You have gathered data on the daily demands for a product in your company. The daily demand average is 12.3, with a standard deviation of 6.4. The average lead time is 3.1 days with a standard deviation of 2.2 days. Each item costs $2.13 to hold inventory for a year. Reorder Point and annual holding costs of the Safety Stock is in the picture attached below.  

The z-value for 90% service level is 1.282; The z-value for a 95% service level is 1.645; The z-value for a 99% service level is 2.326.

a. Prepare a table showing the safety stock holding costs for each service level.

Update your table to reflect:

b. Cutting the average lead time in half.

c. Cutting the lead time standard deviation in half.

d. Cutting the daily demand standard deviation in half.

e. All three reductions simultaneously.

Provide a summary addressing the effect of service level on cost and the sensitivity of cost to changes in the parameters.

 

H LTD = HL HD = 3.1x 12.3 = 38.13 %3D %3D %3D oim = 0, H, +o %3D LTD = 6.42 x 3.1 +2.22 x 12.32 = 859 %3D OLTD = sqrt(859) = 29.3 %3D SS = z oTD = 1.645 x 29.3 = 48.2 Reorder Point = HTD + SS = 38.13 + 48.2 %3D = 86.33 rounded up = 87 %3D %3D Annual Holding Cost of SS = $2.13 x 48.2 = $102.67 %3D