$7.$ A local hardware store has experienced the following demand for flathead screwdrivers over the past $40$ periods.

Period Demand Period Demand Period Demand Period Demand

$1011021963197$

$20120220320$

$301337230330$

$475140247234114$

$5015025833597$

$60160260360$

$7621767270370$

$80180280380$

$9019029039124$

$1054200300400$

Note: use EXCEL to complete all parts of problem $3.$

a$.$ Plot the above sales data. What type of pattern $($e$.$g$.$ level, linear trend, nonlinear trend, seasonal, intermittent$)$ does this data exhibit?

b$.$ Use modified Croston$$s method for intermittent demand to forecast the average demand in periods $41$ and $45.$ Use a smoothing parameter of $\backslash$alpha $=0\mathrm{.}15.$

c$.$ Forecast the size of the next non$-$zero demand.

d$.$ Forecast the number of periods between consecutive non$-$zero demands.

e$.$ Calculate the BIAS, MAD, and MSE for the part a forecasting model.

$8.$ You have been asked to determine the learning curve percentage for a particular assembly task. You perform a random sampling of a worker performing this assembly task and record the number of assemblies performed by this worker $($i$.$e$.$ repetition number$)$ and the assembly time $($in minutes$).$

Repetition Assembly Time $($in minutes$)$

$142\mathrm{.}04$

$831\mathrm{.}40$

$2428\mathrm{.}05$

$4025\mathrm{.}79$

$9222\mathrm{.}87$

$14719\mathrm{.}55$

$21317\mathrm{.}44$

$33317\mathrm{.}09$

$40816\mathrm{.}15$

$75914\mathrm{.}72$

a$.$ Plot the above assembly time data $($you may use either Excel or Minitab$).$ Does the assembly time appear to be decreasing exponentially as the repetitions increase?

b$.$ Using the above data, find the learning curve percentage for this assembly task.