1. 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)

2016

1^st quarter 12

2^nd quarter 8

3^rd quarter 6

4^th quarter 11

2017

1^st quarter 17

2^nd quarter 12

3^rd quarter 10

4^th quarter 15

2018

1^st quarter 25

2^nd quarter 23

3^rd quarter 22

4^th quarter 24

2019

1^st quarter 26

2^nd quarter 22

3^rd quarter 19

4^th quarter 25

2020

1^st quarter 29

2^nd quarter 25

3^rd quarter 22

4^th quarter 30

1. Do the data exhibit any patterns? Please explain.
2. Use an appropriate TIME SERIES REGRESSION procedure to produce forecasts for the first, second, third and fourth quarters of 2021.
3. 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 2021 (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?
4. What is the optimal order size associated with 0.92 service level?
5. What is the implied goodwill cost by the 0.92 service level?
6. If the transportation cost increases to $10,000, how will your answers to parts c, d and e will change