The demand for a product for the past $30$ periods is shown below. Determine the reorder point, R$,$ and order$-$up$-$to$-$level, S$,$ for this product for the next $6$ periods $($periods $31-36).$ Use the following instructions$/$information$.$

$$ Plot the demand data. What types of forecasting models would be appropriate for this demand pattern?

$$ The lead time is $2$ periods.

$$ Fixed ordering cost is $$175/$order and inventory holding cost of $$9\mathrm{.}00/$unit$/$period$.$

$$ Forecast the demand for this product in Minitab using Double Exponential Smoothing with smoothing constants of $\backslash$alpha $=0\mathrm{.}15$ and $\backslash$beta $=0\mathrm{.}20($use Minitab to generate forecasts$).$

$$ Calculate the standard deviation of the one$-$period$-$ahead forecast error using ONLY the most recent n$=8$ periods $($periods $23-30$ only$),$ and $\backslash$alpha MAD $=0\mathrm{.}20($use Minitab to generate one$-$period$-$ahead forecasts$).$

a$)$ Determine the reorder points, R$,$ and order$-$up$-$to$-$levels, S$,$ for the next $6$ periods using a probability of no stockout $($Type$-1$ service$)$ of $0\mathrm{.}94.$

b$)$ Determine the reorder points, R$,$ and order$-$up$-$to$-$levels, S$,$ for the next $6$ periods using a fill rate $($Type$-2$ service$)$ of $94\%.$

$*$See data below

t Dt

$1160$

$2176$

$3183$

$4185$

$5182$

$6184$

$7183$

$8189$

$9190$

$10191$

$11208$

$12210$

$13217$

$14219$

$15221$

$16224$

$17229$

$18243$

$19255$

$20264$

$21277$

$22275$

$23290$

$24295$

$25297$

$26292$

$27286$

$28298$

$29314$

$30331$

$*$data for problem $4$