapter 10 Inventory Management BA 320 Operations Management

Chapter 10 Inventory Management BA 320 Operations Management

Inventory ü Stock of items held to meet future demand ü Inventory management answers two questions ü How much to order ü When to order BA 320 Operations Management

Types of Inventory ü Raw materials ü Purchased parts and supplies ü Labor ü In-process (partially completed) products ü Component parts ü Working capital ü Tools, machinery, and equipment BA 320 Operations Management

Reasons to Hold Inventory ü Meet unexpected demand ü Smooth seasonal or cyclical demand ü Meet variations in customer demand ü Take advantage of price discounts ü Hedge against price increases ü Quantity discounts BA 320 Operations Management

Two Forms of Demand ü Dependent ü Items used to produce final products ü Independent ü Items demanded by external customers BA 320 Operations Management

Inventory Costs ü Carrying Cost ü Cost of holding an item in inventory ü Ordering Cost ü Cost of replenishing inventory ü Shortage Cost ü Temporary or permanent loss of sales when demand cannot be met BA 320 Operations Management

Inventory Control Systems ü Continuous system (fixed-orderquantity) ü Constant amount ordered when inventory declines to predetermined level ü Periodic system (fixed-time-period) ü Order placed for variable amount after fixed passage of time BA 320 Operations Management

ABC Classification System ü Demand volume and value of items vary ü Classify inventory into 3 categories, typically on the basis of the dollar value to the firm CLASS A B C PERCENTAGE OF UNITS 5 - 15 30 50 - 60 PERCENTAGE OF DOLLARS 70 - 80 15 5 - 10 BA 320 Operations Management

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

ABC Classification PART 9 8 2 1 4 3 6 5 10 7 TOTAL PART VALUE $30, 600 1 16, 000 2 14, 000 3 5, 400 4 4, 800 5 3, 900 3, 600 6 3, 000 7 2, 400 8 1, 700 9 $85, 400 10 % OF TOTAL UNIT ANNUAL USAGE VALUECOSTQUANTITY % CUMMULATIVE 35. 9 $ 60 18. 7 350 16. 4 30 6. 3 5. 680 4. 630 4. 220 3. 510 2. 8 320 2. 0 510 20 6. 0 5. 0 4. 0 9. 0 6. 0 10. 0 18. 0 13. 0 12. 0 17. 0 90 40 130 60 100 180 170 50 60 120 6. 0 11. 0 15. 0 24. 0 30. 0 40. 0 58. 0 71. 0 83. 0 100. 0 Example 10. 1 BA 320 Operations Management

ABC Classification PART 9 8 2 1 4 3 6 5 10 7 TOTAL PART VALUE $30, 600 1 16, 000 2 14, 000 3 5, 400 4 4, 800 5 3, 900 3, 600 6 3, 000 7 2, 400 8 1, 700 9 $85, 400 10 % OF TOTAL UNIT ANNUAL USAGE VALUECOSTQUANTITY % CUMMULATIVE 35. 9 $ 60 18. 7 350 16. 4 30 6. 3 5. 680 4. 630 4. 220 3. 510 2. 8 320 2. 0 510 20 6. 0 5. 0 4. 0 9. 0 6. 0 10. 0 18. 0 13. 0 12. 0 17. 0 90 A 40 130 60 B 100 180 170 C 50 60 120 6. 0 11. 0 15. 0 24. 0 30. 0 40. 0 58. 0 71. 0 83. 0 100. 0 Example 10. 1 BA 320 Operations Management

ABC Classification PART TOTAL PART VALUE 9 $30, 600 1 8 16, 000 2 2 14, 000 3 1 CLASS 5, 400 4 4 4, 800 A 3, 900 5 3 B 3, 600 6 6 C 3, 000 5 7 10 2, 400 8 7 1, 700 9 $85, 400 10 % OF TOTAL UNIT ANNUAL USAGE VALUECOSTQUANTITY % CUMMULATIVE 35. 9 6. 0 $ 60 18. 7 5. 0 350 16. 4 % OF TOTAL 4. 0 30 ITEMS 6. 3 VALUE 9. 0 5. 680 6. 0 9, 8, 2 4. 630 71. 010. 0 1, 4, 3 4. 220 16. 518. 0 6, 5, 10, 12. 513. 0 3. 5710 2. 8 12. 0 320 2. 0 17. 0 510 20 6. 0 90 11. 0 A 40 15. 0 % OF TOTAL 130 24. 0 QUANTITY 60 B 15. 030. 0 100 40. 0 180 25. 058. 0 60. 071. 0 170 C 83. 0 50 100. 0 60 120 Example 10. 1 BA 320 Operations Management

