For this semester, students are expected to implement the given heuristic for the Facility Location Problem within the scope of IE$343$ lecture. Problem definition is as follows:

SimitCo, a pastry company, aims to open a certain amount of bakery facilities around Istanbul. Company engineer has found several candidate locations for the facilities and pointed out customers, however, they hesitated to give this long$-$term decision by themselves. At this point, they have reached you to create a good$-$performing heuristic. After analyzing the situation, you've concluded that this is a Facility Location Problem. SimitCo has signed long$-$term contracts with each customer, so customer data is considered as deterministic. After evaluation of possible algorithms, you have concluded to use the following algorithm:

Code this algorithm and propose an improvement heuristic for the given algorithm by using the packages given. Follow the steps:

$1-$Clone the given repository by using Git

$2-$Code the algorithm by given classes and methods.

$3-$Push the project code to a private repository, share it with the course TA's Your repository must include several files, which are:

$1-$ReadMe.md file that explains the part that is written by you and has the answers for questions asked.

$2-$Exactly same files that is sent to you, if you need to add something for those files, you are expected to explain why you needed to add them and how did you implement.

Questions that you need to answer are:

$1-$Which type of Facility Location problem is this? Why?

$2-$How does the execution time change when problem size is increased? Report it by running the same algorithm for given problem sizes $($customer amount$-$candidate facility amount$-$k amount$)$:

$20-5-\frac{3}{40}-10-\frac{4}{60}-15-\frac{5}{80}-20-\frac{6}{100}-25-\frac{7}{150}-30-\frac{8}{200}-35-\frac{9}{250}-40-10$

$3-$How much improvement does your algorithm make compared to the initial algorithm?