Ardavan Asef-Vaziri:	Today, I will explain some basic concepts of the Little's Law and process flow analysis in the context of the little field technologies game. You can assume that this talk is 50% to help you in the game and 50% to help you in understanding the basic concepts of Little's law and process flow analysis. Fifty percent to perform better in the game and 50% to perform better in the tests. In process flow analysis, we have the concept of flow unit. Flow unit in the game is a contract. We have the concept of resource unit. Resource unit in the game is a machine, and we have the concept of resource pool. Resource pool in the game is a station. In process flow analysis, we have minimal flow time or theoretical flow time. This is the minimal time required to produce a product. This is a time the flow unit spend all with the processors. All the time is value adding time, no time in the waiting line. We cannot go below this time. We refer to theoretical flow time as ThT. Then we have minimal inventory or pipeline inventory to refer to it as Ip, that is the minimum inventory we require to produce a product in the theoretical flow time. That is the absolute minimal inventory we need. In the context of the game, we can refer to it as Min-WIP. Then we have Max-WIP. We cannot go beyond that Max-WIP because if we go beyond that maximum WIP, given our capacity, we cannot meet the float. Throughout the game, we need to make sure that our WIP, we'll stay below maximum WIP, but not much below because if it stays much below Max-WIP, we will lose production. We refer to the time in the waiting line as Ti to the time with the processors as Tp. We refer to the number of flow units in the waiting line as Ii and the number of flow unit with the processors as Ip. This is the interface of the game because we always have the data for the first 50 days, we can compute these numbers. Average utilization in each station. Where is the bottle neck? The bottle neck is the station with maximal utilization. Station 2 is the bottle neck. Station 1 is the next bottle neck. Station 3 is the most relaxed station, the least utilization. Suppose throughput is 5.5, compute capacity of each machine. We know that utilization is equal to throughput, divided by capacity, and therefore, capacity is equal to throughput, divided by utilization. We have throughput divided by utilization, divided by utilization, divided by utilization. Throughput, utilization, capacity, capacity per watt, capacity per day, because this is per day. Compute Tp unit load, and the time that each machine spends on a product, Rp is equal to C, number of machines divided by Tp. We have Rp, and we have the number of machines. We can easily compute Tp in terms of day. If you want to compute it in terms of hours, you just multiply these by 24 and you get Tp in hours. Now we have more data, we have more knowledge about the game about this game with these numbers, compute capacity of the system, a chain is as strong as its weakest link, capacity of the system now is six. If you want to increase it, the next bottle neck is here, you need to add to the capacity of this one. We have 8, 6, and 10. If you want to increase the capacity, you can make this 12. Now the bottle neck is eight. If you increase the capacity of that 16, now the capacity is 10. If you increase the capacity, this one to 20, now capacity is 12. You can do some computations and increase the capacity of your system based on the demand that you have. Compute theoretical flow time, theoretical flow time is the minimal time that the flow unit should spend inside the system that is this time only with the processors that is the pure value adding time. We cannot go below that. As we saw, it is summation of these three, 9.4 hours or about 0.4 days. Theoretical flow time does not depend on the number of machines and it does not depend on the throughput. It purely depends on the capacity of machines and the routing that the product should go through as long as there is no change in the capacity of the machine and the routing of operations, theoretical flow time is always 9.4 hours or 0.4 days. This is the absolute minimal flow time, and flow time is usually much larger than theoretical flow time. Pipeline inventory is the minimal inventory that we need to produce the product. We can compute pipeline inventory using the little saw throughput was 5.5, flow time or theoretical flow time was 9.4 hours. RT is equal to I, R is 5.5. T is 9.4, but this is hours, this is day. Either we should divide 5.5 by 24 to make it in terms of or divide this one by 24 to make it in days, 5.5*9.4/24, that is a equal to Ip or pipeline inventory, 2.15. Compute pipeline inventor using utilization. We have utilization of three stations. Let's see what this 0.55 means. It means we have a resource unit, 55% of time, it is with one flow unit and 45% of time with zero flow units. On average, it is with 0.55 flow units and the same for all other resources. They are with this much, plus this much, plus this much contract flow units. If we add those numbers, we get the same 2.15. This part of my talk is especially useful in the game. It gives us a better understanding of the Little's law. It is very useful if we learn it and implement it in the game. Suppose we are in a situation where WIP is equal to 19.2, our throughput is 5.5. Therefore, flow time under