Operations Management: Processes and Supply Chains, 12th Edition

Solution

1. We use the learning curve formulas to calculate the time required for the 38th unit:

   $$b=\frac{\text{log }r}{\text{log }2}=\frac{\text{log }0.8}{\text{log }2}=\frac{-0.09691}{0.30103}=-0.322$$ $$k_n=k_1{n}^b=\left(1,000\text{ hours}\right){\left(38\right)}^{-0.322}$$ $$=\left(1,000\text{ hours}\right)\left(0.3099\right)=310\text{ hours}$$

2. Table I.1 gives the data needed to calculate the cumulative number of hours through each month of the schedule. Table I.2 shows these calculations.

   Table I.2 Cumulative Total Hours

   Month	Cumulative Units	Cumulative Average Time per Unit	Cumulative Total Hours/Month for All Units
   1	3	$1,000\left(0.83403\right)=834.03\text{h}\text{r}/\text{u}$	$\left(834.03\text{h}\text{r}/\text{u}\right)\left(3\text{u}\right)=2,502.1\text{h}\text{r}$
   2	10	$1,000\left(0.63154\right)=631.54\text{h}\text{r}/\text{u}$	$\left(631.54\text{h}\text{r}/\text{u}\right)\left(10\text{u}\right)=6,315.4\text{h}\text{r}$
   3	20	$1,000($