1. Since Pages 142 to 151 of the text are rather difficult to read, the following is a presentation of…

2. An Alternate to Pages 142-151 of “Supply Chain Logistics Management” by Bowersox, Closs, Cooper “Statistical Methods of Calculating Safety Stock Requirements and Average Inventory”

3. “Statistical Methods of Calculating Safety Stock Requirements” Assumptions: –Daily demand is different day by day. –When the supply is replenished the number of days it takes for the replenishment to arrive varies. –Therefore, we have variable demand and a variable replenishment cycle.

4. Demand Varies Each day we ship out a different amount Day 1 Warehouse

5. Demand Varies Each day we ship out a different amount Day 2 Warehouse

6. Demand Varies Each day we ship out a different amount Day 3 Warehouse

7. Replenishment Varies Supplier Every time we order a replenishment of stock, delivery time is different. Warehouse 3 Day Delivery

8. Replenishment Varies Supplier Every time we order a replenishment of stock, delivery time is different. Warehouse 5 Day Delivery

9. Replenishment Varies Supplier Every time we order a replenishment of stock, delivery time is different. Warehouse 6 Day Delivery

10. “Statistical Methods of Calculating Safety Stock Requirements” Assumptions: –Daily demand is different day by day. –When the supply is replenished the number of days it takes for the replenishment to arrive varies. –Therefore, we have variable demand and a variable replenishment cycle.

11. How Much Safety Stock Do We Need?

12. Safety stock = Safety stock required when there is variability in both demand and lead time. Mean of replenishment rate ( Standard deviation of daily sales ) plus Mean of daily sales squared ( 2 Standard deviation of replenishment rate ) 2

13. The next slide shows a table listing 25 days of sales for a hypothetical company.

14. DaySales in Cases DaySales in Cases DaySales in Cases 11001011019110 2801113020120 370121202170 4601310022100 580148023130 690159024110 712016902590 811017100 9 18140 From Strategic Logistics Management by Stock and Lambert

15. We can see there is variability in sales from day to day.

16. Demand Varies Each day we ship out a different amount Warehouse

17. Now here’s a table with a hypothetical list of the required delivery times for our company’s last 16 orders.

18. Order NumberDays required to receive order Order NumberDays required to receive order

19. Order NumberDays required to receive order Order NumberDays required to receive order 17

20. Order NumberDays required to receive order Order NumberDays required to receive order 17 210

21. Order NumberDays required to receive order Order NumberDays required to receive order 1798 210 9 3 119 4131210 5121310 6111411 781511 891612

22. We can see there is variability in the time it takes to replenish our stock.

23. We can see there is variability in the time it takes to replenish our stock Supplier Every time we order a replenishment of stock, delivery time is different. Warehouse Different Delivery Times

24. How Much Safety Stock Do We Need?

25. Safety stock = Safety stock required when there is variability in both demand and lead time. Mean of replenishment rate ( Standard deviation of daily sales ) plus Mean of daily sales squared ( 2 Standard deviation of replenishment rate ) 2

26. Safety stock = Safety stock required when there is variability in both demand and lead time. Mean of replenishment rate ( Standard deviation of daily sales ) plus Mean of daily sales squared ( 2 Standard deviation of replenishment rate ) 2 We have seen our daily sales

27. DaySales in Cases DaySales in Cases DaySales in Cases 11001011019110 2801113020120 370121202170 4601310022100 580148023130 690159024110 712016902590 811017100 9 18140 From Strategic Logistics Management by Stock and Lambert

28. Safety stock = Safety stock required when there is variability in both demand and lead time. Mean of replenishment rate ( Standard deviation of daily sales ) plus Mean of daily sales squared ( 2 Standard deviation of replenishment rate ) 2 We have seen our daily sales We will need to know the mean of daily sales and the standard deviation of daily sales

29. Safety stock = Safety stock required when there is variability in both demand and lead time. Mean of replenishment rate ( Standard deviation of daily sales ) plus Mean of daily sales squared ( 2 Standard deviation of replenishment rate ) 2 First, determine the mean of daily sales

