AMPL Optimization Problem: To manage its excess cash over the next 12 months, a
ID: 2756863 • Letter: A
Question
AMPL Optimization Problem:
To manage its excess cash over the next 12 months, a company may purchase 1-month, 2-month or 3-month certificates of deposit from any of several different banks. The current cash on hand and amounts invested are known, while the company must estimate the cash receipts and expenditures for each month, and the returns on the different certificates.The company’s problem is to determine the best investment strategy, subject to cash requirements. (As a practical matter, the company would use the first month of the optimal solution as a guide to its current purchases, and then re-solve with updated estimates at the beginning of the next month.)
Suppose that the company’s estimated receipts and expenses (in thousands of dollars) over the next 12 months are as follows:
month
receipt
expense
1
3200
200
2
3600
200
3
3100
400
4
1000
800
5
1000
2100
6
1000
4500
7
1200
3300
8
1200
1800
9
1200
600
10
1500
200
11
1800
200
12
1900
200
The two banks competing for the business are estimating the following rates of return for the next
12 months
CIT:
1
2
3
NBD:
1
2
3
1
0.00433
0.01067
0.01988
1
0.00425
0.01067
0.02013
2
0.00437
0.01075
0.02
2
0.00429
0.01075
0.02025
3
0.00442
0.01083
0.02013
3
0.00433
0.01083
0.02063
4
0.00446
0.01092
0.02038
4
0.00437
0.01092
0.02088
5
0.0045
0.011
0.0205
5
0.00442
0.011
0.021
6
0.00458
0.01125
0.02088
6
0.0045
0.01125
0.02138
7
0.00467
0.01142
0.02113
7
0.00458
0.01142
0.02162
8
0.00487
0.01183
0.02187
8
0.00479
0.01183
0.02212
9
0.005
0.01217
0.02237
9
0.00492
0.01217
0.02262
10
0.005
0.01217
0.0225
10
0.00492
0.01217
0.02275
11
0.00492
0.01217
0.0225
11
0.00483
0.01233
0.02275
12
0.00483
0.01217
0.02275
12
0.00475
0.0125
0.02312
Formulate and AMPL MOD and DAT file for the presceding problem. Solve the resulting linear program.
Please tell me what I need to put in to a .MOD file and a .DAT file in AMPL. I already know how to do it algebrarically. Please do not answer if you don't know AMPL. Thank you!
month
receipt
expense
1
3200
200
2
3600
200
3
3100
400
4
1000
800
5
1000
2100
6
1000
4500
7
1200
3300
8
1200
1800
9
1200
600
10
1500
200
11
1800
200
12
1900
200
Explanation / Answer
CIT:
The best investment strategy, subject to cash requirements is NBD for 3-month certificates of deposit giving maximum return per year of $59.81.
Month receipt expensesCIT:
1 2 3 NBD: 1 2 3 a b Net Saving (a-b) Net Saving 1 3200 200 3000 12.99 32.01 59.64 3000 12.75 32.01 63.9 2 3600 200 3400 14.858 36.55 68 3400 14.586 36.55 76.5 3 3100 400 2700 11.934 29.241 54.351 2700 11.691 29.241 71.01 4 1000 800 200 0.892 2.184 4.076 200 0.874 2.184 5.76 5 1000 2100 -1100 -4.95 -12.1 -22.55 -1100 -4.862 -12.1 -23.1 6 1000 4500 -3500 -16.03 -39.375 -73.08 -3500 -15.75 -39.375 -74.83 7 1200 3300 -2100 -9.807 -23.982 -44.373 -2100 -9.618 -23.982 -45.402 8 1200 1800 -600 -2.922 -7.098 -13.122 -600 -2.874 -7.098 -13.272 9 1200 600 600 3 7.302 13.422 600 2.952 7.302 13.572 10 1500 200 1300 6.5 15.821 29.25 1300 6.396 15.821 29.575 11 1800 200 1600 7.872 19.472 36 1600 7.728 19.728 36.4 12 1900 200 1700 8.211 20.689 38.675 1700 8.075 21.25 39.304 Total 32.548 80.714 150.289 31.948 81.531 179.417 Return per year 32.548 40.357 50.0963 31.948 40.7655 59.8057