This session is a review session for Module one. If you feel comfortable with all the content that we have covered in this module, you don't need to attend today's class. What I want you to do in that case, is simply go to the Coursera site, and test yourself on the practice problem that we have posted there. We have posted the practice problem as well as the solution for the practice problem. Then, go to the homework assignment for this module. Now, practice problems are not graded, the homework assignments are. To take the home work assignments, just go to the PDF file. Take the assignment at your own leisure. And use the consumer interface to submit the answers. Those will be auto graded. And it's gonna be part of your overall score for this course. The purpose of today's session is to review the content of this module. And to help you practice solving problems. We will do this at the end of each module. Now, these sessions will take a little longer, because I'm gonna read you a lot of content. And so, please be prepared that this is not gonna take the usual ten minutes. But it might take longer than this. You can fast forward, you can skip. And as I said, if you feel comfortable with all the material, today's class is entirely optional to you. Here's how we going to do this. I will post a problem to you In the fall, usual lecture format that we have had all through this module. And you're gonna test yourself, taking these questions. Simply pause the video, and just crunch through the question. Once you're ready to see the answer, fast-forward and look at how I am gonna solve the problem. We do this for typically two, three, four questions per module. And, again, it's there to give you feedback and to improve your learning. Think of those really like a TA office hours, or a recitation session at a regular university curriculum. Let's move to the first question. The question describes a situation of a caregiver, who is infusing electrolytes to patients or to athletes. Please don't think about cycling, don't think of Lance Armstrong here. Is infusing electrolytes using five steps, five activities, and you see the processing times per athlete or per patient over here to the right. It's not that there are five workers in this process. In fact, there are only three nurses, and the first nurse does activity one and two, the second nurse does activity three. And the third nurse does activities four and five. What I suggest we do is you just pause the video here. And whenever your ready you get a sense of how I'm gonna solve the problems. But, you really get much more out of this exercise if you try to tackle these questions here, question one to seven on your own. Okay. So pause me here and whenever you're ready press on play on the monitor again. Now the way I want l-, do you get started with this process analysis, really was almost all process analysis I can think of is draw the process flow diagram. This is a process that ultimately has three resources, first nurse, second nurse and third nurse. The first nurse has a processing time of twenty minutes Per customer, Or per athlete. That is because there are two activities, one taking seven and one taking thirteen minutes. The second step has a twelve minute processing time and the third one has a total processing time of 35minues. So where is the bottleneck? To find the bottleneck we have to look for the resource with the smallest capacity. That would be one over twenty, one over twelve, and one over 35. And so we see that the third step. Is gonna be the bottleneck. Again, we find the bottleneck by looking at the resource with the lowest capacity. It's also in this case, the resource with the longest processing time. But, be careful, if we had two nurses or three nurses staffed at the last step here, this would have the longest processing time, but it would still not be the bottleneck. So, go for the lowest capacity to find the bottleneck. Now what is the process utilization here? What is the utilization of this entire process, assuming, as you can see on the previous slide, assuming that we have unlimited demand? Well, if we have unlimited demand, the flow rate. It's going to be driven by the process capacity. The process capacity in turn is driven by the capacity of the bottleneck which we said was one over 35 athletes per minute. Now the utilization is then simply gonna be 100 percent because again the constraint is the bottleneck not demand. This is different if you want to compute the utilization for a nurse at station number two. For station number two, we look at the utilization as a ratio between the floor rate and the capacity. The flow rate, and the capacity are as follows. Flow rate which I said will look, unlimited demand, we can only get patients through the process, that is the flow of one patient every 35 minutes. And, we divide this by the capacity of station2, which is one over twelve athletes per minute and the gets me a twelve divided by 35, that's gonna be my utilization. What is the cycle time? Well, remember the cycle time is one over the flow rate. It is measuring and one. Pace or, what, intervals athletes are leaving the process. And so you can see here, by just looking at the processing times it says an athlete coming out here, assuming unlimited demand, every 35 minutes. Well, formally we set the cycle time was one over the flow rate, our flow rate was one over 35 and so our cycle time is 35 minutes Between customers. What is the idle time per unit at nurse number one? Remember, the idle time at a resource is the difference between the cycle time and the processing time. So is a processing time. This here, PRT stands for processing time. So the cycle time here, we said, is 35. We have a, excuse me. The cycle time here is 35. We have a processing time of, twenty. And so that gives us fifteen minutes between customers as the idle time at nurse #one. The average labor utilization. Remember, the average labor utilization. Is the ratio between the labor content and the labor content plus all the idle time. The labor content, in this case. Well, the labor content, recall, is the sum of the activity times. So that is twenty. Plus twelve, plus 35, and so that's a total here of 67 minutes per athlete. Divided by the labor content, 67, plus all the idle time. Well there is idle time at station one, which we already found as fifteen minutes. And then there's idle time at station two which we can find as 23 minutes. Why 23 minutes? Because we have a cycle time of 45. 