The lead time is the time from when you decide to produce or order an item until the time at which the item is on hand and ready for sale to the end customer. There are several factors that can cause lead time to vary:  Production delays — If your own production process is variable, this may impact the lead time. In addition, the production process of the products you are ordering may vary. Material defects — If you order 10 units and 2 are defective, you will have to wait for the additional 2 units. Delivery delays — Shipping times can be expected to vary slightly at the best of times, and unexpected events like natural disasters or strikes can further delay delivery. To do so, you will need to adjust your standard deviation of demand to match the lead time period. Multiply your standard deviation of demand (calculated in Part I, step 4) by the square root of the lead time.  This means if you calculated standard deviation on a monthly basis, and lead time was 2 months, you would multiply the standard deviation by the square root of two. Using our previous example, this means: 11 x √2 = 15.56. Make sure to convert lead time to the same unit of time measure that you used to determine standard deviation of demand. For example, if you calculated standard deviation on a monthly basis and lead time was 10 days, you would want to convert lead time to .329 months — i.e. 10 divided by 30.42 (the average days in a month). We can combine formulas to determine safety stock based on demand with lead time factored in as follows:  Safety stock = Z-score x √lead time x standard deviation of demand In our example, to avoid stockouts 95% of the time, you would thus need 1.65 (the Z-score) x √2 (lead time) x 11 (standard deviation of demand) = 25.67 units of safety stock. If demand is constant but lead time variable, then you will need to calculate safety stock using the standard deviation of lead time. In this case, the formula will be:  Safety stock = Z-score x standard deviation of lead time x average demand For example, if aiming for a Z-score of 1.65, with average demand constant at 20 units per month, and lead times over a six month period being 2, 1.5, 2.3, 1.9, 2.1, and 2.8 months, then Safety Stock = 1.65 x .43 x 20 = 14.3 units. If lead time and demand vary independently of one another (i.e. the factors leading to variance are different for each), then safety stock is the Z-score multiplied by the square root of the sum of the squares of demand and supply variability, or:  Safety stock = Z-score x √[(lead time x standard deviation of demand squared) + (standard deviation of lead time squared x average demand squared)] In our example: safety stock = 1.65 x √[(2 x 11squared) + (.43 x 20)squared] = 29.3 units. That is, if the same factors impact lead time and demand variability, you will need to sum the individual safety stock calculations in order to assure yourself of adequate safety stock. In this case:  Safety stock = (Z-score x √lead time x standard deviation of demand) + (Z-score x standard deviation of lead time x average demand) In our example: safety stock = 25.67 + 14.3 = 39.97 units.

Summary: Factor in lead time to account for supply variability. Sync your stock with your supply delivery cycle. Put it all together. Calculate safety stock differently if lead time is the primary variable. Use a third equation to account for independent variation in both lead time and demand. Sum the calculations based on lead time and demand variability if the two factors vary dependently.


Many people over generalize without realizing it. This is toxic to rational thinking. Try to be aware of any over-generalizations you may make in day-to-day life.  Over-generalizations are taking one particular event and seeing it as evidence of how things have always been or always will be. For example, if you do bad on one test you may think, "I'm stupid and always fail at school." In making this statement, you're glossing other academic success you have had in the past in the light of one event.  All-or-nothing thinking is a form of generalizing where you see things in black and white terms. All-or-nothing thinking places things in only one or two categories: good or bad, success or failure, etc. This results in missing the shades of gray in a situation. For example, if you get a mixed review of your performance at work you may see yourself as a failure. In reality, you're likely a competent worker with some areas that need improvement.  Filtering out positive is a thought pattern in which too much focus is placed on the bad aspects of a situation. If 20 good things happen in a day followed by 1 bad thing, you may focus entirely on the negative. For example, say you make a single mistake during a musical performance but otherwise play perfectly. You might be tempted to declare the performance a disaster. In reality, you are probably the only person who noticed a single wrong note. People make assumptions about all kinds of situations. This can lead to unreasonable thinking. Strive to be aware of any assumptions you make.  Sometimes, people engage in mind-reading. That is, you make assumptions about what others think of your or a situation. In reality, it's impossible to know what another person is thinking without asking. For example, you may find yourself thinking "I bet everyone thought I was an idiot in that meeting" or "I bet that co-worker thinks I talk too much." If you notice yourself engaging in such thoughts, try to remind yourself that you are probably not as good at reading people's opinions as you think you are.  Fortune telling is a form of thinking where you think you know what will happen in the future. This can be in the form of a defeatist attitude. For example, "I'll never be able to stick to a diet and lose weight" or "I know I'm going to sound like an idiot during my presentation tomorrow." Keep in mind that, in reality, you cannot know what will happen tomorrow or in the coming weeks. Many people catastrophize situations when they're upset or stressed. For example, you might think you'll be financially bankrupt forever if you need to pay for car repairs one month. If you get rejected romantically, you might decide you're not destined for love. Try to keep in mind that one setback or misfortune is not necessarily indicative of things to come. Oftentimes, people unconsciously read situations in an irrational way. Watch how you think and perceive situations in day-to-day life.  Labeling is the tendency to put a name on a situation. For example, "This person made a mistake" or "I made a bad choice." This leads you to put people and situations into categories based on solitary instances. Try your best not to categorize and avoid the temptation to judge.  Personalization is the tendency to take situations and other people's reactions personally. For example, you may assume a co-worker is mad at you if she doesn't stop to chat in the break room. In reality, she may just be busy. Try not to take situations personally.  Oftentimes, you hold yourself to an unreal ideal. You might see someone else's success as evidence of your shortcoming. Try to keep in mind everyone is different and moves at a different pace.
Summary: Watch for over-generalizations. Do not make assumptions. Avoid catastrophic thinking. Pay attention to how you read situations.