The Massachusetts Electric Company is planning additions to its mix of nuclear and conventional…

 The Massachusetts Electric Company is planning additions to its mix of nuclear and conventional electric power plants to cover a ten-year horizon. It measures the output of plants in terms of equivalent conventional plants. Production of electricity must satisfy the state’s additional requirements over the planning horizon for guaranteed power (kW), peak power (kW), and annual energy (MWh). The state’s additional requirements, and the contribution of each type of plant to these requirements, are as follows:

The Massachusetts Electric Company is planning additions to its mix of nuclear and conventional...-1

The costs for each type of plant include fixed investment costs and variable operating costs per year. The conventional plants have very high operating costs, since they burn fossil fuel, while the nuclear plants have very high investment costs. These costs are as follows:

The Massachusetts Electric Company is planning additions to its mix of nuclear and conventional...-2

For simplicity, we will assume that the annual operating costs are an infinite stream discounted at a rate of(1/(1+r)) per year. The present value of this infinite stream of operating costs is:The Massachusetts Electric Company is planning additions to its mix of nuclear and conventional...-3

and the term 1/r is sometimes referred to as the coefficient of capitalization.

 a) Formulate a linear program to decide what mix of conventional and nuclear power plants to build, assuming that you must meet or exceed the state’s three requirements and you want to minimize the total investment plus discounted operating costs.

 b) There has been a debate at Massachusetts Electric as to what discount rate r to use in making this calculation. Some have argued for a low ‘‘social’’ rate of about 2 or 3 percent, while others have argued for the private ‘‘cost of capital’’ rate of from 10 to 15 percent. Graphically determine the optimal solution for all values of the discount rate r, to aid in settling this question. Comment on the implications of the choice of discount rate.

c) Another difficulty is that there may not be sufficient investment funds to make the decisions independently of an investment limitation. Assuming the ‘‘social’’ discount rate of 2 percent, find the optimal solution for all conceivable budget levels for total investment. What is the impact of limiting the budget for investment?

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