ABC Classification C 100 – B % of Value 80 – 60 – A 40 – 20 – 0 | 20 | | 40 60 % of Quantity | 80 BA 320 Operations Management | 100

Assumptions of Basic EOQ Model ü Demand is known with certainty and is constant over time ü No shortages are allowed ü Lead time for the receipt of orders is constant ü The order quantity is received all at once BA 320 Operations Management

The Inventory Order Cycle Inventory Level Order quantity, Q Reorder point, R Time 0 Figure 10. 1 BA 320 Operations Management

The Inventory Order Cycle Order quantity, Q Inventory Level Demand rate Reorder point, R 0 Figure 10. 1 Lead time Order placed receipt BA 320 Operations Management Time

EOQ Cost Model Co - cost of placing order Cc - annual per-unit carrying cost D - annual demand Q - order quantity Co D Annual ordering cost = Q Cc Q Annual carrying cost = 2 Co D Cc Q Total cost = + Q 2 BA 320 Operations Management

EOQ Cost Model CDeriving D - annual demand o - cost of. Qplacing order Proving equality of opt Cc - annual per-unit carrying costs Q - order quantity at optimal point Co D Cc Q TC = + Q 2 Co D Cc Q Annual ordering cost = = Q 2 C D Cc TC o = 2 + Q 2 Q Cc Q 2 Co. D Annual carrying cost = Q 2 = 2 C 0 D Cc Cc 0= + Q 2 2 Co D Cc Q 2 Co. D Total cost = + Q 2 2 Co. D Qopt = Cc BA 320 Operations Management

EOQ Cost Model Annual cost ($) Order Quantity, Q Figure 10. 2 BA 320 Operations Management

EOQ Cost Model Annual cost ($) Co D Ordering Cost = Q Order Quantity, Q Figure 10. 2 BA 320 Operations Management

EOQ Cost Model Annual cost ($) Cc. Q Carrying Cost = 2 Co D Ordering Cost = Q Order Quantity, Q Figure 10. 2 BA 320 Operations Management

EOQ Cost Model Annual cost ($) Total Cost Slope = 0 Cc. Q Carrying Cost = 2 Minimum total cost Co D Ordering Cost = Q Optimal order Qopt Order Quantity, Q Figure 10. 2 BA 320 Operations Management

EOQ Example Cc = $0. 75 per yard Qopt = 2 Co. D Cc Qopt = 2(150)(10, 000) (0. 75) Qopt = 2, 000 yards Orders per year = = = Example 10. 2 Co = $150 D = 10, 000 yards Co. D Cc Q TCmin = + Q 2 TCmin (150)(10, 000) (0. 75)(2, 000) = + 2, 000 2 TCmin = $750 + $750 = $1, 500 D/Qopt Order cycle time = 10, 000/2, 000 = 5 orders/year = 311 days/(D/Qopt) 311/5 62. 2 store days BA 320 Operations Management

EOQ with Noninstantaneous Receipt Inventory level Q(1 -d/p) Maximum inventory level Q (1 -d/p) 2 Average inventory level 0 Time Figure 10. 3 BA 320 Operations Management

EOQ with Noninstantaneous Receipt Inventory level Q(1 -d/p) Maximum inventory level Q (1 -d/p) 2 Average inventory level 0 Order receipt period Begin End order receipt Time Figure 10. 3 BA 320 Operations Management

EOQ with Noninstantaneous Receipt p = production rate Maximum inventory level = Q - d = demand rate Q d p =Q 1 - d p Q d Average inventory level = 1 p 2 Qopt = 2 Co. D d Cc 1 p Co D Cc Q d TC = Q + 2 1 - p BA 320 Operations Management

Production Quantity Cc = $0. 75 per yard Co = $150 d = 10, 000/311 = 32. 2 yards per day 2 Co D Qopt = Cc 1 - d p D = 10, 000 yards p = 150 yards per day 2(150)(10, 000) = Co D Cc Q d TC = Q + 2 1 - p 32. 2 0. 75 1 150 = 2, 256. 8 yards = $1, 329 2, 256. 8 Q Production run = = = 15. 05 days per order p 150 Example 10. 3 BA 320 Operations Management

