Safety Stock Part 1 (Video 27)

Safety Stock Part 1 (Video 27)



hello again welcome back to operations management and we're continuing with inventory in this session we're going to be working on calculating safety stock and I know that I say part 1 because safety stock is a long thing to talk about so we're going to do it in two parts let's get started as we recall inventory has costs associated with it in terms of holding on to it as well as capital cost which means if money is tied up in inventory we can't use it for anything else we also know that if we don't have enough inventory it could cause a disruption in our manufacturing because we may not be able to have enough inventory to manufacture goods or we won't have the product to provide customers with so we won't be able to meet demand so what we have to figure out is how much safety stock to keep to do this we need to understand a few terms first is stock out stock out means that we are not able to meet demand it's just not there it's not on the shelves it's not in the warehouse another term the cycle service level sometimes just called the service level is that the probability that we will not run out of items so the probability that there will not be a stock out is our service level and safety stock which is a term I've used before is just extra inventory that we hold onto beyond what we expect to use when we go about calculating safety stock we tend to would make the following assumption and that is that the lead time demand can be represented by the normal distribution and it's represented by using the mean of that distribution and its standard deviation so we'll actually get two terms when we're thinking about safety stock we'll get the lead time demand which is the average amount we're going to use and the standard deviation of the lead time demand which represents the variation in demand and when we think about service level it's the probability that the amount we use is actually going to be less than or equal to the amount we have on hand which is their reorder point which also means that our service level equals one minus the probability of running out the probability of a stock out so if we take a look at that normal distribution you'll recognize the standard bell curve but we're going to add a few things to it the center line of this curve is the average amount that we use this is a lead time demand this is what we expect to use during the time we place the order to the time its received but there's also the probability of a stock out and what we need to do is we need to have extra inventory which becomes our safety stock to prevent the probability of a stock out so if the red area is our probability of a stock out then the other area the light green area is our service level because if you recall the entire area under the curve equals one so one minus the probability of a stock out is our service level so what we do is to calculate that extra inventory our safety stock sometimes known as I sub S or I sub safety we need to use the standard deviation and we're trying to figure out how many standard deviations above the mean which is their Z statistic so when we get to our reorder point we're going to have our lead time demand plus that safety stock so our safety stock equals the number of standard deviations above the mean so that our lead time demand plus our safety stock equals a reorder point and so that entire area under the curve not the red part is our service level so to recap our service level is a probability that the amount we use is going to be less than or equal to a reorder point and our service level equals or 1 minus the probability of a stock out so to Firmin our safety stock we're going to need a value for Z because we need to know how many standard deviations above the mean so we're going to have to use either a normal distribution table or Excel my preference is always for Excel because it's a lot easier to plug in the numbers use the formula and get your calculation for Z as opposed to looking up tables so the formula we're going to use is norms inverse n au RMS inv I'm going to input the probability of not having a stock out which is their service level and that will give us our Z statistic so our safety stock becomes Z times the standard deviation of the lead time demand now sometimes we already know the safety stock and the standard deviation of lead time demand and we need to calculate what the service level is so we need to work backwards in this case if we know the safety stock and the standard deviation of the lead time demand our Z equals our safety stock divided by that standard deviation and once we know the Z statistic we can again use a table or Excel to calculate the service level so our service level equals the norms distribution and orm SD is t offer z statistic once we use Excel so let's do a problem Jordan is trying to figure out how much extra inventory of cables to keep during the past year the mean lead time demand ltd for the cable was 105 with a standard deviation of 12 jordan would like to maintain a 90 percent service level so what is the recommended safety stock what is our reorder point and if Jordan keeps 20 cables safety stock what is the service level so here you see that we have a value for our mean lead time demand of 105 and we have a standard deviation of 12 and we're trying to maintain a 90 percent service level using this information we can calculate the safety stock we're going to calculate the Z statistic and then multiply it by the standard deviation of the lead time demand going into Excel we're going to use the norms in Formula and use 90 percent as our service level to get a Z statistic equaling one point two eight so we calculate the safety stock one point two eight times 12 and that's fifteen point three seven we always round up when we're dealing with safety stock so fifteen point three seven becomes sixteen so our reorder point is our lead time demand plus the safety stock so we knew the lead time demand is 105 we add to it the safety stock of 16 so we get a total of 121 so when we're thinking about it we're watching the inventory as soon as we get down to 121 cables in inventory we place our order for a new set of inventory now let's say Jordan wants to keep 20 on-hand how does that safety stock of 20 mean in terms of our service level so now that we know that the safety stock is 20 we can go backwards and calculate the z-statistic safety stock divided by the standard deviation of the lead time demand is one point six seven now we use the n o RM SD ist no mr. butan within Excel using Z of one point six seven and we find out that the service level is 0.95 to two so holding a safety stock of 20 is going to increase our service level the more safety stock you have the higher your service level will be now in our next session we're going to figure out how to calculate the standard deviation of lead time demand sometimes it's not given sometimes we just know that there's a variation in demand and sometimes there's a variation in both the lead time and the demand so we'll cover that in the next session I'll see you then

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