A producer of industrial climate control modules has recently changed to cellular manufacturing. The production facility operates 360 days per year and has annual demand of 10,300 units. They can produce up to 75 modules each day. It costs $20.85 to set up a work cell to produce this module. The cost of each module is $44 and annual holding costs are $4.90 per unit. Setup labor cost is $15 per hour. What is the optimal size of the production run for this module? (Display your answer to the nearest whole number). Given your answer to the previous question, how many production runs will be required each year in order to meet the annual demand? (Round your answer UP to the next whole number.) How much time (in minutes) does it take to set up a work cell? (Display your answer to the nearest whole number.) Suppose the main customer for this module wants to purchase in quantities of 50 units. What is the required setup time (in minutes) to make this order quantity an optimal production run quantity? (Display your answer to the nearest whole number.)
Question
A producer of industrial climate control modules has recently changed to cellular manufacturing. The production facility operates 360 days per year and has annual demand of 10,300 units. They can produce up to 75 modules each day. It costs 44 and annual holding costs are 15 per hour. What is the optimal size of the production run for this module? (Display your answer to the nearest whole number). Given your answer to the previous question, how many production runs will be required each year in order to meet the annual demand? (Round your answer UP to the next whole number.) How much time (in minutes) does it take to set up a work cell? (Display your answer to the nearest whole number.) Suppose the main customer for this module wants to purchase in quantities of 50 units. What is the required setup time (in minutes) to make this order quantity an optimal production run quantity? (Display your answer to the nearest whole number.)
Solution
To answer these questions, we need to use the Economic Production Quantity (EPQ) model.
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The optimal size of the production run (Q*) can be calculated using the formula:
Q* = sqrt((2DS)/H(1-d/p))
where: D = annual demand = 10,300 units S = setup cost = 4.90 d = demand rate = D/360 = 10,300/360 = 28.61 units/day p = production rate = 75 units/day
Substituting these values into the formula, we get:
Q* = sqrt((21030020.85)/(4.9*(1-28.61/75))) = 283 units (rounded to the nearest whole number)
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The number of production runs required each year (N) can be calculated as:
N = D/Q* = 10300/283 = 36.4
Since we can't have a fraction of a production run, we round this up to the next whole number, which is 37 runs.
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The time it takes to set up a work cell can be calculated by dividing the setup cost by the setup labor cost per hour and converting it to minutes:
Setup time = S/(Setup labor cost per hour) * 60 = 20.85/15 * 60 = 83 minutes (rounded to the nearest whole number)
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If the customer wants to purchase in quantities of 50 units, we need to find the setup time that would make this the optimal production run quantity. We can rearrange the formula for Q* to solve for S:
S = H(1-d/p)Q*^2/2D
Substituting Q* = 50 units and the other known values, we get:
S = 4.9*(1-28.61/75)50^2/(210300) = $1.59
Then we can calculate the setup time as before:
Setup time = S/(Setup labor cost per hour) * 60 = 1.59/15 * 60 = 6 minutes (rounded to the nearest whole number)
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