Problem $3$

Chaimae, a very innovative and smart entrepreneur, has recently made a business plan to introduce the Blue Diamond jewelry in the UAE. This brand of jewelry was introduced in $2018$ in several countries such as Switzerland, USA, and Japan, where this jewelry brand has quickly become a big success. Customers like this jewelry for its beautiful design, rich assortment, colors, good quality, and the price.

Chaimae has no doubt that her business will be a great success in the UAE. She has recently contracted retailers $($mostly in malls$)$ in different cities in the UAE that will add the Blue Diamond jewelries to their portfolio and sell it to customers. These retailers do not own the inventories of the Blue Diamond jewelries. Chaimae owns them and she will only get paid for the jewelries after the retailers sell them. The unit inventory holding cost to stock the Blue Diamond jewelries at the retailers is $10\%.$ The retailers are located in: Abu Dhabi, Ajman, Al Ain, Dubai, Fujairah, Ras Al Khaimah, and Al Ain. The Blue Diamond jewelries are produced at a small manufacturing site in Antwerp $($Belgium$)$ and in Hangzhou $($China$).$ Both manufacturing sites can supply the jewelries to the UAE and to not complicate the analysis, you can assume that the manufacturing costs at both manufacturing sites are equal. Given the high value and low volume ratio of jewelries, transportation from the manufacturing sites to the UAE occurs by airplane.

One of Blue Diamond's jewelries is the Khatem ring. The consumer price of this ring at the retailers will be $1,200$ AED. Chaimae will buy this type of ring at a cost of $450$ AED and will sell them to the retailers at a price of $900$ AED. Part of Chaimae's business plan was to estimate the demand for the Khatem ring in each city. The table below shows the expected annual demand for the Khatem ring in the different cities as well as the unit shipping cost that a logistics service provider would charge for shipping the products from DXB to the retailers.

$\backslash$table$[[$City$,\backslash$table$[[$Expected$],[$demand$]],\backslash$table$[[$Standard deviation of the$],[$demand$]],\backslash$table$[[$Unit shipping$],[$cost$]]],[$Abu Dhabi,$170,15,55$ AED$],[$Ajman$,25,3,15$ AED$],[$Al Ain,$76,8,52$ AED$],[$Dubai$,313,40,9$ AED$],[$Fujairah$,19,4,45$ AED$],[$Ras Al Khaimah,$42,6,35$ AED$],[$Sharjah$,105,12,$AED$]]$

The unit shipping cost of one Khatem ring from the Hangzhou factory is $230$ AED and $140$ AED from the factory in Belgium to the DXB $($Dubai International$)$ airport. The lead time from these factories to the DXB airport can be assumed to be $3$ days. The lead time from DXB airport to any of the retailers can be assumed to be $1$ day. Chaimae is not sure whether to ship the products directly from the manufacturers

to the retailers or whether to store them first in a small warehouse next to the DXB airport before shipping them to the retailers in the $7$ cities. Also, she is wondering whether transshipment would be a smart strategy to apply.

For this, Chaimae hired you as a team to give her advice based on a good analysis.

Questions:

a$.$ Assume a direct shipping strategy from the two factories of Blue Diamond to the UAE. What would be the $($minimum$)$ expected total annual transportation costs? Show your calculations.

b$.$ Chaimae wants to offer a $99\%$ customer service level for the Khatem ring at the level of the retailers. How much safety stock $($in units$)$ should all $7$ retailers keep to be able to offer this service level? Show your calculations.

c$.$ What is the total holding costs for these safety stocks? Show your calculations.

d$.$ Discuss three advantages of this direct shipping strategy for Chaimae's business.