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MSBA-204 mathematical formulation
创建日期：2024-08-24 17:55:26
所属分类：数学mathematics
标签： MSBA-204
mathematical formulation

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MSBA-204 Homework 


Submission Requirements:

1.   Please submit ONE PDF only (no Word documents and no multiple picture files.)

2.   Only Canvas submissions will be graded. Remember, you can resubmit as many times as you want up to the deadline. Your latest submission will be graded. After the deadline, you cannot resubmit. It is not a technical issue. It is Canvas’s feature.

3.   For the questions that require creation of the model, please write or type the mathematical formulation of the model. Please know that if you type on the computer, then please type proper symbols and neatly format (like shown in the example below.) If you don’t have the time to write the symbols, then handwrite and scan. It is OK to handwrite. Proper symbols means using ≤ instead of <= (just as an example.) Here is an example of neatly formatted mathematical formulation using correct symbols.

Maximize 0.3R + 0.5P

subject to 0.3R + 0.6P ≤ 18,000 (crude oil)

                    R + P ≤ 50,000 (production)

                           P ≤ 20,000 (demand)

                    R, P ≥ 0

R = Number of gallons of regular gasoline

P = Number of gallons of premium gasoline

4.   Please look at the notebook that I have shared to see the submission requirements. If your submission

doesn’t follow the suggested format, then it will be returned back with a zero grade. Your grade will change after you resubmit the assignment in the suggested format.

Topic: Integer Linear Programming

Problem Number 8 (Investment Net Present Value) on Page 325 of your text. Use only R. No Excel.

Mathematical model is needed and will carry credit. Submission requirement as stated on my notebook. (20 points)

Problem Number 10 (Local Police Substations) on Page 326. Use only R. No Excel. Mathematical model is needed and will carry credit. Submission requirement as stated on my notebook. (20 points)

Topic: Supply-Chain

Case 1 (90 points)

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.

The exchange rates are given in Table 1 below.


Table 1: Currency Exchange Rates

An example of how to read Table 1: 1 Japanese yen = 0.0064 euro. 1 Japanese yen = 0.008 U.S. dollar. The transaction costs as a percentage of the currency being converted are given in Table 2 below.


Table 2: Transaction Cost (%)

Please note that the transaction costs are symmetric, i.e., the transaction cost for exchanging Japanese yen to U.S. dollar is the same as that for exchanging U.S. dollar to Japanese yen.

Table 3 below provides the maximum amounts of domestic currencies (transaction limits) expressed as the current equivalent of thousands of dollars Wall Street Associates is allowed to convert into the Japanese yen, Indonesian rupiah, and Malaysian ringgits.


Table 3: Transaction Limits in Equivalent of 1,000 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 (90 points)

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 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. 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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