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In: Operations Management

Problem 17.3: the ideal cycle time of an assembly machine is 5 sec. the parts feeder...

Problem 17.3: the ideal cycle time of an assembly machine is 5 sec. the parts feeder at one of the workstations has a feed rate of 75 components/min and the probability that the components will pass through the selector is 18%. The active length of the feed track (where the high-level sensor is located) is 350 mm. the low-level sensor on the feed track is located 100 mm from the station work head. The components have a length of 12.5 mm in the feed track direction, and there is no overlapping of parts.

(a) How long will it take for the supply of parts to be depleted from the high-level sensor to the low-level sensor once the feeder-selector device is turned off?

(b) How long will it take for the parts to be resupplied from the low-level sensor to the high-level sensor, on average, after the feeder-selector device is turned on and turned off?

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Expert Solution

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a)Write the relation to calculate the time to deplete from higher level to lower level sensor once the feeder selector is turned off.

…… (1)

Here, is the depletion time, is the cycle rate, is the number of components in feed track at higher level sensor, and is the number of components in feed track at lower level sensor.

Calculate the number of components in feed track at lower level sensor.

Calculate the number of components in feed track at higher level sensor.

Calculate the cycle rate.

Here, is the cycle time.

Substitute for .

Substitute for , for , and for in the equation (1).

Hence, the time to deplete from higher level to lower level sensor once the feeder selector is turned off is .

b)Write the relation to calculate the time to resupply from lower level to higher level sensor once the feeder selector is turned on.

Hence, is the time to resupply, is the frequency, and is the probability that the components will pass through the selector.

Substitute for , for , and for .

Hence, the time to resupply from lower level to higher level sensor once the feeder selector is turned on is .

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keosha answered 1 week ago

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