=11.15. Jakes Machine Shop contains a grinder for sharpening the machine cutting tools. A decision must now
Question:
=11.15. Jake’s Machine Shop contains a grinder for sharpening the machine cutting tools. A decision must now be made on the speed at which to set the grinder.
The grinding time required by a machine operator to sharpen the cutting tool has an exponential distribution, where the mean 1/ can be set at 1 minute, 1.5 minutes, or 2 minutes, depending upon the speed of the grinder. The running and maintenance costs go up rapidly with the speed of the grinder, so the estimated cost per minute is $1.60 for providing a mean of 1 minute, $0.90 for a mean of 1.5 minutes, and $0.40 for a mean of 2 minutes.
The machine operators arrive randomly to sharpen their tools at a mean rate of one every two minutes. The estimated cost of an operator being away from his or her machine to the grinder is
$0.80 per minute.
E
a. Obtain the various measures of performance for this queueing system for each of the three alternative speeds for the grinder. (Set t 5 minutes in the Excel template for the waiting-time probabilities.)
b. Use the cost figures to determine which grinder speed minimizes the expected total cost per minute.
Step by Step Answer:
Introduction To Management Science A Modeling And Case Studies Approach With Spreadsheets
ISBN: 9780078096600
4th Edition
Authors: Frederick S. Hillier And Mark S. Hillier