1. 12 - 1© 2011 Pearson Education, Inc. publishing as Prentice Hall Importance of Inventory One of the most expensive assets of many companies Can be 50% of total invested capital OM must balance inventory investment (opportunity cost of stock) customer service (being able to supply on time)

2. 12 - 2© 2011 Pearson Education, Inc. publishing as Prentice Hall Types of Inventory  Raw material  Purchased but not processed  Work-in-process  Undergone some change but not completed  A function of cycle time for a product  Maintenance/repair/operating (MRO)  Necessary to keep machinery and processes productive  Finished goods  Completed product awaiting shipment

3. 12 - 3© 2011 Pearson Education, Inc. publishing as Prentice Hall The Material Flow Cycle Figure 12.1 InputWait forWait toMoveWait in queueSetupRunOutput inspectionbe movedtimefor operatortimetime Cycle time 95%5%

4. 12 - 4© 2011 Pearson Education, Inc. publishing as Prentice Hall ABC Analysis  Divides inventory into three classes based on annual dollar volume  Class A - high annual dollar volume  Class B - medium annual dollar volume  Class C - low annual dollar volume  Used to focus on the few critical parts (A) and not the many trivial ones (C )

5. 12 - 5© 2011 Pearson Education, Inc. publishing as Prentice Hall ABC Analysis Item Stock Number Percent of Number of Items Stocked Annual Volume (units)x Unit Cost= Annual Dollar Volume Percent of Annual Dollar VolumeClass #1028620%1,000$ 90.00$ 90,00038.8%A #11526500154.0077,00033.2%A #127601,55017.0026,35011.3%B #1086730%35042.8615,0016.4%B #105001,00012.5012,5005.4%B 72% 23%

6. 12 - 6© 2011 Pearson Education, Inc. publishing as Prentice Hall ABC Analysis Item Stock Number Percent of Number of Items Stocked Annual Volume (units)x Unit Cost= Annual Dollar Volume Percent of Annual Dollar VolumeClass #12572600$ 14.17$ 8,5023.7%C #140752,000.601,200.5%C #0103650%1008.50850.4%C #013071,200.42504.2%C #10572250.60150.1%C 8,550$232,057100.0% 5%

7. 12 - 7© 2011 Pearson Education, Inc. publishing as Prentice Hall C Items ABC Analysis A Items B Items Percent of annual dollar usage 80 – 70 – 60 – 50 – 40 – 30 – 20 – 10 – 0 – |||||||||| 102030405060708090100 Percent of inventory items Figure 12.2

8. 12 - 8© 2011 Pearson Education, Inc. publishing as Prentice Hall ABC Analysis  Policies from this may include  More emphasis on supplier development for A items  Tighter physical inventory control for A items  More care in forecasting A items

9. 12 - 9© 2011 Pearson Education, Inc. publishing as Prentice Hall Control of Service Inventories  Can be a critical component of profitability  Losses may come from shrinkage or pilferage  Applicable techniques include 1.Good personnel selection, training, and discipline 2.Tight control on incoming shipments 3.Effective control on all goods leaving facility

10. 12 - 10© 2011 Pearson Education, Inc. publishing as Prentice Hall

11. 12 - 11 Models of Inventory Control  Fixed Quantity  Same quantity is ordered each time the reorder level is reached.  Fixed Period  The order is placed at regular times, but quantity varies according to demand at order time. © 2011 Pearson Education, Inc. publishing as Prentice Hall

12. 12 - 12© 2011 Pearson Education, Inc. publishing as Prentice Hall Holding, Ordering, and Setup Costs  Holding costs  Holding costs - the costs of holding or “carrying” inventory over time  Ordering costs  Ordering costs - the costs of placing an order and receiving goods  Setup costs  Setup costs - cost to prepare a machine or process for manufacturing an order

13. 12 - 13© 2011 Pearson Education, Inc. publishing as Prentice Hall Inventory Decision Models 1.Basic economic order quantity (EOQ) 2.Production order quantity (POQ) 3.Fixed period system (FPS)

14. 12 - 14© 2011 Pearson Education, Inc. publishing as Prentice Hall Basic EOQ Model 1.Demand is known, constant, and independent 2.Lead time is known and constant 3.Receipt of inventory is instantaneous and complete 4.Quantity discounts are not possible 5.Only variable costs are setup and holding 6.Stockouts can be completely avoided Important assumptions

