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Part $1$

The Carbondale Hospital is considering the purchase of a new ambulance. The decision will rest partly on the anticipated mileage to be driven next year. The miles driven during the past $5$ years are as$$ follows:

Year

$1$

$2$

$3$

$4$

$5$

Mileage

Part $2$

$$a$)$ Forecast the mileage for next year using a$2-$year moving average.

$$Mathematically$,$ the simple moving average$($which serves as an estimate of the next$$ period's demand$)$ is expressed as

Moving average$=$

Part $3$

To develop a forecast for year $6$ using a$2-$year moving$$ average, one needs to average across years

$4$ and $5$

$.$

Part $4$

Using a$2-$year moving$$ average, the forecast for year $6=$

$$

$3775$ miles $($round your response to two decimal$$ places$).$

Part $5$

$$b$)$ Find the MAD based on the$2-$year moving average forecast in part$($a$).$

The value of MAD is computed by taking the sum of the absolute values of the individual forecast errors$($deviations$)$ and dividing by the number of periods of data$($n$)$:

MAD$=$

Part $6$

The absolute error for year $4$ is

$$

$75\mathrm{.}00$ miles$($round your response to two decimal$$ places$).$

Part $7$

If a$2-$year moving average is used to make the$$ forecast, the MAD based on this$=$

$$

$133\mathrm{.}33$ miles $($round your response to two decimal$$ places$).($Hint: You will have only $3$ years of matched$$ data.$)$

Part $8$

$$c$)$ Use a weighted$2-$year moving average with weights of and to forecast next$$ year's mileage.$($The weight of is for the most recent$$ year.$)$

A weighted moving average may be expressed mathematically$$ as:

Weighted moving average$=$

Part $9$

For the next$$ year's mileage, the weighted$2-$year moving average is

$$

$.40$

$$

$.60($round your responses to two decimal$$ places$).$

Part $10$

$$Therefore$,$ the forecast for year $6$ is

$$

$3780$ miles$($round your response to two decimal$$ places$).$

Part $11$

What MAD results from using this approach to$$ forecasting?

The MAD for the forecast developed using a weighted$2-$year moving average with weights of and $=$

$$

$170\mathrm{.}0$ miles $($round your response to two decimal$$ places$).($Hint: You will have only $3$ years of matched$$ data.$)$

Part $12$

$$d$)$ Compute the forecast for year $6$ using exponential$$ smoothing, an initial forecast for year $1$ of$3,000$ miles, and $=.$

The basic exponential smoothing formula can be expressed as$$ follows:

$,$

where

is the new$$ forecast,

is the previous$$ period's forecast,

is the smoothing$($or weighting$)$ constant between $0$ and$1,$

is the previous$$ period's actual demand.

Part $13$

Using exponential smoothing with $=$ and a starting forecast for year $1$ being $,$ the forecast developed for years $2$ through $4$ will$$ be:

Year $2=$

Year $3=$

Year $4=.$

The Year $5$ forecast will be calculated as

$$

$3,264\mathrm{.}00($

$$

$3,750$

$$

$3,264\mathrm{.}00)=$

$$

$3,361\mathrm{.}20$ miles $($round your responses to two decimal$$ places$).$

Part $14$

Using exponential smoothing with $=$ and the forecast for year $1$ being $,$ the forecast for year $6=$

$$

enter your response here miles $($round your response to two decimal$$ places$).$