2. Hamburg Power Company Hamburg Power Company, an electric utility is planning the expansion of its generating capacity

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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
(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?
(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?