5. Inventory Classifications Inventory Process stage Demand Type Number & Value Other Raw Material WIP & Finished Goods Independent Dependent A Items B Items C Items Maintenance Dependent Operating

13. EOQ Model: Minimize the overall Costs Order Quantity Cost Holding Cost Curve Total Cost Curve Ordering & Setup Costs Curve Optimal Order Quantity (Q*)

18. Basic EOQ Model (Constant Demand and Lead Time) Reorder Point (ROP) Time Inventory Level Average Inventory (Q*/2) Lead Time Optimal Order Quantity (Q*)

19. Derive the EOQ: Finding Q* that Minimizes the Total Costs Total inventory cost = Order (Setup) cost + Holding cost To minimize TC, we set the derivative of TC with respect to Q* equal to 0 Thus,

20. EOQ Model Equations: How much to Order Optimal Order Quantity Expected Number of Orders Expected Time Between Orders Working Days / Year = = × × = = = = Q* D S H N D Q * T N 2 D = Demand per year S = Setup (order) cost per order H = Holding (carrying) cost

24. POQ Model Reorder Point (ROP) Time Inventory Level Average Inventory Lead Time Optimal Order Quantity (Q*)

25. POQ Model Inventory Levels Inventory Leve l Time Supply Begins Supply Ends Production portion of cycle Demand portion of cycle with no supply

26. POQ Model Inventory Levels Time Inventory Level Production Portion of Cycle Max. Inventory Q·(1- d/p) Q* Supply Begins Supply Ends Inventory level with no demand Demand portion of cycle with no supply

27. POQ Model Equations D = Demand per year S = Setup cost H = Holding cost d = Demand per day p = Production per day Optimal Order Quantity Setup Cost Holding Cost = = - = * = * = Q H* d p Q D Q S p * 1 ( 0.5 * H * Q - d p 1 ) 1 ( ) 2*D*S ( ) Maximum inventory level - d p

29. Quantity Discount Model How Much to Order? Lowest cost not in discount range Order Quantity Total Cost Quantity which would be ordered TC for Discount 2 Quantity to earn Discount 2 Discount 2 Price Quantity to earn Discount 1 TC for Discount 1 Discount 1 Price TC for No Discount Initial Price

31. Probabilistic Models When to Order? Reorder Point (ROP) Optimal Order Quantity X Safety Stock (SS) Time Inventory Level Lead Time SS ROP Service Level P(Stockout) Place order Receive order Frequency

32. ABC Classification: Pareto Principle (Critical few and trivial many) 0 20 40 60 80 100 0 50 100 % of Inventory Items % Annual $ Usage A B C Class % $ Vol % Items A 80 15 B 15 30 C 5 55

34. Heuristics: Fixed Period Model Time Inventory Level Target maximum Period Period Period

36. Lowering Inventory Reduces Waste Scrap Work in process inventory level (hides problems) Unreliable Vendors Capacity Imbalances

37. Lowering Inventory Reduces Waste Scrap Reducing inventory reveals problems so they can be solved. Unreliable Vendors Capacity Imbalances WIP

38. To Lower Inventory, Reduce Lot Sizes Time Inventory Level Lot Size 200 Lot Size 80 Average inventory = 100 Average inventory = 40 Average inventory = (Lot size)/2

39. …Which Increases Inventory Costs Lot Size Cost Holding Cost Total Cost Setup Cost Optimal Lot Size Smaller Lot Size

40. Unless Setup Costs are Reduced Lot Size Cost Holding Cost Total Cost Original optimal lot size New optimal lot size Setup Cost

41. Steps to Reduce Setup Time (Honda Assembly Line) Initial Setup Time Separate setup into preparation, and actual setup, doing as much as possible while the machine/process is running (save 30 minutes) Move material closer and improve material handling (save 20 minutes) Standardize and improve tooling (save 15 minutes) 90 min 60 min 45 min 25 min 15 min Use one-touch system to eliminate adjustments (save 10 minutes) Training operators and standardizing work procedures (save 2 minutes) Step 1 Step 2 Step 3 Step 5 13 min Step 4

42. Reducing Lot Sizes Increases the Number of Lots Small lots increase flexibility to meet customer demands Strategies for eliminating waste and for eliminating waiting

46. Examples of Kanban