$5.$ Ms$.$ Kathleen Boyd, director of logistics for the Scenic Calendar Company, wishes to evaluate two methods of time series

forecasting. She has collected quarterly calendar sales data from the years $2015$ and $2016.$

a$.$ Use the moving averages technique to find forecasted sales for the third quarter of $2016$ based on actual sales from the

previous three quarters.

b$.$ Use simple exponential smoothing to forecast each quarter$$s sales in $2016,$ given that Ms$.$ Boyd qualitatively

forecasted $900$ calendars for quarter $4,2015.$ Ms$.$ Boyd has assigned an alpha factor of $\mathrm{.}1$ for time series sensitivity$.$

c$.$ Repeat the simple exponential smoothing problem above $($part b$)$ with Ms$.$ Boyd employing an alpha factor of $\mathrm{.}2.$

d$.$ How well do the moving averages and simple exponential smoothing techniques seem to work in Ms$.$ Boyd$$s

situation? In what ways do the techniques appear to fail?

$6.$ Michael Gregory, logistics manager of Muscle Man Fitness Equipment, has determined that his current forecast system

for national sales has historically shown a $15$ percent error rate. Due to this level of error, Muscle Man$$s DC managersmaintain inventory at their locations costing the company, on average, $$3,500$ per month.By improving his forecast methodology and shortening forecast horizons, Mr$.$ Gregory anticipates cutting the error level

down to $10$ percent. With improved forecasting, Muscle Man$$s DC managers have indicated that they feel comfortable

with lower inventory levels. Mr$.$ Gregory anticipates monthly inventory carrying cost reductions of $35$ percent.

a$.$ If the forecast system improvement will cost $$1,500$ more per month than the old system, should Mr$.$ Gregory

implement the change?

b$.$ Why might Muscle Man$$s customers encourage the firm to improve its forecasting capabilities?

$7.$ Mr$.$ Stan Busfield, distribution center manager of Hogan Kitchenwares, must determine when to resupply his stock of

spatulas. The DC experiences a daily demand of $500$ spatulas. The average length of the performance cycle for spatulas

is $21$ days. Mr$.$ Busfield requires that $750$ spatulas be retained as safety stock to deal with demand uncertainty.

What is the reorder point for spatulas?