Turkish Ministry of Health supports fast vaccination against the Covid-19 pandemic throughout the country. Authorities are planning to make a new arrangement in cities, and as a start, they decided to test this arrangement in a pilot area. Weekly Covid-19 vaccine demands are calculated. The individuals living in close regions are consolidated, and in total 15 demand points are determined. The demand volume of these demand points are given in Table 1.
Table 1. Weekly demand volume (units) of the demand points
| Demand Point | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| Demand Volume | 475 | 375 | 150 | 200 | 300 | 100 | 50 | 100 | 300 | 275 | 175 | 250 | 600 | 375 | 400 |
The logistics department has determined four alternatives for the locations of the new health centers. The estimated weekly operating costs of health centers A, B, C, and D are 1250, 1400, 1600, and 1300 ₺, respectively. The health centers will be capable of satisfying at most 2500 units weekly. The distances between the potential health centers and the demand points are given in Table 2. Each demand point should be assigned to one health center, since partial fulfillment of vaccines is not available.
For the distribution of the vaccines, the logistics department will use trucks with a variable cost of 5 ₺/km. The average speed of the trucks is 30 km/hr and each truck can work for at most 8 hours a week. For simplicity, assume that the trucks make direct shipments (i.e., each time the truck leaves the health center, it transports only one demand point’s demand, and returns back to the health center for reloading), and ignore loading/unloading duration of the trucks. The weekly operating cost of each truck is 40 ₺, 45₺, 50 ₺, and 45 ₺, respectively.
In the first part of the project, you are required to determine which health centers to open, which demand points to assign to which health center and how many trucks to use in each health center.
Write a formal report including the problem definition, your mathematical model in details, and your optimal solution. You may not get any credit if you do not describe your variables, parameters and constraints clearly..
Table 2. Distance (km) between potential health centers and demand points
| Demand Point | ||||||||||||||||
| Potential Health Center | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |
| A | 14.4 | 21.6 | 50.4 | 86.4 | 79.2 | 50.4 | 14.4 | 28.8 | 57.6 | 100.8 | 136.8 | 100.8 | 72 | 72 | 108 | |
| B | 72 | 64.8 | 50.4 | 14.4 | 21.6 | 21.6 | 57.6 | 100.8 | 57.6 | 43.2 | 79.2 | 86.4 | 86.4 | 144 | 136.8 | |
| C | 122.4 | 115.2 | 100.8 | 79.2 | 72 | 57.6 | 93.6 | 93.6 | 50.4 | 21.6 | 28.8 | 21.6 | 36 | 93.6 | 72 | |
| D | 72 | 64.8 | 50.4 | 86.4 | 79.2 | 50.4 | 43.2 | 43.2 | 14.4 | 43.2 | 79.2 | 43.2 | 14.4 | 72 | 64.8 | |
