Speaker 1:	Thank you very much for attending this session. Today, again, I will talk about Capacity and LittleField Game. Please note that the data that I'm using here differs from the game. I use this data mainly for the purpose of teaching. We have finished the first 50 days of the game, and throughput during this period was on average 5.5 contract, or 5.5 products per day. We know that in this game a day is 24 hours. Now, at the same time that time talking about the game, we can generalize these concepts and say, I'm talking about capacity in general. Contract, go to Station 1, then 2, then 3, go back to 2, and then they leave. We have one machine in Station 1, one machine in Station 2, and one machine in Station 3 for the time being. Each contract, each product requires 60 kits, and cost of each kit is $10, which makes it $600 raw material costs. We can be on three contract. On the first one, we get 750, second one, 1,000, and third one 1,250. These three contracts are time dependent, short the time that we have. The larger the amount that get. We also have utilization in these three stations. We have the throughput per day, and we have utilization in stations, and we know that utilization is throughput divided by capacity. Having said that, we have throughput, and we have utilization. Therefore, capacity is equal to throughput divided by utilization. For the first station, if you divide throughput by utilization, we get eight contracts per day, and then using the same computations for Station 2 and 3, you will get capacity of eight for Station 1, six for Station 2, and 10 for Station 3 and because a day is 24 hours, so it takes 24/8, for a product to pass Station 1, no matter we have one machine or 100 machines. If capacity of each machine is eight per day, and if a day is 24 hours, therefore, a product should stay in a machine for three hours. The same is true for Station 3 because capacity is 10 and a day is 24 hours. If there are more than one machine here, when a product comes in, it should go to one of these machines. As soon as it goes there, capacity is 10 per day, 24/10=2.4. It takes 2.4 hours to go out. If you are in Station 1, if no contract is here, or if there are some contracts on machines, but there is one machine empty with no product, if a contract comes in, if a product comes in, it will take three hours to go from start of Station 1 to end of Station 1, which is indeed the front of Station 2. The same is true for Station 3. If a product comes in and if a machine is empty, it takes 2.4 hours to go up. We are in Station 2 capacity of a machine is six contract per day. If a day is 24 hours, therefore, each product should stay in a Station 2 for four hours. Now, suppose a contract comes in, no other contract is here, and if other contracts are there, they are in other machines, and one machine is empty. A contract has come here, then it should go to Station 3. How long does it take this contract to go from here to here? Forget the time interval to go from 2-3, only let me know how long does it take this product to go from here to here. Each contract stay in Station 2 for four hours, but it will go to Station 2 twice. First from Station 2 to Station 3 and then back to Station 2 and then go out. Now, if you have not said that the timing is different in these two arrivals, each contract passes machine two times. One, when it goes to Station 3 and one when it has come back and then it will go up. If the capacity is six per day, it takes four hours on Machine 2, but because it will pass there twice, each time it will be there for two hours. Therefore, if a contract is here and we want to know how long does it take to go from this point to this point or this point, if we ignore the travel time 2-3, it takes two hours. Compute the theoretical flow time, which is easy, no matter if I have one machine in Station 1 or 100 machine, no matter if I have one machine in Station 2 or 100 machine, no matter if I have one machine in Station 3 or 100 machines. When a contract arrives here, beside the time that it will stay in the waiting line, it will stay here for three hours. It will stay here for 2.4 hours. It will stay here for four hours, but in two rounds, in the first round, two hours, in the next round, again, two hours. Theoretical flow time would be 3+4=7+2.4, which is 9.4 hours. This is theoretical flow time 9.4 hours or a little bit more than one third of a day. But the actual flow time may be two days, three days, four days because 9.4 hours will be with machines but the product may be inside waiting lines for 100 hours. We don't know, and that is the difference between flow time and theoretical flow time. Theoretical flow time is the only time that the product spent with machines with production equipment or service resources. If these are the capacity of the three stations, a chain is as strong as its weakest link, and therefore, the capacity of system is six per day. We have produced 5.5 per day, as it was given by the problem. Therefore, if we have delivered all the product within the time interval that we had and if we have collected 750 for each product, on each product, we have made $150 profit multiplied by throughput, it would be about $800 per day. If we assume that we were able to produce at capacity, and we can never do that, no system can produce always at capacity then this profit was 150 instead of 5.5. We would have multiplied it by six, and that would get us $900. The problem tells us that in the first 50 days, you have had 16 contracts per day. But because your working process was limited, not all of them have been able to come into your system because the maximum working process allowable in the game, it was 20, and it has not allowed all the demand coming because at some times the demand was coming, but there were already 20 product inside your system so they have been rejected. The data of this problem tells us you have processed 5.5 units per day, and you have rejected 10.5 per day. The average demand was 16. This is given by the problem 5.5, but you have rejected 10.5. But out of that 10.5, you could have again made $150 per contract that was something around 1,500. But if it is in a