Speaker 1:	This is a talk about pipeline inventory and maximum working process. I'm going to teach this material in the test bed of the idle field technology game. The concepts are general concept in capacity planning and throughput analysis, but I also like to see the instantiations in the little world. For the time being, suppose in this production environment, we have set the maximum WIP. Maximum number of loads that can be inside the system to seven. We have three contracts, Contract 1, we will get 750, Contract 2 1,000, Contract 3,1250. Each product needs 60 kits, and each kit we buy it for $10. Throughput for the time being is 5.5. Number of machines in a Station 3 is one, and utilization is 0.55. Number of machines in a Station 1 is 1, and utilization is 0.6875. Number of machines in Station 2 is 1, and utilization is 0.916667. The process flow is like this. Orders come into the first station, then go to the second station, then go to the third, and then come back to the second station, and then they leave. That is the overall flow. As operations management, our main responsibility is to create a smooth flow. Having said that, compute pipeline inventory. That is the absolute minimal inventory which we need. Flow time in the Station 1 is 3 hours, in Station 2 is 4 hours and in Station 3 is 2.4. Just to let you know, how did we get these numbers? Let me have a very quick review. Here, utilization is 0.55, and throughput is 5.5. Therefore, utilization is equal to throughput divided by capacity, and 0.55 is equal to 5.5 divided by capacity. Therefore, R_p is equal to 10. Now I have capacity equal to ten, ten products per day, and therefore 24 hours because this system is working in 24 hours, divided by 10 is 2.4 hours or indeed 1/10 day. That is the time that we need in Station 3, and that is where this 2.4 is coming from. If we continue computation for all other stations, we will find it out that the capacity of the system is six per day, and now we are performing at 5.52 point. Now, if you want to find the pipeline inventory, we can use two different Procedures 1 is using the Little's Law. If we produce at capacity and if flow time is 9.4 hours, and then I divide it by 24 to make it in day, then flow time times capacity would be the pipeline inventor. We can transform hour into day and use throughput per day, or we can transform throughput per day into throughput per hour and use 9.4, in both of them, we get the pipeline inventor. That is one way of computing the pipeline inventory. The other one is by using utilization. When R is equal to six per day, these are the capacities. That I have computed in my previous video. When we say utilization is 60%, that means the processor is busy for 60% of time and idle for 40%. Therefore, for 60% is with one load, and for 40% with no load. If we compute the average, that is where the utilization comes. Now, utilization of Station 1. That is the number of loads which are with that station, utilization of Station 2, and utilization of Station 3, and those are the number of loads with those three stations. On average, the minimum number of loads that are with those three stations, therefore, we can compute pipeline inventory by using Utilization 2, using utilization or Little's Law and this information can take us to computations of pipeline inventory, the minimal inventory for this system to work at that specific full capacity. Now if we assume that the system is performing at capacity and assuming that we need to deliver the product in three days, therefore, full capacity is here, we multiply it by flow time, and that is the maximum inventory that I have over there to be able to deliver the product, in under three days even at full capacity. We set maximum WIP to 18. We do not allow more than 18 loads to come into the system. But we know that average WIP, average inventory is always less than maximum WIP because it is either maximum WIP or less, therefore, average WIP is always less than maximum WIP. We also know that throughput is always less than capacity. Therefore, while here I'm finding the maximum WIP, and here I am using the capacity because then this capacity will be reduced to actual throughput, and this will be reduced to average inventory. That two approximations still work because throughput is always under six, and average working process is always under 18. The equation more or less remains valid. But in the game, you need to look over there. Sometimes you see while you have set the maximum WIP 218, your flow time is a little bit more than three days, then you need to reduce it. Sometimes, you know, while you have set it over there, your flow time is reasonably under three days, so you may a little bit increase it. You may bring it down to 17 or increase it to 19. This is a good initial estimate, but in the game, we need to have a look. Now, compute the pipeline inventory and Max-WIP for the case when we have three machines in Station 1, three machines in Station 2 and two machines in Station 3, and demand is 16 for the practice. Theoretical flow time still is what it was before because no matter how many machines do we have to pass the product from Station 1, we still need three hours, no matter one machine we have or one million machines. To pass the product through Station 3, we need two point. Four. Two rounds of passing the material from Station 2 also needs four hours, no matter how many machines are there. Therefore, theoretical flow time is 9.4 or 9.4/24 days. Having said that capacity of Station 1, capacity of one machine is eight capacity of three machines is 20 capacity of Station 2, three machines, and capacity of one machine is 16, that is 18, and for Station 3, it is 20. Therefore, the process capacity is the minimum of 24, 18 and 20, which is 18. Since the demand is 16, then according to Little's Law throughput times theoretical flow time is equal to pipeline inventory. But we say there are more than one procedure to compute theoretical flow time and another procedure that we introduced was using utilizations. If throughput is 16, and if these are the capacities of the three stations, we can simply compute utilization in each state. Then if we add these three numbers together, we get 2.36. 