30. DaySales in Cases DaySales in Cases DaySales in Cases 11001011019110 2801113020120 370121202170 4601310022100 580148023130 690159024110 712016902590 811017100 9 18140 From Strategic Logistics Management by Stock and Lambert Mean = 100

31. Safety stock = Safety stock required when there is variability in both demand and lead time. Mean of replenishment rate ( Standard deviation of daily sales ) plus Mean of daily sales squared ( 2 Standard deviation of replenishment rate ) 2 Let’s put our daily sales mean of 100 into our formula to determine safety stock. It’s 100 squared or 10,000

32. Safety stock = Safety stock required when there is variability in both demand and lead time. Mean of replenishment rate ( Standard deviation of daily sales ) plus ( 2 Standard deviation of replenishment rate ) 2 Let’s put our daily sales mean of 100 into our formula to determine safety stock. It’s 100 squared or 10,000 10,000

33. Safety stock = Safety stock required when there is variability in both demand and lead time. Mean of replenishment rate ( Standard deviation of daily sales ) plus ( 2 Standard deviation of replenishment rate ) 2 We have seen our replenishment rates We will need to know the mean of the replenishment rate and the standard deviation of the replenishment rate. 10,000

34. Order NumberDays required to receive order Order NumberDays required to receive order 1798 210 9 3 119 4131210 5121310 6111411 781511 891612

35. Order NumberDays required to receive order Order NumberDays required to receive order 1798 210 9 3 119 4131210 5121310 6111411 781511 891612 First the mean of the replenishment rate

36. Order NumberDays required to receive order Order NumberDays required to receive order 1798 210 9 3 119 4131210 5121310 6111411 781511 891612 First the mean of the replenishment rate Mean = 10

37. Safety stock = Safety stock required when there is variability in both demand and lead time. Mean of replenishment rate ( Standard deviation of daily sales ) plus ( 2 Standard deviation of replenishment rate ) 2 Let’s put our replenishment rate mean of 10 into our formula to determine safety stock. 10,000

38. Safety stock = Safety stock required when there is variability in both demand and lead time. 10 ( Standard deviation of daily sales ) plus ( 2 Standard deviation of replenishment rate ) 2 Let’s put our replenishment rate mean of 10 into our formula to determine safety stock. 10,000

39. Safety stock = Safety stock required when there is variability in both demand and lead time. 10 ( Standard deviation of daily sales ) plus ( 2 Standard deviation of replenishment rate ) 2 Now we need the standard deviation of daily sales and the standard deviation of the replenishment rate. 10,000

40. (Observation – mean) 2 N-1 Find the Standard Deviation of Daily Sales Q S =

41. (Observation – mean) 2 N-1 Now Find the Standard Deviation of the Sales Q S = Remember, the mean or average is 100

42. (Observation – 100) 2 N-1 Now Find the Standard Deviation of the Sales Q S = Remember, the mean or average is 100

43. (Observation – 100) 2 N-1 Now Find the Standard Deviation of the Sales Q S = Now calculate how far each day’s sales are from the mean. Remember, the mean or average is 100

44. DaySales in Cases Deviation from mean Deviation Squared 1100 280 370 460 580 690 7120 8110 9100 Mean = 100 From Strategic Logistics Management by Stock and Lambert

45. DaySales in Cases Deviation from mean Deviation Squared 1100 280 370 460 580 690 7120 8110 9100 Mean = 100 From Strategic Logistics Management by Stock and Lambert minus mean of 100 =

46. DaySales in Cases Deviation from mean Deviation Squared 11000 280 370 460 580 690 7120 8110 9100 Mean = 100 From Strategic Logistics Management by Stock and Lambert

47. DaySales in Cases Deviation from mean Deviation Squared 110000 X 0 = 280 370 460 580 690 7120 8110 9100 Mean = 100 From Strategic Logistics Management by Stock and Lambert

48. DaySales in Cases Deviation from mean Deviation Squared 110000 280 370 460 580 690 7120 8110 9100 Mean = 100 From Strategic Logistics Management by Stock and Lambert

49. DaySales in Cases Deviation from mean Deviation Squared 110000 280 370 460 580 690 7120 8110 9100 Mean = 100 From Strategic Logistics Management by Stock and Lambert minus mean of 100 =