35 cycle time minus twelve processing time gives me an idle time at station two of 23. And so, that gets me 67 minutes divided by 105 minutes as my average labor utilization. And then finally to find the cost of direct labor. We look at the wages divided by the flow rate. So wages divided by the flow rate the wages here $30 for nurse one for per hour, $30 for nurse two, and $60 for nurse two. So we're paying $120. We have to divide this by the flow rate. The flow rate we said was one. Actually, it's every 35. And this is, now careful with the units, this is customers per hour, to multiply this with 60 minutes in an hour. And that gives me then, a total of seventy dollars per customer. Okay, next question. I just returned from a lovely vacation, in, The Bavarian Alps in Germany. And had the pleasure to spend some time in the German city called [inaudible]. And so, this, this city here, I estimate, has about a 1,200 hotel beds. That are especially, you know busy, during winter season. And so, we, we see here that the average guest stays in [inaudible] for ten days. As before, I want you to pause my video right now and then work through these questions that you see listed below. Alright, how do we figure this out? This is a little small question We have a situation, in which we know how many skiers there are in the village. Because we know that all these beds are booked out. And so I know that I have 1,200 skiers. I also know that, that they're staying, on average, for ten days. Little's Law now tells me, that, if I solve this equation here, where the flow rate R, that there are going to be 120 tourists or skiers. Per day, flowing through the village. And that means that these guys, you know, 120 are arriving and 120, different skiers of course, but 120 are leaving. All right, so that was Part A. Part B. So let's figure out. The revenues of the local revenue, of the local restaurants here. Let's figure out their revenues. And for that, we have to keep in mind that every day they are, as we figured out just on the part A there, there are 120 guests per day that are arriving, and so these folks, the question indicates are spending 50 bucks. Per night. Now there are another 1,080, so those are the 1,200 minus 120, there are 1,080 patient, pa-, people. Why do I say patients? Hopefully, they're skiers and won't become patients. 1,080 skiers, and these people are staying, going out for dinner but it's not their first dinner, so they're only paying 30 bucks. And so if you add this up, you're gonna get 38,000. $400 per day. Now, how does this change, when, the, the, the business change when, when, the, the shorter Stay of the skier kicks in. Well, inventory equals flow rate times flow time. The place continues to be booked out. So you have 1,200 skiers, but now the, The, the T here is gonna go down to five days, and that means that the flow rate everyday now, there are 240 people coming to the village. And that's actually good for the restaurants, right?'Cause now you have 240 skiers come and spend 50 bucks, plus now 1,200 minus the 240, 960 skiers who are on their non-first evening. And there continue to spend 30 bucks, and that is now a higher number, and according to my math that gets me 40,800. Dollars per day. So the extra revenue that we're gonna get here is We're gonna get an extra of 2,000. And 400 dollars per day extra. There's another way you can see this, by the way, if you think about the kind of, dollars per night. If you think about the old world, the guest would give you 50 dollars on your first night and then for nine days he would give you 30 dollars. So, nine times 30 and so that gives you a total then of 320 dollars. And they would do this, over ten days, and so, per day You would get, on average, you would get $32 per day. In the new world, you have the guest come for the first dinner, and then they give you four times 30. And so every guest is leaving you $170 in the village, restaurants. But that is not only over five days, and so on a per day basis per day this is now 34. And so, you basically, out of each guest you're making an extra two dollars per day. And, since there are gonna be 1,200 beds, and out of each skiers for the average day, you're gonna make an average two dollars you're gonna get the same $2,400 per day that we computed below. Alright, ready for the next question. This question is called Summer Sweets, and it's about a small gelato store that is having a revenue here of $4.3 million, and cost of $2.6 million dollars. The first question asks you to compute the inventory turns, and the second question asks you to compute the amount of inventory that just needed to run this business. Take some time for yourself and then we'll tackle this together. Alright, for the first question remember that the inventory terms. Is driven by One over the flow time T. So, if the inventory spends 30 days in the process, we speak of one turn a month or twelve turns a year. Now, in this case, we notice that The inventory only stays four one-half days in the system. And so the inventory turns, one over T, is simply one over 4.5. Now, we have to be careful here with the, the units because if 4.5 is expressed in days. If we want to express this in terms of yearly turns, then we have to multiply 365, and we're going to see that we're turning, per year, we're turning this inventory 81.4 times. The second question asked you to compute the inventory, and remember Based off Little's Law, Which is really at the heart of all this inventory turns calculation, I equals r times T. Now in most settings that I have discussed in the lecture, for those three variables I've given you inventory. And I've given you the flow rate. So when you look at the flow rate, just as a reminder, always please look at cogs. Do not use revenue for the flow rates. So, as I said, typically, I've been giving you the inventory. Of course, companies kind of typically know how much inventory they have in their system. This question here has given us a, The days of supply or, as we computed in the first question, the inventory turns. And so, you know, it's the same equation, it's just, you know, you have two different variables this time that you know already. And you're solving this time for I instead of in the other settings we tackled this question we solved for T. Is this practically meaningful? I thought on situations like this where you have R and T, those tend to be