Question: The way to solving this problem is setting it up correctly in excel through excel solver. I need someone to set this up with the
The way to solving this problem is setting it up correctly in excel through excel solver. I need someone to set this up with the correct constraints through simplex LP modeling.
This would help me tremendously.
PLEASE DO NOT ANSWER THE QUESTION if you arent using excel and showing the formulas and work book. Thanks
This problem is a stylized/scaled down version of a typical real-world telecom provider.
A telecom company needs to build a set of cell towers to provide signal coverage for the inhabitants of a given city. A number of potential locations where the towers could be built have been identified. The towers have a fixed range, and due to budget constraints only a limited number of them can be built. Given these restrictions, the company wishes to provide coverage to the largest percentage of the population possible. To simplify the problem, the company has split the area it wishes to cover into a set of regions, each of which has a known population. The goal is then to choose which of the potential regions the company should build cell towers on in order to provide coverage to as many people as possible.
The table below shows which of the regions are covered when a tower is build in that region. Note "-" means the tower build cannot serve the region.
| Region 0 | Region 1 | Region 2 | Region 3 | Region 4 | Region 5 | |
|---|---|---|---|---|---|---|
| Region 0 | 1 | 1 | - | - | - | 1 |
| Region 1 | 1 | 1 | - | - | - | - |
| Region 2 | - | - | 1 | 1 | - | - |
| Region 3 | - | - | 1 | 1 | - | 1 |
| Region 4 | - | - | - | - | 1 | - |
| Region 5 | 1 | - | - | 1 | - | 1 |
The population at each region is stated in the following table.
| Region 0 | Region 1 | Region 2 | Region 3 | Region 4 | Region 5 | |
|---|---|---|---|---|---|---|
| Population | 523 | 690 | 420 | 1010 | 1200 | 850 |
The cost to build a cell tower at each location site is stated in the following table.
| Cost (millions of USD) | |
|---|---|
| Region 0 | 4.2 |
| Region 1 | 6.1 |
| Region 2 | 5.2 |
| Region 3 | 5.5 |
| Region 4 | 4.8 |
| Region 5 | 9.2 |
The allocated budget is $20,000,000
Hint: Objective is to maximize the population covered.
Hint 2: Model this problem as a set-covering problem. An additional constraint on the budget needs to be added to the model.
Difficulty Level: Easy
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