A company is considering opening warehouses in four cities: Ankara, Istanbul, Izmir, and Antalya. Each warehouse can ship 100 units per week, if it is opened. The weekly fixed cost of keeping each warehouse open is $500 for Ankara, $600 for Istanbul, $400 for Izmir, and $200 for Antalya. Region 1 of the country requires 80 units per week, region 2 requires 70 units per week, and region 3 requires 40 units per week. The costs (including production and shipping costs) of sending one unit from a warehouse to a region are shown in the following table. We want to meet weekly demands at minimum cost, subject to the preceding information. Then, we want to construct the constraints for the following restrictions: 1. At most two warehouses can be opened. 2. The Ankara and the Antalya warehouses cannot be opened at the same time. 3. Either the Antalya or the Istanbul warehouse must be opened, but not both. 4. If the Ankara warehouse is opened, then the Istanbul warehouse must be opened. Formulate an IP that can be used to minimize the weekly costs of meeting demand. Clearly define your decision variables and any parameter you introduce.
A company is considering opening warehouses in four cities: Ankara, Istanbul, Izmir, and Antalya. Each warehouse can ship 100 units per week, if it is opened. The weekly fixed cost of keeping each warehouse open is $500 for Ankara, $600 for Istanbul, $400 for Izmir, and $200 for Antalya. Region 1 of the country requires 80 units per week, region 2 requires 70
units per week, and region 3 requires 40 units per week. The costs (including production and shipping costs) of sending one unit from a warehouse to a region are shown in the following table.
We want to meet weekly demands at minimum cost, subject to the preceding information.
Then, we want to construct the constraints for the following restrictions:
1. At most two warehouses can be opened.
2. The Ankara and the Antalya warehouses cannot be opened at the same time.
3. Either the Antalya or the Istanbul warehouse must be opened, but not both.
4. If the Ankara warehouse is opened, then the Istanbul warehouse must be opened.
Formulate an IP that can be used to minimize the weekly costs of meeting demand. Clearly
define your decision variables and any parameter you introduce.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
