Let's review the questions of the productivity module in the same way we did for process analysis. I will share with you a couple of practice problems, and you'll take a shot at these problems on your own. For that, after I explain the question to you, just pause the video, take some time to wrestle with the question, and then restart the video to hear the rest of the question explained by me. Ready? All right. Here's the Tom and Jerry ice cream store question. Tom and Jerry run an ice cream store, and they have an expensive piece of equipment. Since they are currently running at capacity, they consider buying another piece of the same equipment. However, they consider doing an OEE analysis. They find that not all of the capacity is used productively, and so they use a couple of calculations to figure out what's the real percentage of value at time going on here on their ice cream maker? Alright, here's a good moment for you to pause the video. I'll give you some time and then, I show you the solution. All right. Now, it's my turn. Let me crunch the question step by step. The first part of the question asks me, how many good batches of ice cream will there be produced per day? To figure that out, recall that we have basically twelve hours available for production. Of that, one hour is lost due to the start-up effect. Pardon my bad humor here, this is the funniest I could come up with. So, eleven hours are available for production. Eleven hours really means 660 minutes per day. If you think about how long it would take to produce a batch of ice cream, remember a batch of ice cream takes 80 minutes. These 80 minutes are twenty minutes in setup, and 60 minutes of actual production. 80 minutes per batch means that we can really make eight batches per day. Of this, we know that only three quarters are good, and one quarter is defective. And so, that means we are producing six good batches per day. This is real value air time. We know that it's six batches are justifying really 60 minutes per batch of production time, and that gives us 360 minutes of productive time per day. Now, in the last piece of the question, we want to have something brought into the question that talks about every other Fridays. So, over two weeks we going to have thirteen days times six batches, six good batches per day time 60 minutes. So, over thirteen days, we have a total of 4,680 productive value add minutes. How much available time did we have in that two weeks? Well, the available time is simply fourteen days times twelve hours a day, times 60 minutes. That is, according to my calculator, a thousand and, 10,080 minutes. So, this here, on the very right, is the actual value add time 4,680. Here's the available time, so we can solve for an OEE of 4,680 divided by 10,080, which is roughly 60, 46%. Again, you can now start quantifying the capacity loss effect, for example, of setup times or offset defects here. And so, that gets a nice water flow chart that makes up for an OEE analysis. The next question is about linking operational measures with financial measures. In particular, we're going to have an eye on productivity measures and how they influence the bottom line of the firm. Take a look at the question here, before you get to the work, let me point out the notion of an RIC tree. In class, we talked about an KPI tree. Kpi stands for Key Performance Indicator, that's a computation that I did for the Subway case looked at profits as a pretty obvious key performance indicator that an organization would be interested in. When you do and RIC tree, you start with the return on invested capital at the root of the tree. This is simply profits divided by invested capital. And then, you start the tree by having a profit branch, and an investment capital branch. From there, you go as discussed in class. Are you ready? Here you go. The first part of the question is about how many guests we can serve on an evening. Now, take a look at the following thought process. A guest will spend a total of 50 minutes in the restaurant. Then, ten minutes are needed to clean up the table. So, the total time in the system for the guest and the table. So, if you think about the flow time of an order, is 60 minutes. Apply Little's Law, I = R T. And you know that the restaurant is always full. Always full means that, there are always 50 orders in the system, and then R times T, and T is really a quarter of an evening. So, if you look at guests per evening, you can solve for R and see 200 guests. You don't really need to do a little [unknown] to find this, you can also think about the intuition that each table is turned four times per day. So, the table turns are four times per day, there are 50 tables, hence, there are 200 guests for an evening. To draw the hourly seat, we proceed as follows. Again, start with the profit branch and to, to the invest of capital branch. Profits is nothing but revenue minus cost. And revenue is nothing but the revenue per guest times the number of guests per night. The number of guests per night are simply the number of seats that we have available, fifty as we just saw times by the speed with which we turn the seats. This, in turn, is driven really then by the time that the guest in the seat or at the table plus the ten minute of cleaning time. On the cost side, we have really multiple brackets of cost. We have some overhead cost, we have some cost for the labor, and we have some variable cost. The variable costs are largely reflected in the food, and those are simply the number of guests times the amount of dollars that we spend per guest on food related expenses. This gives you in a nutshell, how these variables play together deriving the ROIC. I now turn to Excel and actually run the numbers. Alright. Let's start with the revenue calculations. We begin by looking at the revenue that we get per guest, twenty bucks. Then, we have the time that the guest is on the seat plus the cleaning time, which we said by now is 60 minutes. That allows us, return the table, 240 minutes divided by 60, equals to four times. Since, we have a number of seats equal to 50, we can get revenue so we can get, excuse me, number of guests first per night is simply, so, turns times the number of seat, and there's just 200 guests per night. Next, we'll look at our total revenues. That's simply the 200 guests that we served times $twenty per guest equals to $4,000 revenue per evening. Next, on the cost side, we look at the labor costs first. For the labor costs, we have twenty employees taking home 90 bucks per evening. On the overhead slide, that is simple, it's a flat 1,000. And, on the variable cost for the food, we'll have to now look at the guests that we serve, 200, and multiply this with $5.50. So, our total cost is simply these three numbers added up, and then I get profits of revenue minus cost equals $100. Here, we have to be very careful simply because this is the profit per evening. If I want to compute a return on investment capital, returns have to be recomputed on an annual basis. And so, my profits for a year was simply 365 times my profits per evening. That gives me, then, excuse me, for a