50. DaySales in Cases Deviation from mean Deviation Squared 110000 280-20 370 460 580 690 7120 8110 9100 Mean = 100 From Strategic Logistics Management by Stock and Lambert

51. DaySales in Cases Deviation from mean Deviation Squared 110000 280-20-20 x -20 = 370 460 580 690 7120 8110 9100 Mean = 100 From Strategic Logistics Management by Stock and Lambert

52. DaySales in Cases Deviation from mean Deviation Squared 110000 280-20400 370 460 580 690 7120 8110 9100 Mean = 100 From Strategic Logistics Management by Stock and Lambert

53. DaySales in Cases Deviation from mean Deviation Squared 110000 280-20400 370 460 580 690 7120 8110 9100 Mean = 100 From Strategic Logistics Management by Stock and Lambert minus mean of 100 =

54. DaySales in Cases Deviation from mean Deviation Squared 110000 280-20400 370-30 460 580 690 7120 8110 9100 Mean = 100 From Strategic Logistics Management by Stock and Lambert

55. DaySales in Cases Deviation from mean Deviation Squared 110000 280-20400 370-30-30 x -30 = 460 580 690 7120 8110 9100 Mean = 100 From Strategic Logistics Management by Stock and Lambert

56. DaySales in Cases Deviation from mean Deviation Squared 110000 280-20400 370-30900 460 580 690 7120 8110 9100 Mean = 100 From Strategic Logistics Management by Stock and Lambert

57. DaySales in Cases Deviation from mean Deviation Squared 110000 280-20400 370-30900 460 580 690 7120 8110 9100 Mean = 100 From Strategic Logistics Management by Stock and Lambert minus mean of 100 =

58. DaySales in Cases Deviation from mean Deviation Squared 110000 280-20400 370-30900 460-40 580 690 7120 8110 9100 Mean = 100 From Strategic Logistics Management by Stock and Lambert

59. DaySales in Cases Deviation from mean Deviation Squared 110000 280-20400 370-30900 460-401600 580 690 7120 8110 9100 Mean = 100 From Strategic Logistics Management by Stock and Lambert

60. DaySales in Cases Deviation from mean Deviation Squared 110000 280-20400 370-30900 460-401600 580-20400 690-10100 7120+20400 8110+10100 9 00 Mean = 100 From Strategic Logistics Management by Stock and Lambert

61. DaySales in Cases Deviation from mean Deviation Squared 10110+10100 11130+30900 12120+20400 1310000 1480-20400 1590-10100 1690-10100 1710000 18140+401600 Mean = 100 From Strategic Logistics Management by Stock and Lambert

62. DaySales in Cases Deviation from mean Deviation Squared 1911010100 2012020400 2170-30900 2210000 2313030900 2411010100 2590-10100 Mean = 100 From Strategic Logistics Management by Stock and Lambert

63. (Observation – 100) 2 N-1 Find the Standard Deviation of the Sales Q S = Now add up all the squared deviations, known as “squares” to find the “sum of squares.”

64. DaySales in Cases Deviation from mean Deviation Squared 110000 280-20400 370-30900 460-401600 580-20400 690-10100 7120+20400 8110+10100 9 00 Mean = 100 From Strategic Logistics Management by Stock and Lambert Now add up all the squares

65. DaySales in Cases Deviation from mean Deviation Squared 10110+10100 11130+30900 12120+20400 1310000 1480-20400 1590-10100 1690-10100 1710000 18140+401600 Mean = 100 From Strategic Logistics Management by Stock and Lambert Now add up all the squares

66. DaySales in Cases Deviation from mean Deviation Squared 1911010100 2012020400 2170-30900 2210000 2313030900 2411010100 2590-10100 Sum of squares = 10,000 Mean = 100 From Strategic Logistics Management by Stock and Lambert Now add up all the squares

67. 10000 N-1 Now Find the Standard Deviation of the Sales Q S = Sum of squares

68. 10000 N-1 Now Find the Standard Deviation of the Sales Q S = N= number of days of sales

69. 10000 25-1 Now Find the Standard Deviation of the Sales Q S = N= number of days of sales

