$=$ YOUR STUDENT NUMBER $($e$.$g$.,$ S$01234512345)=$ SUM OF DIGITS OF YOUR STUDENT NUMBER $($e$.$g$.,$ S$0123451+2+3+4+5=15)$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 power outlets across different regions in Europe, Model S$24$ is produced in $4$ variants with different power plugs and transported using air 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 $$100,000$ per production order plus $$(+)$ 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.$$Weekly demand for each variant has the following independent and Normal distributions $($round up to integer$)$:$$Variant $1$Variant $2$Variant $3$Variant $4$Mean$\backslash$times $(+)\backslash$times $(+)\backslash$times $(+)\backslash$times $(+)$Standard Deviation$////$For each variant, D&B uses a periodic review policy with $6$ weeks between orders and incurs a $30\%$ holding cost. Throughout, assume a CSL of $96\%($zCSL $=1\mathrm{.}75),$ and $52$ weeks in a year.$1)[20]$ Calculate the safety stock and the OUL to be used for each variant.$2)[30]$ Under the current strategy, what is D&B$$s total annual cost of Model S$24,$ including all variants?$$D&B management is considering a postponement strategy where the produce design would be changed to make the power plug connector modular so that only the base unit $($without the power plug$)$ can be sourced from the Taiwanese manufacturer and the power plug can be assembled at D&B$$s own processing facility near Hamburg, Germany. Proximity of this facility to an established seaport will also enable D&B to use ocean shipping from Taiwan $($instead of air freight$).$ Ocean shipping would cost only $$2$ per item but have a lead time of $7$ weeks on average with a $1-$week standard deviation.$$The final assembly operation and additional transportation $($from the Hamburg facility to the DC$)$ in total would cost $$70$ per item, but the manufacturer$$s price would be negotiated down to $$().$ 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.$3)[20]$ Calculate the safety stock, the ROP and the optimal order quantity to be used for the base unit.$4)[30]$ Under the postponement strategy, what is D&B$$s total annual cost of Model S$24?$ Does it make sense to implement this idea?