Thirdly, let's take a look at the result of applying the model to the company. Pretty much what we want to do now is about performance evaluation. We have a mathematical model. We make it a computer model, of course, because this problem is somehow too complicated for Excel. We use some other computer commercial servers to deal with this problem. We still write a computer program using that kind of servers. We talked to a company to get some historical results. For the past months, we take the real schedule that is put by the managers, and then we also collect the related information about CSR, about required demands, and so on. About all those scheduling parameters, about the weights and the put off them into our model. We're going to compare the results of the original schedule created manually and the results of our integer programming model. Here we may observe several things. The first thing is that we are minimizing the weighted average of something. We may need to compare, for example, the objective values. Here we may see that after we run this program, the original schedule gets to the objective value which is 223,400. That's somewhat a number with no physical meaning because you do have the weight that is affecting the performance. But anyway, given the same weight, given the same setting, our formulation is going to reach this smaller objective value, which is about 120,000. Roughly we may see a 46 percent reduction. What does that mean? That means by considering all these aspects, our program, our model is roughly getting twice better than the original model, something like that. That's one thing. Unfortunately, if we only report these two managers, they probably cannot get it quite easily because this number is not money, is not hour, is not customer satisfaction, does not really mean anything physically, is a mathematical term. Maybe a better way is to look at, for example, the top priority objective, which is the indicator for efficiency. We want to look at the total shortage. Using their models, using the experienced managers, the total shortage is about 2,250. That's a huge number, but for our case is less than 500. Maybe you want to get a closer look at this. Roughly in each month, you have 22 workdays and for each day is from 09:00 AM-09:00 PM, roughly. We have roughly about 264 periods. With the original schedule roughly in each period in average, you have nine shortage. But now with us, you only have less than two shortage. Roughly you may take a look at the difference between the CSR shortage. You may also agree that our program seems to be a good program. Lastly, on the graph, we also present some mathematical thing if you are interested. You know, when we are solving integer programs, the solver gives you an optimal solution. If you run this program for several minutes, for example, three minutes, our program would stop and then return you an optimal solution. But even if you don't run that program for such a long time, you only run it for five seconds, 10 seconds, 20 seconds, the program is still able to give you some solution that is not optimal, but is actually close to optimal. If you give the program more time, it will gradually improve the solution. But even if you just give the program five seconds, 10 seconds, 15 seconds, you can still get a very good solution. This is just one month, while we are doing the project, we take about eight months and do the comparisons for each month. Basically, the results are satisfactory. Here we just present one month for your reference. We are very close to the end. That program or that model really can help us do good operational decisions. Every month, we know how to schedule CSRs. We are able to save a lot of time for the experienced managers. Previously, he or she needs one day now, only 3-5 minutes. That's good. But actually, the model can do better than that. Once we have this shift scheduling system, we are actually better in evaluating several other things. For example, we are better in evaluating how many CSRs we need. Previously, suppose we have 40 CSRS, maybe we feel that is not enough, sometimes we have shortage, so we may want to talk to the boss and ask him or her to hire a few more CSRs. But then people always would have a question. Do you hear lies our CSR is in the most efficient way? Probably not, because previously indeed you see that in the original model, the shortage is more than 2,000 but actually in the most efficient solution is less than 500. Indeed, with the model, we are partially utilizing CSRs, and then we will be more comfortable about evaluating how many CSRs do we need. Do we need more CSRs? This would be good if we are thinking about how to build our capacity. Also, there may be some situations where you want to change the shift setting or to change some policies. For example, maybe today the company wants to say that, "Okay, we're going to create some more shifts so that our workers may be more flexible to go to jobs." That may be good. Maybe the company is going to say that, "Okay, we're going to have some other situations. We may have some additional policies to protect our CSRs and so on." If you don't have a model all you can do is to try to execute these policies for one month, two months, three months and then see what's the impact on the CSR scheduling. But that's not a very good idea. The way for you to respond to regulation change, the way for you to respond to market change may be too slow and if the policy turns out to be bad, everybody is going to be complaining. This is going to be a chance for us to better utilize our model. Because with the model, actually you just input different things. The model is going to tell you what's going to happen in the most efficient way. We may evaluate the impact of the policy changes before we really do the execution. That's also beneficial. In short, being able to do better operational decisions, almost always help us to do better strategic decisions. The things here I listed are strategic decisions, which means they are long-term decisions. You cannot say today I have this policy tomorrow I have another one. That's not good. You cannot say today I hired three persons, tomorrow I fire two persons. That's also not good. Basically, if you want to do long-term planning, you somehow need to estimate the impact of long-term policy change that requires you to do good operational decisions for every day, for every month, so that you really understand how to deal with the policy changes. That's pretty much the end for today's lecture. Hopefully, this case-study helped you to get an idea or get a taste about how operations research may be applied to the practice. That's the end. Thank you.