the current situation is 3.5. Suppose we are on a contract to deliver in three days. After three days, our revenue per contract will reduce from 800-0 in two days. If we deliver before three days, we earn 800. If we deliver it after five days, we earn zero. Under the current situation, because we are delivering it in 3.5 days, and it goes from 800-0 after five days here at 3.5 would be 3.5-3/5-3*800. That is what we lose. If we subtract it from 800, that is what we earn. Because we are spending $600 on raw material, if we are delivering in 3.5 days, we indeed gain 600-600, which is equal to $0. We need not to allow our WIP to go to this lab. We use our capacity as a surrogate for throughput, and we use Max-WIP as a surrogate for WIP. We want WIP divided by throughput, which is equal to flow time to be less than or equal to 3. Now, instead of WIP, we use its surrogate, which is Max-WIP. Instead of true put, we use its circuit, which is capacity, and we set this to be less than or equal to three, and by this equation, we try to regulate this equation. Capacity times flow time, equal to 6, which is capacity, flow time, which is 3=18, and our Max-WIP should be 18 to ensure delivering in three days. We want our max-WIP to be equal to 18 to make sure that WIP is less than 18. Then through put times flow time is less than per equal to 18. WIP is usually less than 18, and therefore R*T<18, and this R by itself is smaller than Rp. This is to make sure that T stays under three days, but at the same time, we need to be careful not to fill down from the other side of the room. Suppose our current Max-WIP is 100 and we have computed or max-WIP is 18. Should I go and change 100 to 18? Not immediately. Because in this situation, we knew that 19.2 was our WIP. But maybe we are in another situation and Max-WIP is 100 and we have computed that our Max-WIP should be 18. Should I go and switch 100 to 18 immediately? No, I should go and look at WIP. Here we are discussing about delivering in one day. In the previous instance, when I talked about 19.2 WIP, in this example, we were talking about three days delivery. That is why our Max-WIP came out 18. Then when I was trying to explain the situation, I use this example when we are going to deliver in one day and maximum of three days. In the previous one, our contract value was 800 here. It is 1,200 per contract because we need to deliver it soon. Here, I click on this. I need to deliver the contract in one day and I earn 1,200. After three days, I earn zero and the current max WIP is 100 capacity, capacity of the process is equal to 6 so 6*1=6. Max-WIP, should be equal to 6, but now it is 100. Should I go and immediately change? I need to look around first. I click on "Job arrivals". Here is six. I see in most situations, arrival was under six. In one period, it has gone above six, but then it has come down. I have computed six period moving average here, and I see it as still below. You may compute 2, 3, 4, 5 period, whatever you like. I chose six period, and my intention is if six period moving average goes above this, then I switch 100-6. As long as it's below six, I will stay with my current Max-WIP. But they also need to look at other places, completed jobs. I click on "Job counts", and I see I'm still around capacity. Then I click on "Lead time". This is one day lead time. In 2, 3 days, my lead time was more than one day, but in other days I'm well below one day and six period moving average is still below one day. I also look into the revenue and I see, here I have lost some revenue, here I have lost some revenue instead of 1,200 here, for example, 900, but in general, the situation looks good. I also look at my WIP and I see if this is six, my WIP is below six. In two days, I have gone, but I'm still below six, so I do not change 100-6. I wait until this curve goes around six or maybe for one or two period above six, and if it stays above six, then I go and change 100-6. Until then, I will stay with 100. Let me tell you why. Suppose you are expected to get five contract per day, if you set Max-WIP to six, you are fine. Five contracts per day are coming, but suppose in one day you have 15 contracts, and in the next two days, you have zero so because you have set your Max-WIP to six, when 15 contract comes in, you do not let it to come. You only let five or six of them. If Max-WIP is six, you allow six at most to come in, so six comes in, but for next two days, you have zero and zero Therefore, the average incoming contracts are two per day, and this is much below your capacity. You lose Triple due to variability because not exactly five or 5.5 contracts come in per day. They come in with variability because you have kept your ceiling low, you lose some contract in days when the demand is high, and for the days when the demand is low or is zero, you cannot do that is the logic behind it. Do not make any change if WIP is less than Max-WIP of six, have a close look at your WIP. Make sure you are not falling down from two sides of the roof. If you exceed Max-WIP, if you are more than six, your T will go above one, and if your WIP, is quite less than six, then your throughput will be much less than six and you lose revenue by not producing enough product. Here is not by collecting all price, here through not producing enough product. We will have a look on WIP. When it gets close to six, we will set our Max-WIP from 100-6. In the example that I showed, I computed six period moving average, and when six period moving average past six, then I switch. You may compute one period, two period, three period, four period moving average, the one that you like and then if it exceeds the Max-WIP that you have computed, you can switch the current Max-WIP with the max-WIP that you have computed and is less than the current Max-WIP. Also, don't forget producing six units and losing $50 per contract. We'll earn you 3,300, which is better than producing five unit and collecting the whole money, which is 3,000. 