1. OPM 533 9- Operations Management Inventory Management Chapter 9

6. Inventory Classifications OPM 533 9- Inventory Process stage Demand Type Number & Value Other Raw Material WIP Finished Goods Independent Dependent A Items B Items C Items Maintenance Operating © 1984-1994 T/Maker Co.

9. Classifying Items as ABC OPM 533 9- % of Inventory Items 0 20 40 60 80 100 0 50 100 % Annual $ Usage A B C Class % $ Vol % Items A 80 15 B 15 30 C 5 55

18. Inventory Usage Over Time OPM 533 9- Time Inventory Level Average Inventory (Q*/2) 0 Minimum inventory Order quantity = Q (maximum inventory level) Usage Rate

19. EOQ Model How Much to Order? OPM 533 9- Order quantity Annual Cost Holding Cost Curve Total Cost Curve Order (Setup) Cost Curve Optimal Order Quantity (Q*) Minimum total cost

23. EOQ Model Equations OPM 533 9- Optimal Order Quantity Expected Number of Orders Expected Time Between Orders Working Days / Year Working Days / Year = = × × = = = = = = × Q* D S H N D Q * T N d D ROP d L 2 D = Demand per year S = Setup (order) cost per order H = Holding (carrying) cost d = Demand per day L = Lead time in days

24. The Reorder Point (ROP) Curve OPM 533 9- Q* ROP (Units) Slope = units/day = d Lead time = L Time (days) Inventory level (units)

27. POQ Model Equations OPM 533 9- 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. Inventory Usage Over Time Figure 12.3 Order quantity = Q (maximum inventory level) Inventory level Time Usage rate Average inventory on hand Q 2 Minimum inventory

30. Minimizing Costs Objective is to minimize total costs Table 11.5 Annual cost Order quantity Curve for total cost of holding and setup Holding cost curve Setup (or order) cost curve Minimum total cost Optimal order quantity

31. 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 = = ( S ) D Q Annual setup cost = S D Q

32. 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 ) Q 2 Annual setup cost = S D Q Annual holding cost = H Q 2

33. 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 Solving for Q* Annual setup cost = S D Q Annual holding cost = H Q 2 D Q S = H Q 2 2 DS = Q 2 H Q 2 = 2 DS/H Q* = 2 DS/H

34. 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* = 2 DS H Q* = 2(1,000)(10) 0.50 = 40,000 = 200 units

35. 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 D Q* N = = 5 orders per year 1,000 200

36. An EOQ Example 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 = Expected time between orders Number of working days per year N T = = 50 days between orders 250 5

37. An EOQ Example 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 annual cost = Setup cost + Holding cost TC = (5)($10) + (100)($.50) = $50 + $50 = $100 TC = S + H D Q Q 2 TC = ($10) + ($.50) 1,000 200 200 2

38. An EOQ Example with safety stock 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 Safety Stock (ss) = 10 units Total annual cost = Setup cost + Holding cost TC = (5)($10) + (200)($.50) = $50 + $100 = $150 TC = S + ( + ss ) H D Q Q 2 TC = ($10) + (100 + )($.50) 1,000 200 200 2

40. Reorder Point Curve Figure 12.5 Q* ROP (units) Inventory level (units) Time (days) Lead time = L Slope = units/day = d

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

42. Reorder point with Safety Stock Annual Demand = 25,000 units Number of working days in a year 250 days Lead time = 5 days Safety stock (ss) = 2 days usage ROP = d x l + ss d= D / Number of days work in a year d= 25,000 / 250 = 100 units ss= 2 days x 100 = 200 ROP = 100 x 5 + 200 = 700 units

44. Quantity Discount Models Table 12.2 A typical quantity discount schedule Discount Number Discount Quantity Discount (%) Discount Price (P) 1 0 to 999 no discount $5.00 2 1,000 to 1,999 4 $4.80 3 2,000 and over 5 $4.75

46. Quantity Discount Models Figure 12.7 1,000 2,000 Total cost $ 0 Order quantity Q* for discount 2 is below the allowable range at point a and must be adjusted upward to 1,000 units at point b a b 1st price break 2nd price break Total cost curve for discount 1 Total cost curve for discount 2 Total cost curve for discount 3

47. Quantity Discount Example Calculate Q* for every discount Q* = 2 DS IP Q 1 * = = 700 cars order 2(5,000)(49) (.2)(5.00) Q 2 * = = 714 cars order 2(5,000)(49) (.2)(4.80) Q 3 * = = 718 cars order 2(5,000)(49) (.2)(4.75)

48. Quantity Discount Example Calculate Q* for every discount Q* = 2 DS IP Q 1 * = = 700 cars order 2(5,000)(49) (.2)(5.00) Q 2 * = = 714 cars order 2(5,000)(49) (.2)(4.80) Q 3 * = = 718 cars order 2(5,000)(49) (.2)(4.75) 1,000 — adjusted 2,000 — adjusted

49. Quantity Discount Example Table 12.3 Choose the price and quantity that gives the lowest total cost Buy 1,000 units at $4.80 per unit Discount Number Unit Price Order Quantity Annual Product Cost Annual Ordering Cost Annual Holding Cost Total 1 $5.00 700 $25,000 $350 $350 $25,700 2 $4.80 1,000 $24,000 $245 $480 $24,725 3 $4.75 2,000 $23.750 $122.50 $950 $24,822.50