a nonprofit organization, aims to improve the kids' access to books by mobile libraries. CKV opens several culture centers in a city and at each culture center, there is a minivan used as mobile library. On a typical day, the mobile library leaves the culture center with several books, goes to one of the districts of the city, stays at the district all day long serving as a library for kids and turns back to its culture center at the end of the day. The other day, mobile library visits another district.
CKV wants to open a number of culture centers in İzmir, and all 30 districts of İzmir are candidates. In order to spend less time on traffic and provide a longer library (service) time to the kids, CKV wants to locate culture centers in such a way that, each district has a culture center within 75 km driving distance.
The list of districts and distance matrix are given in GAMS format. For CKV, cost of opening a culture center is same for all districts. Answer the following questions:
1) Formulate a mathematical model that will tell CKV how many culture centers should be opened and where they should be located.
a) (60 points) Report your solution (using a map can be very useful for understanding the solution)
b) (40 points) Is there any alternative solution with the same number of culture centers but at different locations? How do you add this constraint to your model? Report your alternative solution.
2) Bonus Question: (30 points). Can you suggest another approach to the problem of CKV? What additional data do you need? In what aspect your approach/solution is better? I need more help please write me (firstname.lastname@example.org)
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