Posted: February 4th, 2016

Formulate a mathematical programming model to determine the least costly way of expanding the companyâ??s generating assets to the minimum required levels.

I’ve been trying to figure out this Managerial Decision Making problem. Please help me out. Thank you!

A power company is considering how to increase its generating capacity to meet expected demand in its growing service area. Currently, the company has 750 megawatts (MW) of generating capacity but projects it will need the following minimum generating capacities in each of the next five years:

Year
_________________________________
1 2 3 4 5
______________________________________________________
Minimum Capacity 780 860 950 1,060 1,180
In Megawatts (MW)

The company can increase its generating capacity by purchasing four different types of generators: 10 MW, 25 MW, 50 MW, and/or 100 MW. The cost of acquiring and installing each of the four types of generators in each of the next five years is summarized in the following table:

Cost of Generators (in $1,000s) in Year
_____________________________________________

Generator Size 1 2 3 4 5 _______________________________________________________________

10 MW $300 $250 $200 $170 $145

25 MW $460 $375 $350 $280 $235

50 MW $670 $558 $465 $380 $320

100 MW $950 $790 $670 $550 $460

a. Formulate a mathematical programming model to determine the least costly way of expanding the companyâ??s generating assets to the minimum required levels.
b. Implement your model in a spreadsheet and solve it.
c. What is the optimal solution?