Tamara MacEwen
IE 416
Page 403 Problem 6
By: Ms. Tamara MacEwen
Parisay’s comment in red.
A company must meet the following demands for cash at the beginning of each of the next six months; month 1, $200; month 2, $100; month 3, $50; month 4, $80; month 5, $160; month 6, $140. At the beginning of month 1, the company has $150 in cash and $200 worth of bond 1, $100 worth of bond 2, and $400 worth of bond 3. The company will have to sell some bonds to meet demands, but a penalty will be charged for any bonds sold before the end of month 6. The penalties for selling $1 worth of each bond are as shown in Table 63.
Table 63
Month of SaleBond / 1 / 2 / 3 / 4 / 5 / 6
1 / $0.21 / $0.19 / $0.17 / $0.13 / $0.09 / $0.05
2 / $0.50 / $0.50 / $0.50 / $0.33 / $0.00 / $0.00
3 / $1.00 / $1.00 / $1.00 / $1.00 / $1.00 / $0.00
a) Solve part(a) as a transportation problem using WinQSB (Network modeling > transportation).
Month 1 / Month 2 / Month 3 / Month 4 / Month 5 / Month 6 / Supply0 / 0 / 0 / 0 / 0 / 0
Cash 1 / 150
0.21 / 0.19 / 0.17 / 0.13 / 0.09 / 0.05
Bond 1 / 200
0.5 / 0.5 / 0.5 / 0.33 / 0 / 0
Bond 2 / 100
1 / 1 / 1 / 1 / 1 / 0
Bond 3 / 400
Demand / 200 / 100 / 50 / 80 / 160 / 140
Input:
Output:
b) Solve part b as a transshipment problem using WinQSB (Network modeling > Network Option).
Assume that payment of bills can be made after they are due, but a penalty of $0.05 per month is assessed for each dollar of cash demands that is postponed for one month. Assuming all bills must be paid by the end of month 6, develop a transshipment model that can be used to minimize the cost of paying the next six months’ bills.
Input:
Output:
Report to Manager:
The company’s financial problem was evaluated in two different ways.
In the first evaluation, the company’s demands were met in the month that they were due. In this manner, the company would have to pay $166.20 in penalties for cashing in bonds before they were due. We will fulfill the demand for month 1 by cash and bond 3, demand for month 2 by bond 1 and 3, demand for months 3 and 4 by bond 1, demand for month 5 by bond 1 and 2, and demand for month 6 by bond 3. At the end of the six months, the company still has $120 in bond 3 still available.
In the second evaluation, bill could be paid after they were due, but the company would assess a late fee. In this manner, the company would have to pay only $48 in fees. We will fulfill the demand for month 1 on time by cash and bond 1, demand for month 2 on time by bond 1. Bills would be paid late in the month of three. They will be paid in month 5 by bond 2. Bills would be paid late in the month four. They will be paid in months 5 and 6 by bonds 2 and 3. Bills would be paid one month late in the month five by bond 3. At the end of month 6, the company had $70 in Bond 3 (as C6 from Bond 3) and $50 in Bond 1.
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