70. 10000 24 Now Find the Standard Deviation of the Sales Q S =

71. Q S = 416.66666 Of which the square root is…

72. Now Find the Standard Deviation of the Sales Q S = 20.4 Rounded to 20

73. Safety stock = Safety stock required when there is variability in both demand and lead time. ( Standard deviation of daily sales ) plus ( 2 Standard deviation of replenishment rate ) 2 Let’s put that daily sales standard deviation of 20 into our formula for safety stock. 10 10,000

74. Safety stock = Safety stock required when there is variability in both demand and lead time. ( 20 ) plus ( 2 Standard deviation of replenishment rate ) 2 Let’s put that daily sales standard deviation of 20 into our formula for safety stock. 10 10,000

75. Safety stock = Safety stock required when there is variability in both demand and lead time. ( 400 ) plus ( 2 Standard deviation of replenishment rate ) 2 Let’s put that daily sales standard deviation of 20 into our formula for safety stock. And square it. 10 10,000

76. Safety stock = Safety stock required when there is variability in both demand and lead time. 400 plus ( Standard deviation of replenishment rate ) 2 Let’s put that daily sales standard deviation of 20 into our formula for safety stock. And square it. 10 10,000

77. Safety stock = Safety stock required when there is variability in both demand and lead time. 400 plus ( Standard deviation of replenishment rate ) 2 And find the standard deviation for the replenishment rate 10 10,000

78. Order Numb er Days required to receive order Deviation from mean Deviation squared 17 210 3 413 512 611 78 89 Replenishment rate mean = 10

79. Order Numb er Days required to receive order Deviation from mean Deviation squared 17 210 3 413 512 611 78 89 Replenishment rate mean = 10 minus mean of 10 =

80. Order Numb er Days required to receive order Deviation from mean Deviation squared 17-3 210 3 413 512 611 78 89 Replenishment rate mean = 10

81. Order Numb er Days required to receive order Deviation from mean Deviation squared 17-39 210 3 413 512 611 78 89 Replenishment rate mean = 10

82. Order Numb er Days required to receive order Deviation from mean Deviation squared 17-39 210 3 413 512 611 78 89 Replenishment rate mean = 10 minus mean of 10 =

83. Order Numb er Days required to receive order Deviation from mean Deviation squared 17-39 2100 3 413 512 611 78 89 Replenishment rate mean = 10

84. Order Numb er Days required to receive order Deviation from mean Deviation squared 17-39 21000 3 413 512 611 78 89 Replenishment rate mean = 10

85. Order Numb er Days required to receive order Deviation from mean Deviation squared 17-39 21000 3 413 512 611 78 89 Replenishment rate mean = 10 minus mean of 10 =

86. Order Numb er Days required to receive order Deviation from mean Deviation squared 17-39 21000 3 0 413 512 611 78 89 Replenishment rate mean = 10

87. Order Numb er Days required to receive order Deviation from mean Deviation squared 17-39 21000 3 00 413 512 611 78 89 Replenishment rate mean = 10

88. Order Numb er Days required to receive order Deviation from mean Deviation squared 17-39 21000 3 00 413 512 611 78 89 Replenishment rate mean = 10 minus mean of 10 =

89. Order Numb er Days required to receive order Deviation from mean Deviation squared 17-39 21000 3 00 413+3 512 611 78 89 Replenishment rate mean = 10

90. Order Numb er Days required to receive order Deviation from mean Deviation squared 17-39 21000 3 00 413+39 512+24 611+11 78-24 891 Replenishment rate mean = 10

91. Order Numb er Days required to receive order Deviation from mean Deviation squared 98-24 1091 1191 121000 131000 1411+11 1511+11 1612+24 Replenishment rate mean = 10

92. Order Numb er Days required to receive order Deviation from mean Deviation squared 98-24 1091 1191 121000 131000 1411+11 1511+11 1612+24 Replenishment rate mean = 10 Sum of squares = 40

93. (Observation – mean) 2 N-1 Q R = Find the Standard Deviation of the replenishment rate

94. 40 N-1 Q = Sum of squares Find the Standard Deviation of the replenishment rate R

95. N-1 Q = N= number orders placed 40 Find the Standard Deviation of the replenishment rate R

96. 16-1 Q = N= number orders placed 40 Find the Standard Deviation of the replenishment rate R

