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8. Inventory Management

8. Inventory Management. Inventory. One of the most expensive assets of many companies representing as much as 50% of total invested capital Operations managers must balance inventory investment and customer service Raw material, work-in-process (WIP), and finished goods.

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8. Inventory Management

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  1. 8. Inventory Management

  2. Inventory • One of the most expensive assets of many companies representing as much as 50% of total invested capital • Operations managers must balance inventory investment and customer service • Raw material, work-in-process (WIP), and finished goods

  3. Functions of Inventory • To decouple or separate various parts of the production process • To decouple the firm from fluctuations in demand and provide a stock of goods that will provide a selection for customers • To take advantage of quantity discounts • To hedge against inflation

  4. Cycle time 95% 5% Input Wait for Wait to Move Wait in queue Setup Run Output inspection be moved time for operator time time Material Flow Cycle

  5. ABC Analysis • Divides inventory into three classes based on annual dollar volume • Class A: High, Class B: Medium, Class C:Low • Establishes policies that focus on the few critical parts and not the many trivial ones • Emphasis on supplier development • Tighter physical inventory control • More care in forecasting

  6. ABC Analysis

  7. ABC Analysis

  8. A Items 80 – 70 – 60 – 50 – 40 – 30 – 20 – 10 – 0 – Percent of annual dollar usage B Items C Items | | | | | | | | | | 10 20 30 40 50 60 70 80 90 100 Percent of inventory items ABC Analysis

  9. Record Accuracy & Cycle Counting • Accurate record is a critical ingredient in production and inventory systems • Items are counted and records are updated on a periodic basis, often used with ABC analysis

  10. Terminology • Independent demand • Dependent demand • Setup cost - cost to prepare a machine or process to manufacture/order • Ordering (production) cost - the cost of placing (producing) an order and receiving goods • Holding cost - the cost of holding or “carrying” inventory over time

  11. Holding Cost

  12. Inventory Models • Need to determine when and how much to order (produce) • Basic economic order quantity (EOQ) • Production order quantity • Quantity discount model • Probabilistic Models

  13. Average inventory on hand Q 2 Usage rate Inventory level Minimum inventory 0 Time EOQ Model Order quantity = Q (maximum inventory level)

  14. Curve for total cost of holding and setup Minimum total cost Holding cost curve Annual cost Setup (or order) cost curve Order quantity Optimal order quantity (Q*) EOQ Model

  15. EOQ Model • Demand is known and constant • Lead time is known and constant • Receipt of order is instantaneous and complete • Stockout is not considered • EOQ model is robust: works well with ‘inaccurate’ parameters and assumptions

  16. Notation Q = Number of items per order Q* = Optimal number of items per order D = Constant demand rate per year S = Setup or ordering cost for each order H = Holding or carrying cost per item per year P = Purchasing cost per item

  17. Q* = 2DS/H Q 2 D Q S = H Q 2 TC = S + H + PD D Q Optimal EOQ

  18. 2DS H Q* = 2(1,000)(10) 0.50 Q* = = 40,000 = 200 units An Example Determine optimal number of needles to order D = 1,000 units S = $10 per order H = $.50 per unit per year

  19. An Example Number of working days per year N Expected number of orders Demand Order quantity D Q* Expected time between orders = N = = = T = 1,000 200 250 5 N = = 5 orders per year T = = 50 days between orders

  20. An Example Q 2 D Q 200 2 TC = S + H + PD 1,000 200 TC = ($10) + ($.50) +1,000P = $100 + 1,000P Determine optimal number of needles to order D = 1,000 units Q* = 200 units S = $10 per order N = 5 orders per year H = $.50 per unit per year T = 50 days Total cost = Setup cost + Holding cost + Purchasing cost

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

  22. D Number of working days in a year d = Reorder Point Example Demand = 8,000 iPods per year 250 working days per year Lead time for orders is 3 working days = 8,000/250 = 32 units ROP = d x L = 32 units per day x 3 days = 96 units

  23. Part of inventory cycle during which production (and usage) is taking place Demand part of cycle with no production Inventory level Maximum inventory t Time Production Order Quantity Model • Used when inventory builds up over a period of time after an order is placed • Used when units are produced and sold simultaneously

  24. = – = pt – dt = p – d = Q 1 – Maximum inventory level Maximum inventory level Total produced during the production run Total used during the production run Q p Q p d p d p Maximum inventory level 2 Q 2 Holding cost = (H) = 1 – H Production Order Quantity Model Q = Number of pieces per order p = Daily production rate H = Holding cost per unit per year d = Daily demand/usage rate t = Length of the production run in days However, Q = total produced = pt ; thus t = Q/p

