In the preceding, we considered making a single investment in a project for the duration of some term, and receiving its return at the end of the term. In practice, we may face a choice among projects that require investments of different amounts in each of several periods (with possibly different budgets available in each period), with the return being realized over the life of the project. In this case, we can still model the problem with variables
the objective is still to maximize the sum of the returns on the projects selected, and there is now a budget constraint for each period. For example, suppose we wish to invest $14,000, $12,000, and $15,000 in each month of the next quarter. We have identified four investment opportunities. Investment 1 requires an investment of $5,000, $8,000, and $2,000 in month 1, 2, and 3, respectivey, and has a present value (a time-discounted value) of $8,000; investment 2 requires $7,000 in month 1 and $10,000 in period 3, and has a value of $11,000; investment 3 requires $4,000 in period 2 and $6,000 in period 3, and has a value of $6,000; and investment 4 requires $3,000, $ 4,000, and $5,000 and has a value of $4,000. The corresponding integer program is
