Q3) Demand Forecasting Problem (20 points) A retailer store will make a decision on the inventory level to satisfy the demand in the next season. To ensure the inventory decision is optimal, the firm must conduct a solid demand forecasting. In the first step, the retailer store management group collects the historical demand data, which is given in excel data file 1. Given the demand data in the past, how would you forecast the demand in the next season? Suppose the demand can take continuous values. In the second step, the firm management group realizes that the demand is not purely random, but instead depends on the firms decision on the retail price. Hence, to precisely predict the future demand, it is better to use the price as one input to predict the output (demand) in order to put the impact of price into consideration. To improve the demand forecasting, the management group collects the data of prices corresponding to each historical demand data point. Please refer to the excel data file 2 for the detailed data of price/demand pairs. We know for the next season, the firms decision on retail price is $10. How would you forecast the demand based on the new data set? And how precise is the demand forecasting in this step? Comparing the demand forecasting in the above two steps, what are the differences between them? Which one is preferable and why?

Data of Demand/Price Demand Data 108556 103632 112232 124969 1179971 152433 133986 140536 150107 134549 111754 116329 143620 151351 119560 119060 149312 129014 115046 143381 123874 143697 105521 120301 134480 114487 136503 140493 125728 114306 137769 Data of Demand/Price Price Demand $ 14.78 108556 $ 14.88 103632 $14.49 112232 $ 12.69 124969 $ 13.96 117997 $ 10.25 152433 $ 11.87 133986 $ 11.13 140536 $ 10.21 150107 $11.84 134549 $ 14.43 111754 $ 14.06 116329 $ 10.75 143620 $ 10.57 151351 $ 13.63 119560 $ 13.87 119060 $ 10.77 149312 $ 12.82 129014 $ 13.69 115046 $ 10.96 143381 $ 12.89 123874 $ 10.63 143697 $ 14.77 105521 $ 13.57 120301 $ 11.98 134480 $ 14.17 114487 $ 12.09 136503 $ 11.53 140493 $ 12.76 125728 $ 14.26 114306 $11.70 137769