15. 12 - 15© 2011 Pearson Education, Inc. publishing as Prentice Hall Inventory Usage Over Time Figure 12.3 Order quantity = Q (maximum inventory level) Usage rate Average inventory on hand Q 2 Minimum inventory Inventory level Time 0

16. 12 - 16© 2011 Pearson Education, Inc. publishing as Prentice Hall Minimizing Costs Objective is to minimize total costs Table 12.4(c) Annual cost Order quantity Total cost of holding and setup (order) Holding cost Setup (or order) cost Minimum total cost Optimal order quantity (Q*)

17. 12 - 17© 2011 Pearson Education, Inc. publishing as Prentice Hall The EOQ Model Q= Number of pieces per order Q*= Optimal number of pieces per order (EOQ) D= Annual demand in units for the inventory item S= Setup or ordering cost for each order H= Holding or carrying cost per unit per year Annual setup cost =(Number of orders placed per year) x (Setup or order cost per order) Annual demand Number of units in each order Setup or order cost per order = Annual setup cost = S DQDQ = (S) DQDQ

18. 12 - 18© 2011 Pearson Education, Inc. publishing as Prentice Hall The EOQ Model Q= Number of pieces per order Q*= Optimal number of pieces per order (EOQ) D= Annual demand in units for the inventory item S= Setup or ordering cost for each order H= Holding or carrying cost per unit per year Annual holding cost =(Average inventory level) x (Holding cost per unit per year) Order quantity 2 = (Holding cost per unit per year) = (H) Q2Q2 Annual setup cost = S DQDQ Annual holding cost = H Q2Q2

19. 12 - 19© 2011 Pearson Education, Inc. publishing as Prentice Hall The EOQ Model Q= Number of pieces per order Q*= Optimal number of pieces per order (EOQ) D= Annual demand in units for the inventory item S= Setup or ordering cost for each order H= Holding or carrying cost per unit per year Optimal order quantity is found when annual setup cost equals annual holding cost Annual setup cost = S DQDQ Annual holding cost = H Q2Q2 DQDQ S = H Q2Q2 Solving for Q* 2DS = Q 2 H Q 2 = 2DS/H Q* = 2DS/H

20. 12 - 20© 2011 Pearson Education, Inc. publishing as Prentice Hall An EOQ Example Determine optimal number of needles to order D = 1,000 units S = $10 per order H = $.50 per unit per year Q* = 2DS H Q* = 2(1,000)(10) 0.50 = 40,000 = 200 units

21. 12 - 21© 2011 Pearson Education, Inc. publishing as Prentice Hall An EOQ Example Determine optimal number of needles to order D = 1,000 units Q*= 200 units S = $10 per order H = $.50 per unit per year = N = = Expected number of orders Demand Order quantity DQ*DQ* N = = 5 orders per year 1,000 200

22. 12 - 22© 2011 Pearson Education, Inc. publishing as Prentice Hall An EOQ Example Determine optimal number of needles to order D = 1,000 unitsQ*= 200 units S = $10 per orderN= 5 orders per year H = $.50 per unit per year = T = Expected time between orders Number of working days per year N T = = 50 days between orders 250 5

23. 12 - 23© 2011 Pearson Education, Inc. publishing as Prentice Hall An EOQ Example Determine optimal number of needles to order D = 1,000 unitsQ*= 200 units S = $10 per orderN= 5 orders per year H = $.50 per unit per yearT= 50 days Total annual cost = Setup cost + Holding cost TC = S + H DQDQ Q2Q2 TC = ($10) + ($.50) 1,000 200 2 TC = (5)($10) + (100)($.50) = $50 + $50 = $100

24. 12 - 24© 2011 Pearson Education, Inc. publishing as Prentice Hall Robust Model  The EOQ model is robust  It works even if all parameters and assumptions are not met  The total cost curve is relatively flat in the area of the EOQ

25. 12 - 25© 2011 Pearson Education, Inc. publishing as Prentice Hall An EOQ Example Management underestimated demand by 50% D = 1,000 units Q*= 200 units S = $10 per orderN= 5 orders per year H = $.50 per unit per yearT= 50 days TC = S + H DQDQ Q2Q2 TC = ($10) + ($.50) = $75 + $50 = $125 1,500 200 2 1,500 units Total annual cost increases by only 25%

