GlobalExchange

GlobalExchange is a global company that operates in Europe, South America, North America, and Asia. Due to the nature of the company's operations, at the end of each month, the firm needs to transfer money to cover its cash requirements, maybe to pay its employees, pay its suppliers in different countries or balance its accounts. For this month, the company ended up with five currency requirements: USD, GBP, EUR, CNY, and BRL.

The cash requirements in millions of monetary units can be found in the table below:

Symbol	Currency	Total Available	Requirements	Max Surplus	Balance
BRL	Brazilian Real	8.5	1.3	6	7.2
CNY	Chinese Yuan Renminbi	23.5	3	15.5	20.5
EUR	Euro	6.8	0.7	30	6.1
GBP	Pound	0	2.1	10.5	-2.1
USD	US Dollar	0	5	200	-5

For example, in order to satisfy the requirement of 2.1 million Pounds, GlobalExchange could use one of the currencies in which it has a surplus, namely BRL, CNY, or EUR. More than that, it could choose to exchange between any of the currencies to then satisfy the requirements.

To do this transfer, the company works with a bank. The currency exchange rates offered by the bank GlobalExchange works are given below:

Symbol	USD	GBP	EUR	CNY	BRL
USD	1	1.23561	1.08251	0.147429	0.192022
GBP	0.809242	1	0.876083	0.119322	0.155225
EUR	0.923776	1.14149	1	0.136199	0.177097
CNY	6.78293	8.38067	7.34219	1	1.30038
BRL	5.20774	6.43826	5.64662	0.769005	1

For each operation, the bank charges two fees: one "national" (based on the base currency) and one "international" (based on the pair being traded). On the other hand, depending on the amount being traded, the bank gives a discount over the international fee. For example, for the Brazilian Real the bank offers the following fee table:

From	To	Tier ID	Exchange Rate	National Fee	Tier Start	Tier End	International Fee
BRL	CNY	1	1.30038	0.014	0	4	0.012
BRL	CNY	2	1.30038	0.014	4	750	0.007
BRL	EUR	1	0.177097	0.014	0	4	0.02
BRL	EUR	2	0.177097	0.014	4	750	0.015
BRL	GBP	1	0.155225	0.014	0	4	0.025
BRL	GBP	2	0.155225	0.014	4	750	0.02
BRL	USD	1	0.192022	0.014	0	4	0.018
BRL	USD	2	0.192022	0.014	4	750	0.013

So, if GlobalExchange decided to exchange 2 Million BRL for CNY it would receive

$$2 \cdot 1.30038 \cdot (1-0.014 - 0.012) = 2.533 \text{Million CNY}.$$

On the other hand, if it chooses to exchange 4 Million BRL for CNY it would receive

$$4 \cdot 1.30038 \cdot (1-0.014 - 0.007) = 5.0922 \text{Million CNY}$$

How can GlobalExchange satisfy the requirements for the next month minimizing the amount paid in fees?

Formulation

See our proposed formulation in the global_exchange_formulation.ipynb Jupyter Notebook.

Additional Complexities

The real scenario can have numerous complexities that can be added to the model as additional rules.

• What if the company works with 20 currencies instead of 5?
• The company could use different banks instead of only one, and choose to trade different pairs between different banks.