Production Quantity Cc = $0. 75 per yard Co = $150 d = 10, 000/311 = 32. 2 yards per day D = 10, 000 yards p = 150 yards per day 2 Co D 2(150)(10, 000) 10, 000 = 2, 256. 8 yards D Qopt = = 32. 2 d Number of production runs = = = 4. 43 runs/year Cc 1 0. 75 Q 1 - 2, 256. 8 150 p d 32. 2 Maximum inventory level = Q 1 = 2, 256. 8 1 Co D Cc Q d p 150 TC = Q + 2 1 - p = $1, 329 = 1, 772 yards 2, 256. 8 Q Production run = = = 15. 05 days per order p 150 Example 10. 3 BA 320 Operations Management

Quantity Discounts ü Price per unit decreases as order quantity increases Co. D Cc Q TC = + + PD Q 2 where P = per unit price of the item D = annual demand BA 320 Operations Management

Quantity Discounts ü Price per unit decreases as order quantity increases Co. D Cc Q TC = + + PD Q 2 where ORDER SIZE P = per unit price 0 - of 99 the item D = annual 100 demand - 199 200+ BA 320 Operations Management PRICE $10 8 (d 1) 6 (d 2)

Inventory cost ($) Quantity Discount Model Figure 10. 4 BA 320 Operations Management

Quantity Discount Model TC = ($10 ) TC (d 1 = $8 ) Inventory cost ($) TC (d 2 = $6 ) Carrying cost Ordering cost Figure 10. 4 Q(d 1 ) = 100 Qopt Q(d 2 ) = 200 BA 320 Operations Management

Quantity Discount Model TC = ($10 ) TC (d 1 = $8 ) Inventory cost ($) TC (d 2 = $6 ) Carrying cost Ordering cost Figure 10. 4 Q(d 1 ) = 100 Qopt Q(d 2 ) = 200 BA 320 Operations Management

Quantity Discount QUANTITY PRICE 1 - 49 50 - 89 90+ $1, 400 1, 100 900 Qopt = For Q = 72. 5 For Q = 90 Example 10. 4 2 Co D = Cc Co = $2, 500 Cc = $190 per computer D = 200 2(2500)(200) = 72. 5 PCs 190 Cc. Qopt Co D TC = + + PD = $233, 784 2 Qopt Cc Q Co D TC = + + PD = $194, 105 2 Q BA 320 Operations Management

When to Order Reorder Point is the level of inventory at which a new order is placed R = d. L where d = demand rate period L = lead time BA 320 Operations Management

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 = d. L = (32. 154)(10) = 321. 54 yards Example 10. 5 BA 320 Operations Management

Safety Stocks ü Safety stock ü buffer added to on hand inventory during lead time ü Stockout ü an inventory shortage ü Service level ü probability that the inventory available during lead time will meet demand BA 320 Operations Management

Variable Demand with a Reorder Point Inventory level Q Reorder point, R 0 Figure 10. 5 Time BA 320 Operations Management

Variable Demand with a Reorder Point Inventory level Q Reorder point, R 0 Figure 10. 5 LT LT Time BA 320 Operations Management

Inventory level Reorder Point with a Safety Stock Q Reorder point, R Safety Stock 0 Figure 10. 6 LT LT Time BA 320 Operations Management

Reorder Point With Variable Demand R = d. L + 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 BA 320 Operations Management

Reorder Point for a Service Level Probability of meeting demand during lead time = service level Probability of a stockout Safety stock z d L Figure 10. 7 d. L Demand R BA 320 Operations Management

Reorder Point for Variable Demand The carpet store wants a reorder point with a 95% service level and a 5% stockout probability d = 30 yards per day L = 10 days d = 5 yards per day For a 95% service level, z = 1. 65 R = d. L + z d L Safety stock = z d L = 30(10) + (1. 65)(5)( 10) = 326. 1 yards = 26. 1 yards Example 10. 6 BA 320 Operations Management

Order Quantity for a Periodic Inventory System Q = d(tb + L) + z d tb + L - I where d tb L d z d = average demand rate = the fixed time between orders = lead time = standard deviation of demand tb + L = safety stock I = inventory level BA 320 Operations Management

Fixed-Period Model with Variable Demand d = 6 bottles per day d = 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 d tb + L - I = (6)(60 + 5) + (1. 65)(1. 2) 60 + 5 - 8 = 397. 96 bottles BA 320 Operations Management