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4. Lead time demand distribution for a product follows a normal distribution which is given in the following table. If it is assumed that the lead time is constant, then how many units of Safety stock are required to provide a service level of 90 percent on any given order cycle? Show it graphically. Lead time Demand 150 200 250 300 350 400 450 Probability 0.01 0.04 0.21 0.55 0.09 0.07 0.03?
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4. Lead time demand distribution for a product follows a normal distri...
Calculation of Safety Stock
To calculate the safety stock, we need to consider the lead time demand distribution and the desired service level. The lead time demand distribution is given in the table as follows:
Lead time Demand Probability
150 0.01
200 0.04
250 0.21
300 0.55
350 0.09
400 0.07
450 0.03
Step 1: Calculate the Mean and Standard Deviation of Demand
To calculate the mean and standard deviation of demand, we multiply each demand value by its corresponding probability and sum them up.
Mean (μ) = (150*0.01) + (200*0.04) + (250*0.21) + (300*0.55) + (350*0.09) + (400*0.07) + (450*0.03)
= 3 + 8 + 52.5 + 165 + 31.5 + 28 + 13.5
= 301.5
Standard Deviation (σ) = √[((150-301.5)^2 * 0.01) + ((200-301.5)^2 * 0.04) + ((250-301.5)^2 * 0.21) + ((300-301.5)^2 * 0.55) + ((350-301.5)^2 * 0.09) + ((400-301.5)^2 * 0.07) + ((450-301.5)^2 * 0.03)]
= √[(30530.25 * 0.01) + (10120.25 * 0.04) + (2950.25 * 0.21) + (202.5 * 0.55) + (2209.25 * 0.09) + (1874.25 * 0.07) + (20736.25 * 0.03)]
= √[(305.3025) + (404.81) + (619.5525) + (111.375) + (198.8275) + (131.1975) + (622.0875)]
= √(2382.1525)
= 48.81
Step 2: Calculate the Z-value
The Z-value corresponds to the desired service level. For a 90% service level, the Z-value can be obtained from a standard normal distribution table or using statistical software. The Z-value for a 90% service level is approximately 1.28.
Step 3: Calculate the Safety Stock
Safety Stock = Z-value * Standard Deviation
= 1.28 * 48.81
= 62.52
Therefore, to provide a service level of 90% on any given order cycle, 62.52 units of safety stock are required.
Graphical Representation
To visually represent the lead time demand distribution and the safety stock, we can create a line graph with the demand values on the x-axis and the corresponding probabilities on the y-axis. The safety stock can be represented as a horizontal line on the graph.
- Plot the
To calculate the safety stock, we need to consider the lead time demand distribution and the desired service level. The lead time demand distribution is given in the table as follows:
Lead time Demand Probability
150 0.01
200 0.04
250 0.21
300 0.55
350 0.09
400 0.07
450 0.03
Step 1: Calculate the Mean and Standard Deviation of Demand
To calculate the mean and standard deviation of demand, we multiply each demand value by its corresponding probability and sum them up.
Mean (μ) = (150*0.01) + (200*0.04) + (250*0.21) + (300*0.55) + (350*0.09) + (400*0.07) + (450*0.03)
= 3 + 8 + 52.5 + 165 + 31.5 + 28 + 13.5
= 301.5
Standard Deviation (σ) = √[((150-301.5)^2 * 0.01) + ((200-301.5)^2 * 0.04) + ((250-301.5)^2 * 0.21) + ((300-301.5)^2 * 0.55) + ((350-301.5)^2 * 0.09) + ((400-301.5)^2 * 0.07) + ((450-301.5)^2 * 0.03)]
= √[(30530.25 * 0.01) + (10120.25 * 0.04) + (2950.25 * 0.21) + (202.5 * 0.55) + (2209.25 * 0.09) + (1874.25 * 0.07) + (20736.25 * 0.03)]
= √[(305.3025) + (404.81) + (619.5525) + (111.375) + (198.8275) + (131.1975) + (622.0875)]
= √(2382.1525)
= 48.81
Step 2: Calculate the Z-value
The Z-value corresponds to the desired service level. For a 90% service level, the Z-value can be obtained from a standard normal distribution table or using statistical software. The Z-value for a 90% service level is approximately 1.28.
Step 3: Calculate the Safety Stock
Safety Stock = Z-value * Standard Deviation
= 1.28 * 48.81
= 62.52
Therefore, to provide a service level of 90% on any given order cycle, 62.52 units of safety stock are required.
Graphical Representation
To visually represent the lead time demand distribution and the safety stock, we can create a line graph with the demand values on the x-axis and the corresponding probabilities on the y-axis. The safety stock can be represented as a horizontal line on the graph.
- Plot the
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4. Lead time demand distribution for a product follows a normal distribution which is given in the following table. If it is assumed that the lead time is constant, then how many units of Safety stock are required to provide a service level of 90 percent on any given order cycle? Show it graphically. Lead time Demand 150 200 250 300 350 400 450 Probability 0.01 0.04 0.21 0.55 0.09 0.07 0.03?
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4. Lead time demand distribution for a product follows a normal distribution which is given in the following table. If it is assumed that the lead time is constant, then how many units of Safety stock are required to provide a service level of 90 percent on any given order cycle? Show it graphically. Lead time Demand 150 200 250 300 350 400 450 Probability 0.01 0.04 0.21 0.55 0.09 0.07 0.03? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about 4. Lead time demand distribution for a product follows a normal distribution which is given in the following table. If it is assumed that the lead time is constant, then how many units of Safety stock are required to provide a service level of 90 percent on any given order cycle? Show it graphically. Lead time Demand 150 200 250 300 350 400 450 Probability 0.01 0.04 0.21 0.55 0.09 0.07 0.03? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 4. Lead time demand distribution for a product follows a normal distribution which is given in the following table. If it is assumed that the lead time is constant, then how many units of Safety stock are required to provide a service level of 90 percent on any given order cycle? Show it graphically. Lead time Demand 150 200 250 300 350 400 450 Probability 0.01 0.04 0.21 0.55 0.09 0.07 0.03?.
4. Lead time demand distribution for a product follows a normal distribution which is given in the following table. If it is assumed that the lead time is constant, then how many units of Safety stock are required to provide a service level of 90 percent on any given order cycle? Show it graphically. Lead time Demand 150 200 250 300 350 400 450 Probability 0.01 0.04 0.21 0.55 0.09 0.07 0.03? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about 4. Lead time demand distribution for a product follows a normal distribution which is given in the following table. If it is assumed that the lead time is constant, then how many units of Safety stock are required to provide a service level of 90 percent on any given order cycle? Show it graphically. Lead time Demand 150 200 250 300 350 400 450 Probability 0.01 0.04 0.21 0.55 0.09 0.07 0.03? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 4. Lead time demand distribution for a product follows a normal distribution which is given in the following table. If it is assumed that the lead time is constant, then how many units of Safety stock are required to provide a service level of 90 percent on any given order cycle? Show it graphically. Lead time Demand 150 200 250 300 350 400 450 Probability 0.01 0.04 0.21 0.55 0.09 0.07 0.03?.
Solutions for 4. Lead time demand distribution for a product follows a normal distribution which is given in the following table. If it is assumed that the lead time is constant, then how many units of Safety stock are required to provide a service level of 90 percent on any given order cycle? Show it graphically. Lead time Demand 150 200 250 300 350 400 450 Probability 0.01 0.04 0.21 0.55 0.09 0.07 0.03? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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