Hoosier Power needs to determine a capacity expansion plan to meet Bloomington’s power needs for the next 20 years. The current capacity is 5,000 kWh. The demand for the current year is 4,000 kWh, and demand is expected to increase by 1,000 kWh in each succeeding year. At the beginning of each year, Hoosier Power must determine the amount of capacity to add, given the following inputs: Any year in which capacity is added, a fixed cost of $120,000 is incurred plus a cost of $120 per kWh of capacity; At most 10,000 kwh of capacity can be added in a single year; It costs $24 per year to maintain a unit of capacity; It costs $12 per year to produce one kWh;

Practical Management Science
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ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
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Hoosier Power needs to determine a capacity expansion plan to meet Bloomington’s power needs for the next 20 years. The current capacity is 5,000 kWh. The demand for the current year is 4,000 kWh, and demand is expected to increase by 1,000 kWh in each succeeding year. At the beginning of each year, Hoosier Power must determine the amount of capacity to add, given the following inputs:

  • Any year in which capacity is added, a fixed cost of $120,000 is incurred plus a cost of $120 per kWh of capacity;
  • At most 10,000 kwh of capacity can be added in a single year;
  • It costs $24 per year to maintain a unit of capacity;
  • It costs $12 per year to produce one kWh;
  • If production does not meet demand, a shortage cost of $75 per kWh short is incurred.

Hoosier Power wants to determine a capacity expansion plan with the minimal total cost to meet Bloomington’s power needs for the next 20 years.

  1. Define the decision variables and write down the detailed mathematical formulation of Hoosier Power’s optimization problem.   

b. Solve the optimization problem by Excel Solver. Write down the optimal capacity expansion plan and total cost for the next 20 years.

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