game, where you can also switch from one contract to another contract and if the most lucrative contract gives you 250, then if you have said no to 10.5 per day, that means 1250-600 is 650. Suppose it is 600, 600*10, that means you have said no to $6,000 a day. I encourage you do not think about reducing the demand by limiting your working process, but think about increasing capacity. At this moment, if we are in at the end of Day 50, we have 218 days to the end of the game, and we need to try to gain this demand to benefit from this demand that we have rejected. For example, if you go to Contract 3, you could make $10,400 per day if you can satisfy 16 orders per day compared to the original of 5.5 orders per day and being on Contract 1, you could make $9,500 per day, more money. If the cost of each machine is $100,000 with this 9,500, for a minute, suppose it is 10,000. If you buy six machines, you should pay $600,000. But if you are making $10,000 more, it needs 60 days, or it needs 64 days, a little bit more to recover the payback period. The days that requires for that investment to come back even if you buy six machines is 64 days of production while you have 218 days left. You can make this much money, something around that, not exactly that and because you start the game with $1 million, and if you have spent $600,000 on machines, you can still finish the game by $2.5 million, $2.6 million plus 10% interest that you can gain throughout the game. Here I have tried to tabulate step by step increase in capacity. This table differs from the actual game that you will play. Do not duplicate what am I saying. I'm just trying to set the stage to enable you to think about your specific individual game. At the beginning, I have one machine at each station. These are the capacity of the three machine three stations, and the smallest one is six. The total number of machines is three. Capacity of the process is six, and demand based on the information given to us is 16. We never can produce at capacity. Always throughput is less than capacity, but for simplicity as estimates, suppose we produce at capacity. If we produce at capacity, therefore throughput would be six and therefore utilization of Station 2 is 100% and Station 1 because its capacity is eight, and we are producing six is 75% and utilization of Station 3 because the capacity is 10 would be 60%. Now, suppose we decide to increase capacity and buy one additional machine here for Station 2. Therefore, the capacity of the station goes from 6-12, but the capacity of the process will not go to 12. Why? Because the internal bottleneck because right now, demand is there, demand is higher than our capacity so bottleneck is not external. It's not demand that requires us to go and do promotion, discount, and something like that. Demand is 16 per day. We can only produce six per day. The bottleneck, the binding constraint, is internal, and that is Station 2. Now we want to relax this constraint, we buy another machine. The capacity of Station 2 goes to 12, but the capacity of the process does not go to 12 because the bottleneck goes from Station 2 to Station 1. Now we have four machines, capacity of the process is 8, demand is still higher than capacity. If we produce at capacity, then utilization of Station 1 is one, utilization of Station 2 and three are there, 0.67 and 0.08. Now, suppose again, we want to increase capacity. Bottleneck is eight. We buy another machine and capacity of Station 1 goes to 16. But the capacity of the process is neither 16, not even 12, but 10, the bottleneck shifts to Station 3. Now, at this specific moment, we have two machines in Station 1, two in 2, and one in 3. We have a total of five machines. Capacity of the process is 10, demand is 16. Binding constraint is still internal. These are utilizations if we produce at capacity. Still, demand is greater than capacity. Still, the binding constraint, the bottleneck is external, and we buy another machine for Station 3, capacity of Station 3 goes to 20, Station 1 is 16. Bottleneck shifts back to Station 2. We have six machines, capacity at this minute is 12. Demand is still higher, and these are utilization of the stations if we produce at capacity. As you can see, when we increase the number of machines from 3-4, from 4-5, from 5-6, each time two units is added to the capacity. Now the bottleneck is Station 2. We buy another machine for this station. At this step, the nature of the system is such that we jump four units from 12-16. Very good investment. Capacity is 16, capacity of the process. These are capacity of Station 2 and 3. These are utilization. At this moment, supply and demand equate each others. Right now, we have a capacity which can satisfy the demand, but indeed, it cannot. You can never produce at capacity. Therefore, if you like to satisfy the demand or if you like to increase the probability of satisfying the demand, you need to increase your capacity. Currently, the bottleneck is Station 1. We buy another machine for this station. Each machine has capacity of eight, and therefore that one goes to 24, and the bottleneck goes to Station 2 with capacity of 18. Now, capacity of the process is 18 and demand is 16. Utilizations are here, 0.67 is good, 0.80 is good, 0.89 it is a little bit scary, especially if variability in demand is high. Here we are talking about 16 per day. Demand is 16 per day. But when we say 16 per day, one day it may be zero, another day, it may be 32. Variability is there, and when variability is there, high utilization is risky. Therefore, we may go one step further by one other machine. If you want to buy one other machine, then bottleneck is 18, and we buy one other machine here. Now, things look very smooth. Capacity of the process is 20, demand is 16. Utilizations are all under 80%, two machines are even under 70%. With high probability, we will be able to produce something close to the actual demand of 16 per day. This is capacity or throughput graph, and these are utilization graphs. This is utilization of Station 2. This is utilization of Station 1, and this is utilization of Station 3. They go up and down as bottleneck moves from one point to the next.