EPA’s constructions grant program. Currently the U.S Environmental Protection Agency funds community water quality improvement project via a priority-ranking scheme using what has been termed “The Funding Line Approach.” In this approach each project is assigned a dimensionless priority number based on the water quality improvement it archiver Project with higher priority number are considered better than lower priority number project. A cost to fund is associated with each project, and a total amount of money is available for all the projects chosen in a particular funding cycle. The procedure of funding is to take the first-, second-, third-, and so on proiority projects in order. adding their costs as they are placed on the list. until the sum of costs of the projects chosen exceeds the amount of the budget. Then the LlsI project added is removed from the list. and the reuuuning projects from the top of the priority list down to the funding line are those chosen for funding in that cycle.
This procedure Inay not yield the most cost. effective collection of projects. Probably you could increase the total priority points achieved within the budget limit by taking the individual project cost into account in the choice of which project to choose next for the list. Construct a method that does this,that maximizes priority points achieved subject to a budget Limit. You will need the following parameters:
II = number of projects.
Cj = cost of the jth project:
Pi = priority points associated with the jth project;
B = budget available for this funding cycle: and
n = number of projects.
Your method should consist first of a zero-one programming formulation and second of a procedure to solve that formulation. Describe the procedure hriefly.
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