So let's go through an example for a Line of Balance calculation. If I ask you to develop a Line of Balance schedule for a particular project, example could be a road, that consists of 20 sections or units. The target output rate for this project, which is r, is three sections per week. So the targeted, the ideal case is each activity, or process we have in the project, needs to produce three sections per week. The target in a typical working week includes five hours per day. And we have the construction of the single section consists of the following five sequential activities or processes. Activity A,B, C, all the way to E. And then for, as I explained to you, we have column 2 and column 3 giving how many man hours per section or per unit. For activity A, 110, for activity B, 320 and so on. And you would need how many laborers per gang or per team to perform that one section. You need 3, 8, 9, 2 and 5 for all these activities. So how we solve that, as I mentioned, we want to fill the table. And I would encourage you to try to go to that table, write on a piece of paper, in addition put all the formulas that we identified and given to you. And try to do the calculations before you move forward in the module here to see the solution. Here are the calculations that I provided, based on the equations that I just shared with you. And let's go column by column quickly to understand the calculations. So first of all what given to us was the first three columns. The name of the activity, the man hours per section and the laborers per gang. Also we have desired, R, which is three sections per week given in the example here. I put it here for you to memorize it so this is R. So column number 4 is then calculate the theoretical gang size at the chosen output rate 3. Which equal G = 3 x the man hours per unit in column number 2, divided by 8 x 5 which is equal to 40 hours per week. If you do the math for each one of them from the 110, 320, and so on these are the theoretical gang size at the chosen output rate 3. For column number 5, We said that the actual gang size, so we can't use 8.25 men per gang. We want how many men or laborers per team to perform the work. In that aspect, we said Ga, or the actual gang size, is equal the multiple of G. From here, 8.25, we took 9, 24 we can keep it as 24. 27.38 we keep it 27, And, the 2.63, we took 4, and 15.75 we took 15. Let's stop here just quickly and mention that when you take a multiple of G, that's mean, the G size let's say is 3 here. And the multiple of G would be 9 and it would be the closest number to 8.25 which is the theoretical gang size. I will repeat that again. For column number 5 when you solve it, you look at the number that is a multiple of column number 3. And when you find that multiple you find the closest number, Of the multiple of G to the number you found on column number 4. So a multiple of G of 3 would be 6 and 9. Because, 6 and 9 is closer to the 8.25 that you calculated. Which one is closest to the 8.25? Is it the 6 or the 9? The answer is the 9. It's closer to the 8.25 that's why you choose the 9. The multiple for process B of 8 is 24, we have. This is easy because we found the 24 straightforward. Now, a multiple of the 9 and the closest number to the 27.38 would be then a 27. And for the process let's go with E not D, we have 5. A multiple of 5 closest to the 15.75 is 15. You can have a multiple of 5 of 10 but it's far from the 15.75. You can have a multiple of 5 of 20 but also is far from 15.75. So 15, a multiple of 5, also closer to the 15.75. Now why I left D here because the multiple of 2 that closest to 2.63. We took 4 because some common mistake, you might come and say no, no, no we have 2. 2 is equal to the number 2 here but it's not a multiple. So the minimum multiple for the 2 here would be 4. And the other reason why we don't choose the exact same number, because that mean that we only have one gang or one team or one crew that has two laborers for the entire project. And as a suggestion or recommendation, have at least two crew, two gang size, two gangs to work in the entire project. Process A, we choose three teams or three crews to work on your project. How did I find the 3 is the number 3 here is 3 laborers per team, per gang, per crew and we chose 9 laborers. So you have 3, 9 divide by 3, 3. And the same goes for everyone here, for process E, for example, we'll have 5 laborers per crew or per gang. And we chose 15 laborers, so we have 15 divided by 5, we have also 3 crews. For activity D now, we didn't choose number 2, which would be closer to the 2.63, we chose 4 because we need more than one crew or one gang in the entire project to work. So in this case we chose the number 4. So moving forward, With column number 6, to find based on the actual gang size. The 9, 24, 27, 4 and 15, we want to calculate the actual, Output rate, which is number 6 here. The actual output rate Ra = 3 x Ga/G. Which is 9 divided by 8.25, Times 3. So in that's the case, we have for the first one 3.27, 3.00 and so on. If you noticed when we try to find the actual output rate, based on the actual gang size, these numbers will be the slope of the production rate, or production, the slope of the production line. Or the lines, in the line of balance diagram. So from that, if you notice on activity D here, we have a high actual output rate, a 4.56. Because we only need, as I mentioned, around 2.63 laborers to perform the work to satisfy the three sections per week. But we put another crew which increase the slope, make it more steeper, for activity D and the output rate became more productive. So increase the number to 4.56. If you notice here most of the numbers were trying to be closer, as much as possible, to the number 3 here. That chosen output rate or the desired output rate in your project. Section number 8, or table number 8, column number 8, I'm sorry, in the table is finding the time from the start on first unit, to start on last unit. As I explained before in one of the slides. To find T number of working days per week times N minus 1 the number of sections, 20 divided by the Ra which is column number 6. So in this case, as we are saying, when we start the first section of process A, we'll say at, day zero. The last section of process A will start after 29.05 days from the beginning of the first section of the road. And then in the question we highlight that we need a minimum buffer time of five days. This is an assumption,it could be three, four, but we ask you to have it as a five days as a minimum buffer or a lag time.
