The Universal Manufacturing Company produces a particular product in an assembly-line operation. One of themachines on the line is a drill press that has a single assembly line feeding into it. A partially completed unit arrives at the press to be worked on every 8 minutes, onaverage, according to an exponential distribution. Themachine operator can process an average of 10 parts perhour (Poisson distributed). Determine the average numberof parts waiting to be worked on, the percentage of timethe operator is working, and the percentage of time themachine is idle.

The Universal Manufacturing Company produces a particular product in an assembly-line operation. One of themachines on the line is a drill press that has a single assembly line feeding into it. A partially completed unit arrives at the press to be worked on every 8 minutes, onaverage, according to an exponential distribution. Themachine operator can process an average of 10 parts perhour (Poisson distributed). Determine the average numberof parts waiting to be worked on, the percentage of timethe operator is working, and the percentage of time themachine is idle.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 18P

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The Universal Manufacturing Company produces a particular product in an assembly-line operation. One of the machines on the line is a drill press that has a single assembly line feeding into it. A partially completed unit arrives at the press to be worked on every 8 minutes, on average, according to an exponential distribution. The machine operator can process an average of 10 parts per hour (Poisson distributed). Determine the average number of parts waiting to be worked on, the percentage of time the operator is working, and the percentage of time the machine is idle. The management of Universal Manufacturing Company likes to have its operators working 90% of the time. What must the assembly line arrival rate be in order for the operators to be as busy as management would like?
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