year, that then gives me my ROIC. As the ratio between the profits that I have here, and the investment capital that I just squeezed in here. That is 18.25%. Now, the reward of all this tricky calculation is that a sensitivity analysis as quite simple. For example, the question of roots to the case that I could shorten the time of the seat to 55 minutes by accelerating the cleaning process. I just type this in, all the numbers we compute, and we see this dramatic increase in ROIC. Though, I admit, this is based on the assumption that there is really an infinite amount of demand that, particularly, we can squeeze these extra customers in. But, again, don't be too cautious on the assumptions here because we're assuming that with unlimited demand, that average time, it doesn't really mean that there's always four customers being served per seat per night. Some will stay shorter, some stay longer. And, as long as there's an infinite demand, we'll always get the extra guests through the system. Anyway, you see now, draw the ROIC tree, compute the ROIC, and then do the sensitivity analysis. Alright. The last question is a line balancing question. You see that there are six tasks given to you, and a current assignment of tasks to workers. Your job is to balance the line. In the second part of the question, you were supposed to compute the takt time, and the target manpower calculation. Now, a word of caution as we start the optimization here to maximize capacity given these four workers. Besides that in class, there is a way of mathematically formalizing a fancy mathematical optimization problem. But, this is really overshooting it. With the numbers as small as they are here, it's a process of trial and error. You have to just try out different assignment combinations to see if you can further increase the capacity. Good luck. Alright. We have a shot here at this problem. Really, we're dealing with the process that consists of the four resources, namely, the four workers. The first resource is just working on task one, which gives it a processing time of 30 seconds per unit. 25 for the second worker. And then, here, we combine three and four. So, 75 seconds per unit at station three. And, for work number four, we have, 45 seconds per unit. So, we've done this often enough by now in class, that we can quickly see that one over 75, and this is now units per second, is going to be the bottleneck, and thus this is the capacity of the current line. So, this is, again, one over 75 times 3,600 seconds in a hour. Now, let's assume the tasks are allocated differently. You want to balance the line. And clearly, this doesn't look like a really balanced line because there's a big difference between the fellow working here, and the fellow working here. So, let's see how good we can do. Now imagine, the first person here would work on task one and task two. They would give us a 55 second processing time. Then, the next person will just work on this one here, 35 seconds for the next one, 40 on the next one, and then, 45 for the third step. This will give me an activity time or processing time at the bottleneck of 55 seconds. How did I come up with that solution? Don't ask me. This is a little bit of iteration, a little bit of trial and error. I started with 30, but I doubted that I could get all the way down to a processing time of a bottleneck of 30. Then, I tried 30 plus 25, and went from there onward. Could I combine activities such as the processing time at the bottleneck is 55? Yes, I could. Again, this is trial and error as long as you don't learn mathematical programming which could do this assignment optimally for you. With this in mind, we have a activity time at the bottleneck of one of 55, and that's the capacity of the bottleneck of one over five, 55 units per second. The third question is equally tricky. In the third question, you can assume that you can reshuffle these tasks. Now, typically, when you do these, you'd, since you're gaining a degree of flexibility, you would be able to squeeze down the processing time at the bottleneck further. However, I couldn't find a combinations of activity times such that the 55 seconds were beaten. Just try it yourself. So, maybe you want to combine 30 and fifteen, it gives you a 45 per, per seconds per unit activity time at the bottleneck. Then, you could try a 55 up here, that makes it longer. Try it yourself. I couldn't come up with anything faster. So far, we have looked at the effect of capacity only. We have maximized capacity. Now, we have some information about demand. Demand here is 50 units per hour. Since there are 3600 seconds in an hour, and we want to have 50 units, we have a 72 second between units takt time. I can quickly compute the labor content of the process, it's simply the sum of these individual processing time and get the labor content of 175 seconds per unit. My target manpower is then simply, these 175 seconds of work divided by the takt time of 72, which is 2.43 people. Round this up, and you see that you should hire three workers. Now, the last question is going to be tricky. As we go from the target manpower to the actual staffing level, we have to, once again, tackle the problem of assigning workers to tasks. Let's take a look at this together. Now, here are the processing times. They work, excuse me, I didn't want to log us out here. 30 seconds for the first, 25 seconds for the second, 35 for the fifteen and 30 seconds per unit, respectively. Let's first consider the case where we can do the task in any order that we want. Remember, our takt time was 72 seconds. So, I want to create bundles of tasks that are very close to 72 seconds. I'll combine 40 and 30, that gives me 70 seconds that the worker would just have two seconds idle time. Remember, we want to hire n = three workers, that we know by our target manpower calculation. That's the best we can do. Well, then, from here onwards, it's easy. Fifteen plus 35 already gives me another 50 seconds. I combine the first, and that gives me with n equals three workers gives me the process staffing that I need. It's somewhat tricky, unfortunately, if I want to keep the sequence of tasks as they were described in the questions. Again, let's write them all down. And, let's remember that once again, we are after a takt time of 72. So, if I combine the first two, I'm going to get back to my assignment of 55 seconds of the cycle time, or of the processing at the bottleneck which we saw previously that was not enough to get me down to n = three, I have n = four. However, if I include all of these three tasks, to [inaudible] the first worker, I'm over the 72 seconds takt time. So, that means, first worker really has to have these two tasks assigned to them. Same logic on the next step. If I combine tasks three and four, I'm over my takt time, and so, that doesn't work. And so, I have to unfortunately, hire them. Let's just hire 35 seconds here. Then, the next person would be staffed this way, and then the next station this way. So, unless I can break up the tasks further and move seconds from one task to the other. Unfortunately, in that case, I will need four workers.