97. 15 Q = 40 Find the Standard Deviation of the replenishment rate R

98. Q = 2.66666 Of which the square root is… Find the Standard Deviation of the replenishment rate R

99. Q = 1.634 Find the Standard Deviation of the replenishment rate R

100. Safety stock = Safety stock required when there is variability in both demand and lead time. 400 plus ( Standard deviation of replenishment rate ) 2 Let’s put that replenishment rate standard deviation of 1.634 into our formula for safety stock. 10 10,000

101. Safety stock = Safety stock required when there is variability in both demand and lead time. 400 plus ( 1.634 ) 2 Let’s put that replenishment rate standard deviation of 1.634 into our formula for safety stock. 10 10,000

102. Safety stock = Safety stock required when there is variability in both demand and lead time. 400 plus 2.669 Let’s put that replenishment rate standard deviation of 1.634 into our formula for safety stock. And square it. 10 10,000

103. Safety stock = Safety stock required when there is variability in both demand and lead time. 400 plus 2.669 And work our formula. 10 10,000

104. Safety stock = Safety stock required when there is variability in both demand and lead time. (400) + (2.669) And work our formula. (10)(10,000)

105. Safety stock = Safety stock required when there is variability in both demand and lead time. And work our formula. 30,700

106. Safety stock = Safety stock required when there is variability in both demand and lead time. 175 cases of safety stock required.

107. Let’s bring it all together.

108. Back to our daily sales.

109. DaySales in Cases DaySales in Cases DaySales in Cases 11001011019110 2801113020120 370121202170 4601310022100 580148023130 690159024110 712016902590 811017100 9 18140 From Strategic Logistics Management by Stock and Lambert

110. The lowest number of sales in a day was 60.

111. The highest number of sales in a day was 140.

112. Back to our replenishment rate

113. Order NumberDays required to receive order Order NumberDays required to receive order 1798 210 9 3 119 4131210 5121310 6111411 781511 891612

114. The fastest we received an order was 7 days.

115. The slowest we received an order was 13 days. Therefore…

116. We have daily sales variation from 60 to 140 cases. We have replenishment rate variability from 7 to 13 days. We calculated that we would need 175 cases of safety stock to provide adequate inventory for…..

117. We have daily sales variation from 60 to 140 cases. We have replenishment rate variability from 7 to 13 days. We calculated that we would need 175 cases of safety stock to provide adequate inventory for…..Well, we can’t know how adequate that is, can we?

118. Yes, we can know.

119. Yes, we can know. By looking at service levels.

120. And by remembering that in our formula for finding safety stock we were working with 1 standard deviation for our daily sales and our replenishment rate.

121. We’ve seen this before: Standard deviation represents an average of how far observations are away from the mean.

122. There are certain characteristics of standard deviation in a normal distribution… We’ve seen this before:

124. We have a mean of x

125. We have a standard deviation of y

126. If we determine 1 standard deviation above and below the mean… We have a mean of x We have a standard deviation of y

127. If we determine 1 standard deviation above and below the mean… x+y = 1 standard deviation x-y = 1 standard deviation We have a standard deviation of y We have a mean of x

128. If we determine 1 standard deviation above and below the mean… x+y = 1 standard deviation x-y = 1 standard deviation We have a standard deviation of y We have a mean of x In a normal distribution about 68% of the observations will usually be within 1 standard deviation of the mean.

129. If we determine 1 standard deviation above and below the mean… x+y = 1 standard deviation x-y = 1 standard deviation We have a standard deviation of y We have a mean of x In a normal distribution about 68% of the observations will usually be within 1 standard deviation of the mean. 68.26%

130. If we determine 1 standard deviation above and below the mean… x+y = 1 standard deviation x-y = 1 standard deviation We have a standard deviation of y We have a mean of x 68.26% 1 standard deviation of safety stock will give us an 84.13% service level.

