In this module, in this video, we're going to talk about inventory management with variabilities in our demand. As the previous module, in Module 1, we mentioned that was the inventory management in a steady state. So there's no variability. The demand line, if you refer back to the video previously from Module 1, you'll see that the demand line in a steady state is a straight line. The demand or the slope of the line, the way the radar it diminishes is constant and is predictable. But now you'll see that in the state with variabilities the demand line varies. The slope is not the same so the rate of diminishing depletion, it changes and it's based on the demand at a given time so it is not the same at any two points and will not be the same over time. There may be some similarities, but may not be exactly the same period of time from one-time point to the next. This is what this graph here attempt to depict that the grade of changes now is different. There are some variations. Then, the key is we need to account, we need to understand what these changes are. What is the change in the slope in my demand, the rate of demand that I need to account for that so I can buffer for enough inventory in place to buffer for this? In the previous module, we computed the reorder point, but that was based on the constant rate of change. There's no variation. Now, with this variabilities, we need to reconsider how this can be done. This is what the purpose and the objective of this video. We still have the setup is the same. We have a lead time in our system, in our supply chain. This V time, again, could be various things like the manufacturing lead time, transit lead time, and so forth, so that you need to take that into consideration. What we need to do today or in this module is to figure out where this reorder point should be so when I replace an order, I have enough inventory to cover my lead time based on the various variabilities for this product. Now we're going to come by to Sheet 2. The same thing, in order to figure that out, we need to figure out what the optimal order quantity is. Again, this is the same formula as what we saw in Module 1 that is, two times my annual demand times the ordering cost or setup cost, and divide it by the annual holding cost. When I take a square root of this value, that'll give me that Q optimal. Here, because we have variations, we have variabilities in our demand, we need to understand a few more things. First, we need to understand the lead time, my mean demand in my lead time, so you subscript l, that is the same as the mean or demand, my daily demand times the lead time. I need to understand the standard deviation. Sigma is a Greek symbol that denotes, since standard deviation, I also need to know the standard deviation of demand during lead time. Sigma subscript L, capital letter L, equals the standard deviation of my daily demand times the square root of my lead time. Finally, we also need to compute what the safety stock should be. Double S stands for safety stock and we need to know the Z-score times the standard deviation of the daily demand, and then times the square root of lead time. For example, just a quick illustration, that if you have shipment or some order records, you'll see that this usually captured on a daily basis for a product. How do you compute this daily means or daily demand and the standard deviation? One way we can do is for the daily demand, you can figure it out, the change it to UD. This is the daily demand. It basically means, when I say mean is the average. We can take the average. For example, this one is data points here. I take the average of these three values. Then standard deviation, in Excel, there is a formula called stdev. Now calculate the standard deviation for the dataset. If you have 10,000 rows for example, or if you're looking at it for six months or a year, you have x number of rows of data. You can do the same thing as what I just did with these three rows of data. Use the average function to calculate the mean and then to calculate the standard deviation using stdev. In this way, we have the mean demand on a daily basis, and then now I have the standard deviation Sigma t, standard deviation of the demand on a daily basis. Then I usually will be given you usually, know whether the time is, you take that standard of the time, then you have the mean demand over the time. Same thing, similar with the R&D. The standard deviation side, where you take the standard deviation on a daily basis times the square root of my Theta. Then, I'll show you how to calculate z-score adn. Using the same example as we did in Module 1, that you demand is 10,000 on an annual basis, you are holding cost of five dollars per item per year. Then, you have the order cost is $10 per order. Then my lead time stay the same at two weeks. My Q optimal I have to follow again to this formula here. It's square root. I'm going to use when the two times my annual demand and then times the order cost divided by the holding cost. Suppose on a square root, so I get 200, same as before. Now, here is to compute safety stock, I need to have these different values that I just mentioned before. Again, to compute the mean of daily demand, I'm going to make an assumption here. I'm going to insert a few more rows. I'm going to move this here, and then this is my Mu and then this is Sigma. Then I'm going to make an assumption. My mean or daily demand, let's say, is 10 and then my standard deviation, maybe 1.5. Now, here you need to, now given assuming that we computed these two values based on the dataset that we have using the average and then the standard deviation stdev formula. Now we can calculate the mean of demand over my lead time. That will be 10 times, my lead time is two. But I need to convert this. It's 10 times 2, but I need to convert it to days. Seven days in a week. I need to make sure to do that. Then you need to make sure the units between my lead time, and then these what their means and Sigmas, where they refer to, is the same. But here because I referred it to as the daily demand in this case, I need to convert weeks into days. That's why I multiply by seven here. Since I didn't do it before out here, but you can do it prior. Then you don't need to do it here. The same here is that my standard deviation of daily demand is 1.5 times square root of 2 times 7. Making sure my units are the same and I get a certain value. This should be here and I get rid of this. Now I computed the mean demand over lead-time and the standard deviation of demand over lead-time. Now I can compute what my safety stock is. But before I do that, I need to also make a claim for my Z value. This Z value has to do with service level. Then I'm going right now to assert a service level. This is what you typically hear if I want to ship at 95 percent, and 95 percent of the time, I want to fulfill my order. In whatever 100, if 100 orders 95 of them will be shipped and packed on time, ready to go. They ship on time either by or before the due date or the ship, the requested date. Let me just do another one so it's clear that to compute Z. You going to use the formula called norms inverse. Then what it asked for is a probability value, so now that now is 95 percent, 0.95. It gives me a 1.64448 and so forth. It's a continuous number, so it all run around forever. We get about approximately 1.64. If you're familiar with the normal distribution, the bell curve, and this is the numbers far or how far away from the mean it is to the right. We're going 1.6448 out. In this case now, I have all the values. I have a Z-score. I know what my standard deviation or our daily demand and I know my lead-time. What I do is now I take this, my Z-score, and then following the formula here, times a daily demand and then times the square root of the lead-time. This is the same as Sigma_d and times the square root L, is the same as the Sigma_L. That is just my standard deviation of demand over the time. I just take that and times this value. It gives me a safety stock value of 9.23. What this means, we calculated ROP before, from previously. That's my demand times the daily demand times the lead-time. I can just take that and then adding the ROP, now the reorder point now is the reorder point that we did in the past, in Module 1 plus the safety stock. Now, we have defined a new reorder point. Now reorder point has the safety stock and value, to buffer. We now understand a bit more on the variabilities in our demand. We took that into account by using the means and the standard deviation to account for the variances. Then in computing safety stock, we also introduced a fulfillment level or service level. What's the level we desire to achieve, and that gives us a value of how much in my distribution if I want to achieve 95 percent, this is the amount of areas under the curve I need to cover. That translated to a safety stock value that we compute. You add this onto it, too while we follow the same formula to calculate the reorder point as before and plus the safety stock. Now, we have the reorder point. Let me just do this. Notice now this is the reorder point with safety stock to account for demand variability. Then you can use the same, ROP here is the same way as we computed before and then adding on safety stock. This is the how to compute the new reorder point value with safety stock to account for the mean variabilities in our system.