Okay, so now it remains to do performance evaluation for our heuristic algorithm. So we may also generate a lot of random instances to test the performance. But because this is a case study, so why don't we just input the real data provided by the company to our heuristic algorithm to see what will be the outcome? So we still see that we will still do downsizing, okay? So we will still downsize one, two, three, four, five. We will downsize five facilities, but the five facilities chosen by our heuristic algorithm is somewhat different from the five facilities chosen by our optimal solution. That also tells us why there is a difference between the total cost, okay? So somehow this is telling us that our heuristic algorithm in this case does not find an optimal solution. Well, if that's the case, you may feel disappointed. Maybe you want to take a look at the optimality gap, okay? So if you use 104 ta, ta, ta, minus 98ta, ta, ta, divided by 98, then you're going to see that the difference is about 5.8%. So you don't know whether that's good or whether that's bad, but at least now you have a way to evaluate how good your heuristic is. In this particular case, because your heuristic is not so different from your current solution. so maybe this is a sign telling us that maybe there is a better way to do our heuristic, to refine our heuristic. We're not going to tell you what's that way, because that's not the most important thing in this particular lecture. What's important is that if you don't have optimization, if you don't have or if you don't have mathematical programming, then the only thing you may have is this heuristic solution. You don't know whether there exists a better one. Even if you invent other heuristic algorithms, you invent one, two, three, four, five, you invent it or you invent 100 different heuristic algorithms. You do something like 104, 103, 102, or even 98, 99. You don't know whether you are already close enough to an optimal solution. You may correctly evaluate how good your algorithm is only if you have an optimal solution or as we mentioned, if you have a lower bound of your optimal solution. That all relies on our mathematical programming, okay? So, I hope all in all in this particular lecture we gave you several things. So first we show you a real study, a real case, a real problem. And then we show you how we do the real modeling to solve this practical problem. I hope we showed you that by using mathematical programming, you may solve 7% or 8% of the total cost. That can be a lot. Or we demonstrate one heuristic algorithm and then try to convince you again that designing an algorithm is easy, but evaluating it is hard. Hopefully we have convinced you that mathematical programming has its value. Especially if you want to know whether you should feel comfortable to stop inventing a better heuristic. Probably now, we still want to put some efforts to improve our heuristic. But if you have a heuristic that can get 99 or something as your total cost, maybe you know it's time to stop, okay. So that's pretty much all I have for today. Hope you enjoyed it. Thank you and then see you next time.