131. If we determine 1 standard deviation above and below the mean… x+y = 1 standard deviation x-y = 1 standard deviation We have a standard deviation of y We have a mean of x 68.26% 1 standard deviation of safety stock will give us an 84.13% service level. Just figure 100%-68.26%

132. If we determine 1 standard deviation above and below the mean… x+y = 1 standard deviation x-y = 1 standard deviation We have a standard deviation of y We have a mean of x 68.26% 1 standard deviation of safety stock will give us an 84.13% service level. Just figure 100%-68.26% = 31.74%

133. If we determine 1 standard deviation above and below the mean… x+y = 1 standard deviation x-y = 1 standard deviation We have a standard deviation of y We have a mean of x 68.26% 1 standard deviation of safety stock will give us an 84.13% service level. Just figure 100%-68.26% = 31.74%, then divide 31.74% by 2

134. If we determine 1 standard deviation above and below the mean… x+y = 1 standard deviation x-y = 1 standard deviation We have a standard deviation of y We have a mean of x 68.26% 1 standard deviation of safety stock will give us an 84.13% service level. Just figure 100%-68.26% = 31.74%, then divide 31.74% by 2 = 15.87%

135. If we determine 1 standard deviation above and below the mean… x+y = 1 standard deviation x-y = 1 standard deviation We have a standard deviation of y We have a mean of x 68.26% 1 standard deviation of safety stock will give us an 84.13% service level. Just figure 100%-68.26% = 31.74%, then divide 31.74% by 2 = 15.87% Add that to 68.26%

136. If we determine 1 standard deviation above and below the mean… x+y = 1 standard deviation We have a standard deviation of y We have a mean of x 68.26% 1 standard deviation of safety stock will give us an 84.13% service level. Just figure 100%-68.26% = 31.74%, then divide 31.74% by 2 = 15.87% Add that to 68.26% 15.87% + 68.26% = 84.13%

137. That’s how we know 175 cases of safety stock for our hypothetical company will provide us with enough stock 84% of the time.

138. Safety stock = Because when we calculated this formula, we were using 1 standard deviation. Mean of replenishment rate ( Standard deviation of daily sales ) plus Mean of daily sales squared ( 2 Standard deviation of replenishment rate ) 2

139. Safety stock = If we wanted higher service levels (and 84% is not very good), we would increase the standard deviation when we calculated the formula. Mean of replenishment rate ( Standard deviation of daily sales ) plus Mean of daily sales squared ( 2 Standard deviation of replenishment rate ) 2

140. Service Levels 1 standard deviation of safety stock = 1-.6826 +.6826 =.8413 2

141. Service Levels 1 standard deviation of safety stock = 1-.6826 +.6826 =.8413 2 2 standard deviation of safety stock = 1-.9544 +.9544 =.9772 2

142. Service Levels 1 standard deviation of safety stock = 1-.6826 +.6826 =.8413 2 2 standard deviation of safety stock = 1-.9544 +.9544 =.9772 2 3 standard deviation of safety stock = 1-.9974 +.9974 =.9987 2

143. Service Levels 1 standard deviation of safety stock = 1-.6826 +.6826 =.8413 2 2 standard deviation of safety stock = 1-.9544 +.9544 =.9772 2 3 standard deviation of safety stock = 1-.9974 +.9974 =.9987 2 84% service level

144. Service Levels 1 standard deviation of safety stock = 1-.6826 +.6826 =.8413 2 2 standard deviation of safety stock = 1-.9544 +.9544 =.9772 2 3 standard deviation of safety stock = 1-.9974 +.9974 =.9987 2 84% service level Almost 98% service level.

145. Service Levels 1 standard deviation of safety stock = 1-.6826 +.6826 =.8413 2 2 standard deviation of safety stock = 1-.9544 +.9544 =.9772 2 3 standard deviation of safety stock = 1-.9974 +.9974 =.9987 2 84% service level Almost 98% service level. Almost 100% service level

146. Service Levels 1 standard deviation of safety stock = 1-.6826 +.6826 =.8413 2 2 standard deviation of safety stock = 1-.9544 +.9544 =.9772 2 3 standard deviation of safety stock = 1-.9974 +.9974 =.9987 2 84% service level Almost 98% service level. Almost 100% service level On the next page is a service level chart. It tells you the standard deviation to use to achieve a specific service level.