26. 12 - 26© 2011 Pearson Education, Inc. publishing as Prentice Hall An EOQ Example Actual EOQ for new demand is 244.9 units D = 1,000 units Q*= 244.9 units S = $10 per orderN= 5 orders per year H = $.50 per unit per yearT= 50 days TC = S + H DQDQ Q2Q2 TC = ($10) + ($.50) 1,500 244.9 2 1,500 units TC = $61.24 + $61.24 = $122.48 Only 2% less than the total cost of $125 when the order quantity was 200

27. 12 - 27© 2011 Pearson Education, Inc. publishing as Prentice Hall Reorder Points  EOQ answers the “how much” question  The reorder point (ROP) tells “when” to order ROP = Lead time for a new order in days Demand per day = d x L d = D Number of working days in a year

28. 12 - 28© 2011 Pearson Education, Inc. publishing as Prentice Hall Reorder Point Curve Q*Q* ROP (units) Inventory level (units) Time (days) Figure 12.5 Lead time = L Slope = units/day = d Resupply takes place as order arrives

29. 12 - 29© 2011 Pearson Education, Inc. publishing as Prentice Hall Reorder Point Example Demand = 8,000 iPods per year 250 working day year Lead time for orders is 3 working days ROP = d x L d = D Number of working days in a year = 8,000/250 = 32 units = 32 units per day x 3 days = 96 units

30. 12 - 30© 2011 Pearson Education, Inc. publishing as Prentice Hall 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

31. 12 - 31© 2011 Pearson Education, Inc. publishing as Prentice Hall Production Order Quantity Model Inventory level Time Demand part of cycle with no production Part of inventory cycle during which production (and usage) is taking place t Maximum inventory Figure 12.6

32. 12 - 32© 2011 Pearson Education, Inc. publishing as Prentice Hall 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 = (Average inventory level) x Annual inventory holding cost Holding cost per unit per year = (Maximum inventory level)/2 Annual inventory level = – Maximum inventory level Total produced during the production run Total used during the production run = pt – dt

33. 12 - 33© 2011 Pearson Education, Inc. publishing as Prentice Hall 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 = – Maximum inventory level Total produced during the production run Total used during the production run = pt – dt However, Q = total produced = pt ; thus t = Q/p Maximum inventory level = p – d = Q 1 – QpQp QpQp dpdp Holding cost = (H) = 1 – H dpdp Q2Q2 Maximum inventory level 2

34. 12 - 34© 2011 Pearson Education, Inc. publishing as Prentice Hall 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 D =Annual demand Q 2 = 2DS H[1 - (d/p)] Q* = 2DS H[1 - (d/p)] p Setup cost =(D/Q)S Holding cost = HQ[1 - (d/p)] 1212 (D/Q)S = HQ[1 - (d/p)] 1212

35. 12 - 35© 2011 Pearson Education, Inc. publishing as Prentice Hall Production Order Quantity Example D =1,000 units p =8 units per day S =$10 d =4 units per day H =$0.50 per unit per year Q* = 2DS H[1 - (d/p)] = 282.8 or 283 hubcaps Q* = = 80,000 2(1,000)(10) 0.50[1 - (4/8)]

36. 12 - 36© 2011 Pearson Education, Inc. publishing as Prentice Hall Production Order Quantity Model When annual data are used the equation becomes Q* = 2DS annual demand rate annual production rate H 1 – Note: d = 4 = = D Number of days the plant is in operation 1,000 250

37. 12 - 37© 2011 Pearson Education, Inc. publishing as Prentice Hall

38. 12 - 38 Fixed Period System Model  Inventory level checked at fixed times.  Order placed to bring level up to maximum.  Can use EOQ to find best time period, by T = Q* / D (time period = EOQ / demand) © 2011 Pearson Education, Inc. publishing as Prentice Hall

39. 12 - 39 FPS Maximum Inventory Level M = d (T+ L) Maximum = average demand (Time period + lead time) © 2011 Pearson Education, Inc. publishing as Prentice Hall

40. 12 - 40 FPS Order Size Q t = M - IP t Quantity (at ‘t’) = maximum- inventory (at ‘t’) © 2011 Pearson Education, Inc. publishing as Prentice Hall