Local shop expects to sell 1000 unit annually for a product. However, the demand during the lead time has been observed uncertain with normally distributed mean of 30 units and a standard deviation of 10 units. Each ordering results a cost of 25 OMR and annual holding cost per unit is 20 percent of the unit price. Price per unit is 15 OMR. Assuming there are 240 workdays, if the firm is willing to accept only 2 stockouts per year then what is the probability of having a stockout in any cycle during the year, assuming continuous review policy?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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