2. Hamburg Power Company

Hamburg Power Company, an electric utility is planning the expansion of its generating capacity for the next five years. Its current capacity is 800 Megawatts (MW), and forecasts of future total demand (capacity needed) for each of the next five years are:

Year

1 2 3 4 5

Total Capacity Needed (MW) 880 960 1050 1160 1280

The utility can increase its generating capacity by installing 10-, 50- or 100- MW generators. The cost of installing a generator depends on its size and the year it is brought online. A generator brought online in a particular year is available to satisfy demand in that year and each subsequent year. Any number of generators of any type can be added in any year. The costs

(in $1,000s) of bringing the

Year 1 Year 2 Year 3 Year 4 Year 5

different generators online in each year are:

Costs (in $1,000s) 10-MW 50-MW 100-MW

$300 $1211 $250 $1158 $208 $965 $173 $887 $145 $722

$1950 $1791 $1659 $1549 $1458 

1. (10 points) Formulate an integer (linear) decision model that minimizes the cost of bringing generators online while satisfying the capacity requirements. What is the optimal plan to expand capacity? What is the total cost?

2. (5 points) Assume now that at most one generator of each type can be brought online in any one year. What is the cost of satisfying the capacity requirements now? How has the optimal plan changed?