situations where you are planning for a business expansion or even an entirely new business. And those are situations where you want to figure out I to compute the working capital. In an existing ongoing business, chances are you know your I. So is this question realistic? Yes typically if this is a chain that is growing and is making predictions for capital needs in the future. So I equals R times T, we've said that the R here, the flow of money through the organizations cost is 200. $2,600,000 per year. We said that T, If we wanna express this in years now, it's 4.5 divided by 365. And then we gonna get, if we multiply this all out, we gonna get I and inventory of 32,000 And, $54. Alright, the last question in this module review is about the Department of Motor Vehicles. You have In the Department of Motor Vehicle in my example here, you have 400 people who are arriving and want to have an application. Make an application, excuse me, make an application for a driver's license. About one percent of them fail because of cannot f-, they're not able to produce an appropriate identification. Fifteen percent then go on and fail the written exam. And 30 percent then fail in the driving test. And, if you buy me a drink at some point, I'm happy to share with you my experience In the driver's license test in California some long time ago. Anyway take your time. Read the question. As you can expect, you're asked to find the bottleneck in this question. Take your time and then press on play again whenever you're ready. Alright. The, the way we wanna start this question is just drawing the process flow diagram. The first step here, is the, you know? The identification of the, customer. And some people fail, right? One percent fail to, do this appropriately. The question says, we have these 400 people a day arriving. So 400 flown in. One percent failing, so there's f-, four people a day that, that fail to do this and that leaves 396 who are arriving at the second step, the written examination. So the second step then, examination, we said you know, 85 percent are, are, are able to do the written exam, and fifteen%, fifteen percent of those 396 are failing. So 396 times fifteen%, if my math is correct, is 59.4, which then leaves us with 300. And 36.6 people who actually wanna take or allowed to take the road exam and from those we said 30 percent would fail and so that's about 101 a 100.98 to be exact that are failing this and from those. Excuse me, from those, then 235.62 will be passing the exam and they would be good to go. And so that really gives us the answer to the first question. If there's unlimited capacity, we are able to serve all these demands, all of these 400 customers and just because of the attrition loss, this will give an output of 235.62 applications per day. Now that is a big if, right? That's assuming that we have unlimited capacity. And so that's most likely not gonna be the case. And so we wanna do a separate calculation for the case where we wanna find the bottom x. So let's do this one next. Alright. How do we figure out the station that is the bottleneck in this case here? Well, guess what? There are exactly three candidates who could be the bottleneck. The one is the identity check, the, written exam and the road exam. It's gonna be one of the three. And we now have to figure out which one it is. So let's start with, the processing times here. The processing times are as follows. The processing times are five minutes then they are three minutes per application for the exam and twenty minutes for the road test. There is a hidden assumption in here, I have to reveal that, we will be assuming there are enough computers, so that the computers will never become the bottle neck. And, so we can focus just on the three minutes, that it takes people to administer the exam and get the people ready. The next one is the number of people, or the number of resources at each of the three stations here, that would be four then there will be a two, and then there will be fifteen. And that allows us to compute the capacity. And remember capacity is the number of resources, divided by the processing time. Now careful here that this is expressed in applications per minute. And if we wanna get to the capacity in terms of applications per day, we have to multiply this with the 60 minutes that are in an hour and the eight hours in a day that they work. So that would be this cell here times 480 minutes in a day, which gets me a daily capacity of 384. Alright the next thing I have to figure out is demand. Right. So demand is we know for the identify check there are 400 people showing up to get their demand checked excuse me their identity checked. We have on the process flow diagram a moment ago identified that there would be 396 coming to the written exam and then the course of failure in the written exam there would be 336.6 people showing up for the road test. Okay. And so that allows us now to compute an implied utilization. Remember the implied utilization, as the ratio between demand and the capacity. And that is 104 percent here. 123 percent here and 93 percent at the last step. So you might now say, well look, wait a minute. You know really, the identity, The, kind of the capacity shortage at the identity check is really keeping the flow from these people to the written exam. Because you have already have a capacity constraint upstream to the written exam that doesn't matter for the implied utilization. Implied utilization is demand by capacity at the most binding constraint on this process is where the implied utilization is at its highest, and you see that, that is at the written exam. So this is gonna be the constraint on the system. That means that the system can only handle 320 Applications per day, that are gonna be processed at the written exam. Okay, so 320 folks can take the written exam. And we know from the case, we know from the question, that, 85 percent of them will succeed and show up for the driver's test. And then up to 70 percent, again, will succeed of, passing the road test. And that leaves a total of 190 point four people who will succeed getting their license, acknowledging though that there is a capacity constraint. All right. That concludes the review session. You saw these four types of questions that I think I can, you know, ask you in the homework and the exam, and, I hope I also reviewed the basic calculations and definitions that we covered in this first module.