147. Service Level Table Service LevelNumber of standard deviations of safety stock needed. 84.1%1 90.3%1.3 94.5%1.6 97.7%2 98.9%2.3 99.5%2.6 99.9%3

148. So how do we apply this?

149. Suppose we want a 94.5% service level.

150. So how do we apply this? Suppose we want a 94.5% service level. That means that when a customer wants a product, 94.5% of the time the product will be in stock.

151. Service Level Table Service LevelNumber of standard deviations of safety stock needed. 84.1%1 90.3%1.3 94.5%1.6 97.7%2 98.9%2.3 99.5%2.6 99.9%3 We multiply the standard deviations of our formula by 1.6

152. Safety stock = Safety stock required when there is variability in both demand and lead time. Mean of replenishment rate ( Standard deviation of daily sales ) plus Mean of daily sales squared ( 2 Standard deviation of replenishment rate ) 2 times 1.6

153. In Our Original Formula… We used 1 standard deviation. Standard deviation of daily sales was 20 The standard deviation of the replenishment rate was 1.634

154. In Our New Formula… We will use the standard deviation times 1.6 Standard deviation of daily sales was 20 The standard deviation of the replenishment rate was 1.634 Therefore, we multiply 20 by 1.6 = 32. And 1.634 by 1.6 = 2.6144

155. Safety stock = Safety stock required when there is variability in both demand and lead time. Mean of replenishment rate ( Standard deviation of daily sales ) plus Mean of daily sales squared ( 2 Standard deviation of replenishment rate ) 2 1 standard deviation =20 1 standard deviation =1.634 times 1.6 = 32 times 1.6 = 2.6144 Meaning our original formula will now be changed to…

156. Safety stock = Safety stock required when there is variability in both demand and lead time. Mean of replenishment rate ( Standard deviation of daily sales ) plus Mean of daily sales squared ( 2 Standard deviation of replenishment rate ) 2 1 standard deviation =20 1 standard deviation =1.634 times 1.6 = 32 times 1.6 = 2.6144 Meaning our original formula will now be changed to…

157. Safety stock = Safety stock required when there is variability in both demand and lead time. Mean of replenishment rate () plus Mean of daily sales squared ( 2 ) 2 32 2.6144 Meaning our original formula will now be changed to…

158. Safety stock = Safety stock required when there is variability in both demand and lead time. 10 () plus 10,000 ( 2 ) 2 32 2.6144 Meaning our original formula will now be changed to…

159. Safety stock = Safety stock required when there is variability in both demand and lead time. 10 plus 10,000 = 280.333 rounded to 280 1024 6.8350XX

160. To Provide a 94.5% Service Level… We need 280 units of safety stock.

161. We’ve Just Seen How to Determine Safety Stock. But how much average inventory should we have to achieve various levels of customer service? We need to –Determine our service level. –Determine our Economic Ordering Quantity (EOQ) –Determine our average cycle stock. –Determine our safety stock level. –Add average cycle stock and safety stock.

162. To Determine Average Inventory: Determine our service level. Let’s say it’s 84.1% Determine our Economic Ordering Quantity (EOQ). Determine our average cycle stock. Determine our safety stock level. Add average cycle stock and safety stock.

163. To Determine Economic Ordering Quantity 2C o D EOQ = C i U Where EOQ = Economic ordering quantity. C o = ordering cost (dollars per order) C i = Annual inventory carry costs (% product cost or value) D= Annual demand (number of units) U = Average cost or value of one unit of inventory

164. To Determine Economic Ordering Quantity 2C o D EOQ = C i U Where EOQ = Economic ordering quantity. C o = ordering cost (dollars per order) C i = Annual inventory carry costs (% product cost or value) D= Annual demand (number of units) U = Average cost or value of one unit of inventory We will use some data from the hypothetical organization we looked at earlier.

165. DaySales in Cases DaySales in Cases DaySales in Cases 11001011019110 2801113020120 370121202170 4601310022100 580148023130 690159024110 712016902590 811017100 9 18140 From Strategic Logistics Management by Stock and Lambert Mean = 100

166. To Determine Economic Ordering Quantity 2C o D EOQ = C i U Where EOQ = Economic ordering quantity. C o = ordering cost (dollars per order) C i = Annual inventory carry costs (% product cost or value) D= Annual demand (number of units) U = Average cost or value of one unit of inventory We will use some data from the hypothetical organization we looked at earlier.

