Chaimae is wondering whether it is smart to rent a small, secured warehouse next to the DXB airport where the Blue Diamond's Khatem rings can be stored and from where the customers $($the retailers in the $7$ cities$)$ will be supplied. Chaimae found a suitable warehouse with sufficient space and the rent is $20,000$ AED per year. This cost includes the rent, insurance, and security cost. Under this distribution strategy, the Khatem rings will first be shipped to this warehouse where the rings will be kept in stock. Then, once an order is received, the rings will be shipped to the retailers. Since larger volumes will be shipped $($per shipment$)$ to the UAE, the unit shipping cost will drop by $10\%$ due to economies of scale.

e$.$ What would be the $($minimum$)$ expected total annual costs $($transportation $+$ safety stock costs$)$ if the warehouse is used as a traditional warehouse where the safety stocks are kept $($with the same target service level of $99\%)$ instead of at the retailers? Show your calculations.

f$.$ Discuss two main disadvantages of this distribution strategy for Chaimae's business.

g$.$ Which strategy would you recommend to Chaimae based on the total cost? Show your calculations.

Chaimae follows your recommendation under question $g.$ and applies the better performing distribution strategy. However, due to capacity constraints, the factories in Antwerp $($Belgium$)$ and Hangzhou $($China$)$ will only be able to produce the following maximum quantities, which are the maximum supply quantities.

objective function, and formulate the constraints.

i$.$ Solve the LP model that was introduced under question $h.$ What is the optimal solution? And what is the optimal value of the objective function?

Chaimae considers allowing transshipments $($inventory sharing between retailers$)$ between different retailers, especially between those that are close to each other. The table below shows between which two retailers transshipments will be allowed with the unit shipping cost between the two retailers.