3,300 is better than 3,000. Now suppose you have more than one machine, you have three machines in Station 1, three in Station 2, and two in Station 3, where is the bottle neck? Obviously, bottle neck is here without computing capacity because utilization is higher than any other station. Suppose throughput is 16. Capacity of stations just Rp=R/U, and we compute it for all stations. Twenty-four, 18, and 20. What is capacity of each machine? We divide 18/3, which is 6, 24/3 which is 8, and 20/2, which is 10, is capacity of each machine. Capacity is 10. We have 1/10=Tp, 1/10 day, if you want to make it in hours, we multiply it by 24. As I explained before, theoretical flow time does not depend on the throughput, and it does not depend on the number of machines. Does not depend on throughput and does not depend on number of machine. It does depend on capacity of each single machine, and we assume capacity of all machines are equal to each other. It also depends on the routing of production. Tp depends on capacity of each machine and routing of the production for a product. Tp for each station only depends on capacity of the machine in that station. Tp for a product, which is theoretical flow time depends on these capacities and also the routing of production, but not on throughput and not on number of machines. Given this justification, theoretical flow time here is the same as theoretical plot before; three hours, four hours, 2.4 hours. Theoretical flow time is exactly as it was before. Pipeline inventory shows the number of flow units with the processors, not in the waiting line and this is the absolute minimal inventory that we need. We can use Little's Law. In this example, throughput was 16 and theoretical flow time was 9.4 Min-WIP or pipeline inventory is a equal to 16*9.4/24 and that is 6.267. We can also compute it by using utilizations. We have utilizations of all stations. Then we have the number of machines in each station. We multiply number of machines by utilization, and we get pipeline inventory. Suppose we need to deliver the product in half a day to earn the full revenue of each product. Therefore, we use Max-WIP, equal to capacity times flow time as a surrogate for WIP, equal to throughput times flow time, and we get nine as Max-WIP. Since Max-WIP=9, WIP is always less than nine. Since capacity is 18, throughput is always less than 18, but if current WIP is less than nine we do not go and quickly change current Max-WIP to nine. We wait and look at WIP. We wait until WIP goes to 8, 9, 10, we may compute two period moving average, three period moving average, four period moving average. For example, if three period moving average exceeds nine, then we may switch. If current WIP is 7.8, then if throughput is 16, what is the flow time? It is below half a day, and it is below 12 hours. How long a flow unit spent in a waiting line? Flow time is equal to 11.7. They call flow time, we computed that is the time that the flow unit spends with processors was 9.4. Therefore, the time in the waiting line, which we refer to it as Ti is equal to 2.3 hours. Compute the number of flow units in the waiting line. WIP is 7.8. Pipeline inventor is 6.27, 6.3-7.8, 1.5. 1.5 flow units are in the waiting lines, 1.53 to be exact. Suppose there are 40 contract in this system, compute flow time, throughput is 16 times flow time is equal to WIP or average inventory 16*T=40, therefore T=2.5 days. How long each load spent in the waiting line? 2.5 days or there. If I multiply by 24, that would be it was 60 hours, and I had 9.4 hours with processors. Therefore, that is 50.6 hours in the waiting line. How many flow units are in the waiting lines? We have 40 in the system, and we had 6.27 in the waiting lines, 6.27, that would be 33.73. Compute cycle time and tact, cycle time is equal to 1, divided by capacity, and that is 1/18 days. If I multiply by 24, that would be my cycle time. Takt time is equal to 1/R, that is 1/16. If I multiply by 24, 1.33 and 1.5. Thank you very much for attending this session. I have another example below this example. You can do it for practice. As I explained, this concept of Max-WIP and not allowing WIP to fall into opposite sides of a slippery roof become more than what you have computed as Max-WIP, increase the flow time and therefore reduces the revenue that you make out of each product. There is one side, the other side to make sure that your WIP is not too much below the maximum WIP that you have computed. If it is, let Max-WIP to be larger than what you have computed and only switch it to what you have computed when WIP gets close to the maximum WIP that you have computed. This part of special useful in the game, but understanding all the material is useful to have better performance in the exams.