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Chapter Six: Inventory

Chapter Six: Inventory. Part Five “Service Levels.”. But it is rare when all these conditions can be met. When it is time to order (with constant demand, lead time, and price), this is how many units we should order. As a result we need safety stock, but how much?.

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Chapter Six: Inventory

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  1. Chapter Six: Inventory Part Five “Service Levels.”

  2. But it is rare when all these conditions can be met. When it is time to order (with constant demand, lead time, and price), this is how many units we should order. . As a result we need safety stock, but how much?

  3. This is where need to apply the concept of standard deviation.

  4. This is where need to apply the concept of standard deviation. • Standard deviation represents an average of how far observations are away from the mean.

  5. This is where need to apply the concept of standard deviation. • Standard deviation represents an average of how far observations are away from the mean. • There are certain characteristics of standard deviation in a normal distribution…

  6. If you do not understand the concept of a normal distribution, see the slide presentation entitled “Some Basic Statistics Concepts.” . . . . .

  7. Mean = 70

  8. Mean = 70 Standard deviation = 20 .

  9. If we determine 1 standard deviation above and below the mean… Mean = 70 Standard deviation = 20

  10. If we determine 1 standard deviation above and below the mean… Mean = 70 Standard deviation = 20 70 -20 = 50 70 +20 = 90 20 20

  11. If we determine 1 standard deviation above and below the mean… In a normal distribution about 68%% of the observations will usually be within 1 standard deviation of the mean. Mean = 70 Standard deviation = 20 70 -20 = 50 70 +20 = 90 20 20 .

  12. If we determine 1 standard deviation above and below the mean… In a normal distribution about 68%% of the observations will usually be within 1 standard deviation of the mean. Mean = 70 70 -20 = 50 70 +20 = 90 20 20 68.26%

  13. If we determine 2 standard deviations above and below the mean… Mean = 70 20 20 20 20

  14. If we determine 2 standard deviations above and below the mean… Mean = 70 70 -40 = 30 70 +40 = 110 20 20 20 20

  15. If we determine 2 standard deviations above and below the mean… Mean = 70 70 -40 = 30 70 +40 = 110 20 20 20 20 95.44%

  16. If we determine 2 standard deviations above and below the mean… In a normal distribution about 95%% of the observations will usually be within 2 standard deviations of the mean. Mean = 70 70 -40 = 30 70 +40 = 110 20 20 20 20 95.44% .

  17. If we determine 3 standard deviations above and below the mean… Mean = 70 20 20 20 20 20 20

  18. If we determine 3 standard deviations above and below the mean… Mean = 70 70 -60 = 10 70 +60 = 130 20 20 20 20 20 20

  19. If we determine 3 standard deviations above and below the mean… In a normal distribution over 99%% of the observations will usually be within 3 standard deviations of the mean. Mean = 70 70 -60 = 10 70 +60 = 130 20 20 20 20 20 20 99.87%

  20. Applying Standard Deviation to Service Levels. • Assume daily sales are at a mean of 70. • Assume standard deviation is 20. • That means that 68 percent of the time, daily sales fall between 50 (70-20) and 90 (70+20) units each day. .

  21. Assume daily sales are at a mean of 70. Assume standard deviation is 20. That means that 68 percent of the time, daily sales fall between 50 (70-20) and 90 (70+20) units each day. In a normal distribution about 68%% of the observations will usually be within 1 standard deviation of the mean. Mean = 70 20 20 68.26% 50 90

  22. Assume daily sales are at a mean of 70. Assume standard deviation is 20. That means that 68 percent of the time, daily sales fall between 50 (70-20) and 90 (70+20) units each day. If mean sales are 70, and we carry 1 standard deviation of safety stock, we are carrying 20 units of safety stock. Mean = 70 20 20 68.26% 50 90

  23. Assume daily sales are at a mean of 70. Assume standard deviation is 20. That means that 68 percent of the time, daily sales fall between 50 (70-20) and 90 (70+20) units each day. 1 standard deviation of safety stock will give us an 84.13% service level. Mean = 70 20 20 68.26% 50 90

  24. Assume daily sales are at a mean of 70. Assume standard deviation is 20. That means that 68 percent of the time, daily sales fall between 50 (70-20) and 90 (70+20) units each day. 1 standard deviation of safety stock will give us an 84.13% service level. Just figure 100%-68.26% Mean = 70 20 20 68.26% 50 90

  25. Assume daily sales are at a mean of 70. Assume standard deviation is 20. That means that 68 percent of the time, daily sales fall between 50 (70-20) and 90 (70+20) units each day. 1 standard deviation of safety stock will give us an 84.13% service level. Just figure 100%-68.26% = 31.74% Mean = 70 20 20 68.26% 50 90

  26. Assume daily sales are at a mean of 70. Assume standard deviation is 20. That means that 68 percent of the time, daily sales fall between 50 (70-20) and 90 (70+20) units each day. 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 Mean = 70 20 20 68.26% 50 90

  27. Assume daily sales are at a mean of 70. Assume standard deviation is 20. That means that 68 percent of the time, daily sales fall between 50 (70-20) and 90 (70+20) units each day. 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% Mean = 70 20 20 68.26% 50 90

  28. Assume daily sales are at a mean of 70. Assume standard deviation is 20. That means that 68 percent of the time, daily sales fall between 50 (70-20) and 90 (70+20) units each day. 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% Mean = 70 20 20 68.26% 50 90

  29. Assume daily sales are at a mean of 70. Assume standard deviation is 20. That means that 68 percent of the time, daily sales fall between 50 (70-20) and 90 (70+20) units each day. 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% Mean = 70 20 20 68.26% 50 90

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

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

  32. 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

  33. Service Levels 84% service level 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

  34. Service Levels 84% service level 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 Almost 98% service level.

  35. Service Levels 84% service level 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 Almost 98% service level. Almost 100% service level

  36. Service Level Table

  37. The formula to find safety stock required when there is variability in both demand and lead time. Safety stock = ( ) ( ) Mean of replenishment rate 2 2 Standard deviation of daily sales Mean of daily sales squared Standard deviation of replenishment rate plus We’ll look at this later. .

  38. 6-8 Symptoms of Poor Inventory • Increasing numbers of back orders • Increasing dollar investment in inventory with back orders remaining constant. • High customer turnover rate. • Increasing number of orders being canceled. • Periodic lack of sufficient storage space. • Wide variance in inventory turnover among distribution centers and major inventory items.

  39. End of Program.

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