MSBA-204 Integer Linear Programming Assignment

Assignment Task

Case 1

Wall Street Associates, an investment firm on the Wall Street, specializes in currency trading. Benson Hughes is a manager in charge of Asian foreign investments. This entails investing in Asian currency markets – Japan, Indonesia, and Malaysia. Not too long ago, Japanese market had performed better than expected over the past year. Because of this, Benson had increased investments in Japan from $2.5 million to $15 million only a few weeks ago at the exchange rate of 80 yen/U.S. dollar. In addition to the investment in Japanese holdings, Wall Street Associates has cash holdings of 10.5 billion Indonesian rupiahs and 28 million Malaysian ringgits. The big news today on the Bloomberg channel talks about the Japanese economic collapse.

The collapse in the Japanese markets will drag the Indonesian and Malaysian financial markets down as well. Japanese yen has devalued from 80 yen/U.S. dollar to 125 yen/U.S. dollar. Benson has been advised by the president of the Wall Street Associates to get all the money out of Japan, Indonesia, and Malaysia into safe U.S. investment instruments. Benson realizes that while liquidating these investments, the loss while converting the foreign currency back into U.S. dollars would be significantly huge.

Transaction fees are charged by banking partners for converting one currency into another through wire transfers. If there is a huge outflow of foreign investments, then the nations’ economies can experience a complete economic collapse. To prevent this from happening, the governments of Japan, Indonesia, and Malaysia have imposed limits on how much money can be exchanged from the domestic currency into some foreign currency and withdraw it from the country. Benson’s objective is to determine the most cost-effective way to convert these foreign investments into U.S. dollars.

1. Formulate Benson’s problem as a minimum-cost flow problem. As a part of your solution, state which currency transactions should Benson perform to convert currencies from yen, rupiah, and ringgits into U.S. dollars to ensure that Wall Street Associates has the maximum dollar amount after all transaction costs have occurred. You also need to determine what the total minimized transaction cost is and how much money will Benson have to invest in the U.S.

2. Now, assume no transaction limits. Repeat part 1 above.

3. For this part, assume that the Indonesian government now imposes a 300% increase in transaction costs for transactions of rupiahs. Still assuming no transaction limits, repeat part 1 above.

Use R and not Excel. Please follow the submission requirement. Create the mathematical model if you find it useful to conceptualize the implementation. It won’t carry any credit, so no need to show me. I will look at the R code and run it for everybody so that I know that you created the solution and not just copied the answers.

Case 2 

A leading automobile company in the U.S. uses many large machines to work on building automobiles. These machines require frequent maintenance because of wear and tear, and the company finds that it is sometimes advantageous, from a cost standpoint, to replace machines rather than continue to maintain them. For one class of machines, the company has estimated the quarterly costs of maintenance, the salvage value from reselling an old machine, and the cost to purchase a new machine. Let us assume that the maintenance cost and the salvage value depend on the age of the current machine (at the beginning of the quarter). However, to keep the problem moderately simple, let us assume that the maintenance costs, the salvage values, and the purchase cost do not depend on time. In other words,

we assume no inflation. Specifically, we assume the following:

• The purchase cost of a new machine is always $3530.
• The maintenance cost of a machine in its first quarter of use is $100. For each succeeding quarter, the maintenance cost increases by $65. This reflects that machines require more maintenance as they age.
• The salvage value of a machine after one quarter of use is $1530. After each succeeding quarter of use, the salvage value decreases by $110.

The company would like to devise a strategy for purchasing machines over the next five years. As a matter of policy, the company never sells a machine that is less than one year old, and it never keeps a machine that is more than three years old. Also, the machine in use at the beginning of the current quarter is brand new. Use linear programming to find the optimal replacement strategy by modeling the problem as an equivalent shortest path problem. Hint: Formulate this problem like the Sarah problem we covered in the class under the topic of network models.

Please follow the submission requirements. Create the mathematical model if you find it useful to conceptualize the implementation. It won’t carry any credit, so no need to show me. Use R and not Excel. I will look at the R code and run it for everybody so that I know that you created the solution and not just copied the answers.

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