The following data represent the quarterly sales by HCDIST, inc. a heavy construction equipment distributor, of HCE01 which is their top selling product. The manufacturer, HCMAN, always introduces its new model in December of each year and these models are available for sale by HCDIST on January 1 of the following year. HCMAN requires HCDIST to place its order for the entire year in the beginning of December of the previous year. For inventory and working capital planning purposes HCDIST needs quarterly forecasts.

YEAR SALES (units)

2018 1st quarter 12 2nd quarter 8 3rd quarter 6 4th quarter 11

2019 1st quarter 17 2nd quarter 12 3rd quarter 10 4th quarter 15

2020 1st quarter 25 2nd quarter 23 3rd quarter 22 4th quarter 24

2021 1st quarter 26 2nd quarter 22 3rd quarter 19 4th quarter 25

2022 1st quarter 29 2nd quarter 25 3rd quarter 22 4th quarter 30

c. HCDIST buys HCE01 from the manufacturer at a unit price of $200,000 and pays another $5,000 for transportation. Each unit of HCE01 sells for $260,000. HCDIST uses the sum of quarterly forecasts for 2022 (rounded up to the nearest integer) as the estimate of the mean of the normal distribution describing the annual demand for HCE01. Standard deviation of the distribution is estimated as 10% of the mean. Any HCE01 not sold by the year end (that is, before the new model is introduced) is sold at a 30% discount. How many units of HCE01 should HCDIST order to maximize its expected profits?

d. If the transportation cost increases to $15,000, how will this change your answer to part (c) above?

e. What is the optimal order size associated with 0.92 service level?

f. What is the implied goodwill cost by the 0.92 service level given that the transportation cost is $5,000?