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You are the inventory controller for the successful new Shack4Shades retail chain. Your business specializes exclusively in the retailing of sunglasses to the lover of the outdoors. You need to come up with a model to forecast sales of sunglasses in the coming quarter in order to build up inventory levels.
You have created a chart of your sales for the last eight quarters. Looking at this chart, you theorize that sales are growing according to a linear trend line, but with rather sizable seasonal variations. Sales pick up in the summer months when people head to the beaches and again in winter when they head for the ski slopes. Given this, you have come up with the following theoretical function to forecast sales as a function of time:
Predicted_Sales( t) = Seasonal_Factor( t) * ( Base + Trend * t)where,
Predicted_Sales( t) represents predicted sales for quarter t,You would like to come up with a LINGO model to estimate the six parameters of your function (i.e., the four seasonal factors, the trend line base, and the trend line slope). To do this, you will let LINGO choose values for the parameters that minimize the sum of the squared differences between predicted and observed sales for the historical data.
Seasonal_Factor( t) is one of four multipliers (one for each quarter of the year) to account for seasonal variations ,
Base is the y-intercept of the hypothesized linear function, and
Trend is the slope of the linear function.