  25. 1 2 (D/Q)S = HQ[1 - (d/p)] 2(1,000)(10) 0.50[1 - (4/8)] Q* = = 80,000 = 282.8 or 283 hubcaps 2DS H[1 - (d/p)] Q* = p Production Order Quantity Model Setup cost = Holding cost D = 1,000 units p = 8 units per day d = 4 units per day S = $10 H = $0.50 per unit per year

  26. Quantity Discount Model • Reduced prices are often available when larger quantities are purchased • Trade-off is between reduced product cost and increased holding cost

  27. Total cost curve for discount 2 Total cost curve for discount 1 Total cost $ Total cost curve for discount 3 b a Q* for discount 2 is below the allowable range at point a and must be adjusted upward to 1,000 units at point b 1st price break 2nd price break 0 1,000 2,000 Order quantity Quantity Discount Model

  28. 2(5,000)(49) (.2)(5.00) 2(5,000)(49) (.2)(4.80) 2(5,000)(49) (.2)(4.75) Q1* = = 700 cars/order Q2* = = 714 cars/order Q3* = = 718 cars/order An Example D = 5,000 units H = 20 percents of P S = $49 per order 1,000 — adjusted 2,000 — adjusted

  29. Q 2 TC = S + H + PD D Q An Example Total cost = Setup cost + Holding cost + Product cost

  30. Probabilistic Models • Used when demand is not constant or certain • Use safety stock to achieve a desired service level/cost minimization and avoid stockout ROP = demand during lead time + safety stock

  31. Minimum demand during lead time Maximum demand during lead time Mean demand during lead time Inventory level ROP = 350 + safety stock of 16.5 = 366.5 ROP  Normal distribution probability of demand during lead time Expected demand during lead time (350 kits) Safety stock 16.5 units 0 Lead time Time Place order Receive order Probabilistic Models

  32. An Example Expected demand during lead time = 50 units Stockout cost = $40 per item Orders per year = 6 Carrying cost = $5 per item per year

  33. Risk of a stockout (5% of area of normal curve) Probability ofno stockout95% of the time ROP = ? Mean demand 350 Quantity Safety stock z 0 Number of standard deviations Demand Distribution

  34. Service Level Satisfaction • Use prescribed service levels to set safety stock when the cost of stockouts cannot be determined ROP = demand during lead time + safety stock = demand during lead time + zs where z = number of standard deviations s = standard deviation of demand during lead time

  35. An Example Average demand = m = 350 kits Standard deviation of demand during lead time = s = 10 kits 5% stockout policy (service level = 95%) Using Appendix I, for an area under the curve of 95%, the Z = 1.65 Safety stock = Zs= 1.65(10) = 16.5 kits Reorder point = expected demand during lead time + safety stock = 350 kits + 16.5 kits of safety stock = 366.5 or 367 kits

  36. Probabilistic Models with Variable Demand and/or Lead Time ROP = demand during lead time + safety stock where safety stock = z Xs = z X lead time X variance of daily demand + daily demand2 X variance of lead time

  37. Example 1 ROP = (15 units x 2 days) + Zs = 30 + 1.28(5)( 2) = 30 + 9.02 = 39.02 ≈ 39 • Daily demand: Normally distributed with mean 15 units and standard deviation 5 • Lead time is constant at 2 days • 90% service level with z = 1.28

  38. Example 2 • Daily demand is constant at 10 units • Lead time: Normally distributed with mean 6 days and standard deviation 3 • 98% service level with z = 2.055 ROP = (10 units x 6 days) + Zs = 60 + 2.055(10)(3) = 60 + 61.65 = 121.65 ≈ 122

  39. Example 3 ROP = (150 units x 5 days) + Zs = (150 x 5) + 1.65 (5 days x 162) + (1502 x 12) = 750 + 1.65(154) = 1,004 • Daily demand: Normally distributed with mean 150 units and standard deviation 16 • Lead time: Normally distributed with mean 5 days and standard deviation 1 • 95% service level with z = 1.65

  40. Periodic Review System Orders are placed at the end of a fixed period Order brings inventory up to target level Appropriate in routine situations May result in stockouts between periods

  41. Periodic Review System Target quantity (T) Q4 Q2 P Q1 Q3 On-hand inventory P P Time

  42. An Example • Target value: 50 • If inventory is 10 then order 40 • If inventory is -5 then order 55

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