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Detroit Steel Ltd has just accepted an order to produce 500 pieces of a new component. Each piece will require 7 operations in the production process. The product manager, Roger Clark, has promised delivery within three weeks, which means that the production time between starting the job and having the batch ready for shipping would have to be no more than 15 days (360 hours), assuming it could be started at 10 am tomorrow.
“Can we start this order tomorrow at 10 am, Pete, and can it be done within 360 hours?” Roger inquired of his production scheduler, Pete Williams.
“Yes, there’s no problem with starting at 10 am tomorrow, but I do not know whether we will be able to finish it in 360 hours. We have not done a job exactly like this before. If you areworried, why don’t you designate it as a ‘rush’ order? We can save a few hours through having a ‘progress-chaser’ assigned to an order.”
Roger was reluctant to commit himself to the ‘rush’ designation. The allocation of a ‘progress chaser’ would cost an extra $1,000 and he was not convinced that it would actually make any difference. He had some data on the previous 20 orders of a similar nature (Table 2) and decided to see if he could somehow estimate the required time.
TIME = time to complete the job
PIECES = number of pieces in the job
OPS = number of operations per piece
RUSH = a dummy variable equal to 1 if the job is a ‘rush’
1. What is the estimated model (equation) that relates production time to the number of pieces in an order, the number of operations per piece and whether they were “rushed”? Should any variables be deleted from the model? How useful is the model as a whole for prediction?
2. What is the average effect of designating an order as a “rush”?
Create an additional variable—OPS*PIECES— by multiplying number of pieces in the job by number of operations per piece. Run new regression analysis. Explain the results.
4. Try to improve your model by removing irrelevant variables. Run new regression analysis. Explain the results.
5. What is your assessment of the time this order is going to take? Explain your view. Should Roger designate it a ‘rush’ order? Why or why not? Are there other assumptions of regression analysis you would like to check before accepting the above conclusions?
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