Lastly, let's take a look at if you are still interested in Operations Research and if you want to take our course two or course three, what do we have in our next course and why do we need them? We already know how to formulate a problem into mathematical programs. That's very good. Once we formulate a problem into a mathematical program, we may use, for example, Excel Solver to solve the problem and then really generate solutions. If that's the case, then what's the point of taking future courses? Sometimes this is not enough. For example, even if we are just using Excel Solver, we also know that there are still some parameters we may try to set to tune the performance of this solver, and that's still possible. If you have no idea about how it works, you will have no idea about how to tune the parameters to get satisfactory performance. Maybe you sometimes want to deal with problems that a solver cannot solve. That's possible. For example, maybe unfortunately, in your company there is a nonlinear integer program. If that's the case, solvers cannot help you. Sometimes you want to solve a specific problem, your problem can be solved by a solver, but it's so special. There should be something you may customize the solver to do and to do your program to make it faster, to make the solution even better, that's possible. If you have no idea about how solvers solve a problem, then again, you don't know how to do customization. Then lastly, maybe even we want to build our own solvers, this is rare, only if you go to some solution vendor company that produce or that develop solvers, that may happen. If you are really interested in Operations Research, interested in all of these, maybe you want to go to a Solver company. If that's the case, then of course you need to know a lot of underlying ideas. That's why we need to study algorithms, which is the main focus of our next course. The next course is Operations Research II, which focus on algorithms. What is algorithm? An algorithm is a systematic way to solve a problem. Whatever problem you give me, I'm going to solve it. You give me linear problem, I solve it, you give me integer problem, I solve it, something like that. We're going to tell you how to solve large-scale linear, integer, nonlinear problems. Keywords are simplex method, branch-and-bound algorithm, gradient descent, Newton's methods. We will give brief introduction about how these algorithm works, when it works, when it does not work, and tell you how close the underlying principle about these algorithms, give you examples to let you know how it goes through each steps. Hopefully eventually you can get some ideas about these algorithms so that if you need to tune the parameters, so that if you need to customize these algorithms, you are able to do it. Even if you just don't want to do it, maybe you are just curious. You have these programs. The program is less complicated. Solvers can solve it. Why? Maybe you just want to understand why, how it may be solved. Then the next course will also help you. The next course also do something that is beyond algorithms. We will give you a more powerful solver, Gurobi, I mean give you introduction, that will give you the solver. When we want to solve really complicated problems, Excel is limited because Excel is not designed to do optimization. If you are really running a company, you don't use Excel. You may, for example, write Python, write C++, write Java, to invoke this optimization library Gurobi to solve problems. In the next course, we will require you or we will expect you to do some simple computer programming. You need to have that ability so that you may import Gurobi into your program and then really solve complicated problems. Although that takes some time, but that would be very interesting. Then we will see another case study about how I apply operations research to help a company to solve another real problem. There, we will see the problem is solved by a solver to get an optimal solution, but we also develop our own algorithm and compare the performance with these two things and help the company to determine whether they should use the solver or whether they should use the customized algorithm. Both are having some pros and cons. A company needs to make this decision and we will present the whole study process to you to help you know more about algorithms and know more about the real applications of operations research. That's the plan for the next course. That's all I have for the whole course. That's the end of these six weeks. Hopefully we may see you again in the next course. Thank you.
