Problem $6$

The planned weekly demand for new components from a German manufacturer is $5,000$ units. The standard deviation is unknown, one estimate is $100$ units per week $($very stable demand$),$ the other $1,000$ units per week $($very volatile demand$).$ The weight and cost per unit is $2lbs$ and $$10$ respectively. The holding cost rate is $30\%$ and the $)=(2\mathrm{.}576.$ Assume operations take place $52$ weeks per year. Assume $2$ weeks of production$/$prep lead time with a standard deviation of $0$ days; ordering costs are $$1,000$ per order. In both cases, the shipping quantity will be $20,000$ units $($a container load$).$

GMX$.$ Transit time is $4$ weeks, standard deviation of $1$ week. The rate per CL is $$3,200.$

NHK$.$ Transit time is $4$ weeks, standard deviation of $0\mathrm{.}5$ weeks. The rate per CL is $$4,600.$

What is the recommendation for each of the two values for the standard deviation?