Probabilistic Capacity Planning The XYZ Chemical Company estimates the annual demand for a certain product as follows: Thousands of Gallons 100 110 120 130 140 Probability .10 .20 .30 .30 .10 a. If capacity is 130,000 gallons, how much of a capacity cushion is there? b. What is the probability of idle capacity? c. If capacity is 130,000 gallons, what is the average utilization of the plant? d. If lost business (stockout) costs $100,000 per thousand gallons and it costs $5,000 to build 1000 gallons of capacity, how much capacity should be built to minimize total costs?
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!
Probabilistic Capacity Planning The XYZ Chemical Company estimates the annual demand for a certain product as follows:
Thousands of Gallons 100 110 120 130 140
a. If capacity is 130,000 gallons, how much of a capacity cushion is there?
b. What is the probability of idle capacity?
c. If capacity is 130,000 gallons, what is the average utilization of the plant?
d. If lost business (stockout) costs $100,000 per thousand gallons and it costs $5,000 to build 1000 gallons of capacity, how much capacity should be built to minimize total costs?
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