Speaker 1:	I go to the website of the game. I'll go here and I click on this. This window comes up, it tells me for each order, I get $1,000 if I deliver it in one day and that $1,000 goes to zero, if I deliver it in three days or more. Between one day and three day, the $1,000 will linearly change. That means if I deliver it in two days, I will get only $500. Or I go here and I click on job arrivals, I download this data and I open it. I copy this data, and I will paste it here. I paint it that color. I go back here, and I go to completed jobs, plot completed jobs. Download, open, copy it, and paste it here, and paint it. Remove those additionals. Now I do have this table. My inputs are here, my outputs are here. In the first day, I have received two orders, but I have only completed one order. The other one, I may just have started it, or it may be very close to completion. We don't know, but I have not sent it out. Therefore, equal to two orders have come in. One of them has gone out, and therefore, one of those orders at the end of day one after 24 hours of day one, which in our life is one hour. After day one, I still have one unit inside my system. That one unit could have been just started or it could be very close to completion. We don't know, but it is still inside the system. In day two, I have what I had in day one, plus what has come in in day two minus what has gone out in day two. Therefore, inventory at the end of day two is still one. But this one is different than the previous one because previous one we have already completed it. This is another. I go here for day three, ending inventory of period two or day two plus incoming of day three minus outgoings of day three. There is one unit of inventory in my system. Day four, inventory at the end of the previous day, plus what has come in, minus what has gone out, and that's it. These are inventory in some of other days. For example, here, I have three units in inventory, and here are my inventories for all days. As you can see, at the end of each day, I have had some inventory. We may assume throughout that day, on average, we have had that much inventory. I'll go down here. First, I hide some of these points to make my work a little bit easier. Now I come here and compute some statistics. The first one is mean, I type equal to average. Average, and I go from row one to row 50, and the average of input was 3.06. Then I type equal to STD, standard deviation of the sample. That's standard deviation of this sample. Therefore, average was three, standard deviation is four. Coefficient of variations is defined as standard deviation divided by average, and that is 0.67 median. What is the number where 50% of observations are on one side and 50% on the other side. Median was three, max, I type max, mean, I can just copy this down. Now, we refer to one row below, so I go back over there, and instead of max, I type mean. Range is equal to max minus mean. Then I compute range divided by median. That is also an index of variability, like coefficient variations and standard deviation. Count. I know I have 50 observations, but sometimes in reality, when I'm dealing with data, I don't know how many units of data are there. The last one is confidence margin. In the statistic, we refer to mean as point estimate. We say, if we have 50 observations and we want to estimate the average of any other observation of the same size which comes exactly from this sample, then with 95% confidence, that average may move in what range? I type equal to confidence norm. The first item it asks me is Alpha. If I am talking about 95% confidence, Alpha is 5% or 0.05, or I can enter 5%. It says, What is your standard deviation? I click on it. What is your sample size and click on this? Then I get this number, which is about 0.6. What this 0.6 means is, if you were able to find another set from the same population, and if we have computed its average, that average with 95% confidence was between this number, minus this number, and plus this number. If I compute this one and I lock it minus this one and I lock it, and then I copy this down, and I change the minus to plus. If I go and collect another sample of size 50 of the same data, the average obviously will not be 3.06, but with 95% confidence, it will be between 2.49 and 3.63. I also place these two here for you. Take this one down. We can call it lower limit, and upper limit. 95% confidence. 95% confidence. I have these numbers. Now, all I need is to take these numbers to the right. Then I have computed the averages for everything. Inventory, output, and so on. My maximum inventory was nine in one day. Minimum was zero, average was 2.18. Before going further, I should explain a mistake I have made here. Please ignore my mistake in the rest of this recording. Do you remember I said, in order to compute lower control limit what I will do equal to average and I lock the average, minus 95% confidence margin, and then I locked it to make my job a little bit easier. Then I came down and copied it down, and then I went over there, and I changed the negative to positive. Therefore, I have lower control limit and upper control limit. The mistake I made was not here. It was not for this column. But if I decide to copy this to the right, because those two cells are referent, absolutely, then these numbers repeat themselves. Therefore, in order to fix that mistake, I will go here. I have locked row 57 and row 66, and that is correct. Those two should be locked. But I really don't need to lock C. I remove dollar sign from C and from C here, Enter. I come down here also, I will remove from here and from here. Now, if I copy this to the right, you see here, I have 2.49 and 3.65, but the numbers are different over here and over here. Here in these two columns, I do have the same thing over there. Indeed, I really even didn't need to lock anything. I could have just typed the formula twice. I could have written lower control limit is this one minus this one without locking anything. Then I come here and say, upper control limit is this one plus this one, and that's it. I can then copy to the right the same thing. What I did over there was I put a dollar in front of 57 and dollar in front of 66, which makes it still correct. Here, just a dollar in front of 57 and a dollar in front of 66. If I do it still, everything is correct. But if I had made a mistake and have put a dollar in front of both of them, then when I copy to the right, that is incorrect. This is correct, partial referencing is also correct. Thank you very much. You may watch the rest of the lecture. Could you tell me what is the flow time in this system? We said if flow time is under one day we collect all the $1,000. If it is more than one day, we do not get $1,000. If it is more than three days, we don't get anything. Can I estimate the flow time in this system? Yes, I know the Little's Law, which states R*T= I. Throughput times Flow Time is equal to input. Throughput, average output is 2.88, average input is 3.06. They are not exactly equal, but I can assume that the trhoughput is equal to output. Whenever input and output are not the same or not very close, we assume throughput is equal to output. This is my throughput R is equal to, that's my throughput, I is equal to average inventory is this one, and I know that T is equal to I divided by R, T is equal to I divided by R, and that is 0.76 days. If I want it in hour, it is equal to this and 24 hours per day because our factory here works 24 hours per day, and therefore T is equal to 80 hours. It is very close to 24 hours. We need to go to different stations and see what the situation is. Perhaps if there is a large waiting line over there, we need to think about buying machines. For example, if I go to station one, and if I look at waiting line, these are 60 kits. Each order contains 60 kits. Therefore, if I have 60 kits, that means I have one order. Not too much. One order is waiting. I'll go here. More than 240 are waiting there. That means about more than four orders, but we need to have a look on this station. Here we have gone up to two orders, but we're not fine. You need to be careful. You need to look at different stations. If you feel that inventory built up in front of a station is too high, then you need to think and buy machines for that station. In order to buy machines, you go here, and when game starts, you have a ready box over here. You click on that and you change, for example, the number of machines from 1-2. In this station, each machine is $90,000. If you sell it, you only get 10,000. You need to try to buy machines when they are needed. Not sooner, not later, but the damage of buying sooner is much less than the damage of buying late. Thank you for your attention.