167. To Determine Economic Ordering Quantity 2C o D EOQ = C i U Where EOQ = Economic ordering quantity. C o = ordering cost (dollars per order) C i = Annual inventory carry costs (% product cost or value) D= Annual demand (number of units) U = Average cost or value of one unit of inventory Our hypothetical company had mean daily sales of 100. We multiply That by 250 business days which gives annual demand of 25,000

168. To Determine Economic Ordering Quantity 2C o (25,000) EOQ = C i U Where EOQ = Economic ordering quantity. C o = ordering cost (dollars per order) C i = Annual inventory carry costs (% product cost or value) D= Annual demand (number of units) U = Average cost or value of one unit of inventory Our hypothetical company had mean daily sales of 100. We multiply That by 250 business days which gives annual demand of 25,000

169. To Determine Economic Ordering Quantity 2C o (25,000) EOQ = C i U Where EOQ = Economic ordering quantity. C o = ordering cost (dollars per order) C i = Annual inventory carry costs (% product cost or value) D= 25,000 U = Average cost or value of one unit of inventory Our other values will be arbitrary for the sake of this exercise.

170. To Determine Economic Ordering Quantity 2(28)x (25,000) EOQ = C i U Where EOQ = Economic ordering quantity. C o = $28 C i = Annual inventory carry costs (% product cost or value) D= 25,000 U = Average cost or value of one unit of inventory Our other values will be arbitrary for the sake of this exercise.

171. To Determine Economic Ordering Quantity 2(28)x (25,000) EOQ =.32 x U Where EOQ = Economic ordering quantity. C o = $28 C i = 32% D= 25,000 U = Average cost or value of one unit of inventory Our other values will be arbitrary for the sake of this exercise.

172. To Determine Economic Ordering Quantity 2(28)x (25,000) EOQ =.32 x 4.37 Where EOQ = Economic ordering quantity. C o = $28 C i = 32% D= 25,000 U = $4.37 per case Our other values will be arbitrary for the sake of this exercise.

173. To Determine Economic Ordering Quantity EOQ = 1,000 Where EOQ = Economic ordering quantity. C o = $28 C i = 32% D= 25,000 U = $4.37 per case

174. To Determine Average Inventory Determine our service level. Let’s say it’s 84.1% Determine our Economic Ordering Quantity (EOQ). Determine our average cycle stock. Determine our safety stock level. Add average cycle stock and safety stock.

175. To Determine Average Cycle Stock… As we saw earlier, it is one half of order quantity

176. The Effect of Reorder Quantity on Average Inventory Investment with Constant Demand and Lead Time a 6-3 a Cycle stock is one-half the ordering quantity. From instructor’s material: “Strategic Logistics Management” by Stock and Lambert(2001).

177. Cycle Stock = ½ Ordering Quantity EOQ = 1,000 Where EOQ = Economic ordering quantity. C o = $28 C i = 32% D= 25,000 U = $4.37 per case 2 = 500

178. To Determine Average Inventory Determine our service level. Let’s say it’s 84.1% Determine our Economic Ordering Quantity (EOQ). Determine our average cycle stock. Determine our safety stock level. Add average cycle stock and safety stock.

179. Safety stock = Safety stock required when there is variability in both demand and lead time. Mean of replenishment rate ( Standard deviation of daily sales ) plus Mean of daily sales squared ( 2 Standard deviation of replenishment rate ) 2 Using our data from our hypothetical organization, we have already seen that for an 84.1% service level, we need 175 cases of safety stock.

180. To Determine Average Inventory Determine our service level. Let’s say it’s 84.1% Determine our Economic Ordering Quantity (EOQ). Determine our average cycle stock. Determine our safety stock level. Add average cycle stock and safety stock.

181. To Determine Average Inventory Average cycle stock plus safety stock for this service level (84.1%) 500 cases Average cycle stock + 175 Safety stock = 675 cases Average inventory

182. To Determine Average Inventory Determine our service level. Let’s say it’s 84.1% Determine our Economic Ordering Quantity (EOQ). Determine our average cycle stock. Determine our safety stock level. Add average cycle stock and safety stock.

183. End of Program.