Optimizing Power Distribution: Scenarios and Constraints

1. Scenario A:No Power Plant Constraints - In this scenario, the assignment aims to find the optimal solution where there are no restrictions on the amount of power supplied. The task is to determine the cities supplied by each power plant while minimizing the total distribution cost.
2. Scenario B:Power Plant Constraints - In this scenario, the problem is expanded by introducing constraints that limit each power plant to supply at most 4,000 MW of power. The assignment seeks to identify the new optimal solution, calculate the total annual power distribution cost under these constraints, and quantify the annual increase in distribution cost compared to Scenario A.

Scenario A: No Power Plant Constraints

This involves optimizing the allocation of power from multiple plants to various cities, without any restrictions on power supply. The goal is to find the most cost-effective solution, minimizing the total annual power distribution cost, while ensuring that each city's demand is met efficiently.

Optimal Solution:

For this scenario, there are no restrictions on the amount of power that can be supplied by any of the power plants. The optimal solution, cities supplied by each power plant, and the total annual power distribution cost are as follows:

Optimal Solution:

Cities Supplied by Each Power Plant:

Total Annual Power Distribution Cost: The total annual power distribution cost for this solution is $2,552,382.81.

This solution optimally meets the demand in each city while minimizing the total distribution cost.

Scenario B: Power Plant Constraints

This scenario introduces a constraint where each power plant is limited to supplying a maximum of 4,000 MW. The objective is to find a new optimal solution under these constraints and calculate the total annual power distribution cost. Additionally, it quantifies the annual increase in distribution cost compared to Scenario 1, showcasing the impact of these limitations on cost-effectiveness.

Optimal Solution:

In this scenario, the constraint is introduced that at most 4,000 MW of power can be supplied by any one of the power plants. The optimal solution and the annual increase in power distribution cost resulting from these constraints are as follows:

Total Annual Power Distribution Cost with Constraints: The total annual power distribution cost with the new constraints is $2,652,949.22.

Annual Increase in Power Distribution Cost: The annual increase in power distribution cost is calculated as the difference between the total cost with constraints and the total cost without constraints.

Annual Increase = Total cost with constraints - Total cost without constraints

Annual Increase ≈ $100,566.41

Hence, the annual increase in power distribution cost resulting from adding the constraints (at most 4,000 MW per plant) to the original formulation is approximately $100,566.41.