Then let's see another example which is facility location. In the previous videos, this problem professor has formulated before, and it is where we're going to choose to build distribution center among these five locations. After building it, it will ship books to different regions. According to the previous videos, we have set the parameters and the decision variables. The parameters including weekly operating cost, shipping cost, capacity, and the book demand. The decision variables including whether a distribution center should build at this location or the number of books shipped need to be determined. The formulation of this example can be the following. We are going to minimize the total operating cost plus the total shipping cost. The constraint is each distribution has their own capacity, and each region has their demand, and the construction should be zero or one. We should only chose to build it or not build it. Here, the last one is that the number of books we ship should be non-negative. After this, we can use Solver to solve it, find an optimal solution. Let's switch to Excel. Here, you can see that we already filled in our input parameters, and here is the description of our constraint. Our objective value is the orange box, which is the operating cost total plus the total shipping cost. We use the sum product function to multiply and sum them together. The first constraint is that the throughput in each center shouldn't be greater than the capacity. Here, we should fill in the total throughput in each center and so on. Each center will be one constraint cell. The second constraint is that the supply in each market shouldn't be less than the demand. Here, the second constraint cell we should fill in the sum of the supply in each market, which shouldn't be less than the demand. The green box is our decision variables. After filling these functions and input the variables, we can start using Solver to solve it. Here, we set objective cell, and we want to minimize our total cost. Here, we should check min, and here, we will drag and point our decision variable cells. Our subject is the following. This constraint is that a construction should only be zero or one, so it should be binary. This one is that the supply in each market shouldn't be less than the demand. Other constraint is that the throughput in each center shouldn't be greater than the capacity. After setting these constraints, we should check, make unconstrained variables non-negative. Then here, the solving method, we should choose evolutionary since we are going to solve it by integer programming. After setting this, we can click "Solve." I'm waiting for a few minutes. Since we [inaudible] a lot of constraints, so it still takes much more time to solve it. You can see that here, the subproblem is increasing. Let's wait for a few minutes. Excel has found the solution, let's see. These constraints are satisfied, and the constraint 2 satisfies too. Here, there's a very small number, we can just see it as zero. Let's go back to our presentation. An optimal solution of this integer programming is obtained by Excel Solver and you can see that we are going to build distribution center at location 2, location 4, and location 5. These are the number of books we are going to ship. Let's put this optimal solution into a map. In this map, you can see that for the Northwest region, there's only Reno distribution, will ship 8,000 books to Northwest region. For the Middlewest region, there will be two distribution centers will ship the books to them, which will be Harrisburg will ship 8,000 books to them, and Jacksonville sends 1,000 books to them. This is our integer programming using Excel Solver to solve it. Thank you.