4.36, where did I go wrong? Because in my previous computation, I got pipeline inventory to 6.26. How come? It is now 2.36. Where I did go wrong. I did go wrong because I did not consider the number of machines in each station. Yes. This is utilization Station 1, 0.67. That means anything which is there is busy for 0.67 of time, 67% of time. That means on average, it is with 0.67 load. Everything over there on average is with 0.67 loads, but there are three of them over there. I cannot just write this one. I should write 3 times its utilization plus 3, which is for a Station 2, plus 2, which is for Station 3. Then when I add them up, I get the same number. Suppose we need to deliver the product in three days. What is the maximum allowable inventory? What is Max-WIP? We use capacity because we are estimating maximum WIP. We use capacity. Then maximum WIP would be always greater than average WIP. Throughput will always be lower than capacity. Therefore, while we are estimating pipeline inventory based on capacity and based on Max-WIP, because this one become inventory gets smaller, and this one when becomes throughput gets smaller, still, we can hope to deliver in three or less days. We use these two because we know them, but these two, we really do not know them. After setting these two, we can look at the real life situation and see what will happen to the other two. We put these numbers, capacity, which is 18, flow time, which is three. If we put it into the equation, we get Max-WIP equal to 54, we can allow 54 inside our system. But if we were under a contract which expects us to deliver the product in one day or less, then the maximum WIP should be set to 18. If we need to deliver in five days, then the maximum WIP will be 9. Again, this is our estimate. When game is running, we need to look around. Sometimes we can increase it by one or two. Sometimes we need to decrease it by one or two, and all depends on the variability in demand and also variability in processing times. But let's only be concerned about variability in demand for the time being. Let's do a little bit more computations. Theoretical flow time in all cases, no matter how many machines are there, no matter what throughput is theoretical flow time is always 9.4 hours or 9.4/24 days. Because we work 24 hours. That is theoretical flow time. Under these number of machines in the last assumptions, the process capacity is 18, and throughput is 16. Cycle time. What is cycle time? Up to now, we have you find flow time. This one is the theoretical flow time. What is the difference between theoretical flow time and flow time? Theoretical flow time only considers the times with the processors. Only the time that is real value at a time, makes the load closer to its final shape, final form, final quality, final everything. These times are considered in theoretical flow time. But what is flow time? Flow time also includes the time that these parts spend in waiting lines. Also, if we have finished good inventory. Therefore, the difference between [inaudible] flow time and flow time is the time that loads spend in waiting lines. We also have something called very theoretical flow time. Very theoretical flow time or the times that I have shown in blue, these times. But it is when we go inside each of these processes and try by training by improving new technology, by improving methods by improving management techniques, by implementing new technologies, we try to reduce this time to make this time smaller. Then if we add those times will form very theoretical flow time. Very theoretical flow time means we have flow time. We have gone inside value added activities and we have tried to eliminate nonvalue adding parts of those activities. That is done by implementing better technology, improving methods, training, and better management. That is theoretical flow time, flow time, and very theoretical of flow time. But what is cycle time? Cycle Time is the capability of the process to send out two consecutive parts, the time that takes for the process, the time between two consecutive parts. Therefore, it is mainly related to capacity. If in one day, we produce 18 units, how long does it take to produce one unit. That is what we call it a cycle time, one multiply by 1/18, which is 1/18 days, or if I multiply by 24, that is 1.33 hours. Don't forget the capacity of the process was capacity of the bottleneck. No matter what the other resource pools can do, a chain is as strong as its weakest link here, capacity was 18. Therefore, in one day, we can send out 18 product. We can send out one product in 1/18 day. If you multiply that by 24, it is 1.33. Every 1.33 hours, we can send out another product that is capability of the system. Having said that, what is Takt Time? Takt Time is the time interval when market needs two consecutive products. Cycle time goes to capability of the process. Takt time goes to requirements of the market. Here, our throughput was 16, and we assume it was defined by the market. Therefore, in one day we can send out 16. In how many days we can send out one product, and therefore, Takt time is equal to 1.5 hours. Note that wild throughput is always less than or equal to capacity. Takt time, what the market needs is always greater than or equal to Cycle time. Otherwise, if market needs us to send out one product every 1 hour, and if we can send out one product in every 1.33 hour, we can never meet the market. In a stable system, throughput is always less than capacity, and Takt Time, which is related to throughput is always greater than or equal to cycle. Thank you very much for attending this session.