Problem
The comptroller of a Corporation has $100 million of funds to invest. She has been instructed to invest the entire amount for one year in either stocks or bonds (but not both) and then to reinvest the entire fund in either stocks or bonds (but not both) for one year more. The objective is to maximize the expected monetary value of the fund at the end of the second year. The annual rates of return on these investments depend on the economic environment, as shown in the following table.
Rate of Return
Economic Environment Stocks Bonds
Growth 10% 5%
Recession -5% 7%
Depression -50% 15%
The probabilities of growth, recession, and depression for the first year are 0.7, 0.2, and 0.1 respectively. These probabilities remain the same for the second year. Construct the decision tree for this problem and then analyze the decision tree to identify the optimal policy.
The CFO for the Shelton Corporation has $1.2 million to allocate to the following budget requests from five departments:
Dept.1 Dept.2 Dept. 3 Dept. 4 Dept. 5
$450,000 $310,000 $275,000 $187,500 $135,000
Because the total budget requests exceed the available $2 million, not all the requests can be satisfied. Suppose the CFO considers the requests for departments 2 and 3 to be twice as important as those from departments 4 and 5, and the request from department 1 to be twice as important as those from departments 2 and 3. Further suppose the CFO wants to make sure each department receives at least 70% of the requested amount.
I. Formulate and solve a GP model for this problem.
II. Suppose the CFO regards all deviations from the original budget amounts (including the $1.2 million available) to be equally undesirable. What solution minimizes the maximum percentage deviation from the budgeted amounts?