Please work on this HW manually, without using Excel. Submit your scanned papers on LMS$.$ Show your work on calculations; "result only" answers will get only half credit even if they are correct, and will not get any partial credit if they are wrong.

V $=$ YOUR STUDENT NUMBER $($e$.$g$.,5012345->12345)$

V $=$ SUM OF DIGITS OF YOUR STUDENT NUMBER $($e$.$g$.,5012345->1+2+3+4+5=15)$

D&B$,$ a major hardware brand, works with a manufacturer in Taiwan for a particular model of its power tools $($Model S$24)$ for sale in Europe through their distribution center $($DC$)$ near Munich, Germany. Due to the variety of plug types across different regions in Europe, Model S$24$ is produced in $4$ variants with different plugs and transported using freight from Taiwan. Air freight charges $$20$ per item shipped and delivers in $1$ week regularly, thanks to fixed schedules.

The Taiwanese manufacturer operates with a make$-$to$-$order approach, charging $$100,000$ per production order plus $($$$10+$ V$)$ per item, and requiring a $2-$week lead time to prepare each order. Assume that D&B takes ownership of the orders as soon as they leave the manufacturer's facility.

Weekly demand for each variant has the following demand and Normal distributions:

Variant $1|$ Variant $2|$ Variant $3|$ Variant $4$

Mean $250($x $(10+$ V$))200($x $(10+$ V$))150($x $(10+$ V$))50($x $(10+$ V$))$

Standard Deviation V$/10$ V$/10$ V$/10$ V$/25$

For each variant, D&B uses a periodic review policy with $6$ weeks between orders and incurs a $30\%$ holding cost. Throughout, assume a CL of $91\%($Z $=1\mathrm{.}34),$ and $52$ weeks in a year.

$[20]$ Calculate the safety stock and the OUL to be used for each variant.

$[30]$ Under the current strategy, what is D&B$\text{'}$s total annual cost of Model S$24,$ including all variants?

D&B management is considering a postponement strategy where the produce design would be changed to make the power plug connector modular so that the plug base unit $($without the power plug$)$ can be sourced from the Taiwanese manufacturer and the power plug can be assembled at D&B$\text{'}$s own processing facility near Hamburg, Germany. Proximity of this facility to the channel ensured better overall ease of shipping from Taiwan $($instead of air freight$).$ Ocean shipping would cost only $$2$ per item but have a lead time of $7$ weeks on average with a $1-$week standard deviation.

The final assembly operation and additional transportation $($from the Hamburg facility to the DC$)$ in total would cost $$5$ per item, but the manufacturer's price would be negotiated down to $$210-$ V$.$ For the base unit inventories, D&B would use a continuous review policy and estimates a holding cost rate of $20\%.$ Assume that D&B will be able to negotiate to take ownership of these items only on delivery.

$[20]$ Calculate the safety stock, the ROP and the optimal order quantity to be used for the base unit.

$[30]$ Under the postponement strategy, what is D&B$\text{'}$s total annual cost of Model S$24?$ Does it make sense to implement this idea?