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# Personnel Linear Programming problem in POM-QM

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The nuclear plant currently has 350 fully trained workers. They need to know how many workers need to be trained for the remainder if the year.

Month Personnel Hours Needed
August 40,000
September 45,000
October 35,000
November 50,000
December 45,000

The law permits no more than 130 hours per month per employee. Slightly over 1 hour per day is used for check-in and check-out, record-keeping and for daily radiation scans. Policy is that no layoffs are permitted in those months when the plant is over staffed. So, if more workers are trained than are needed in any month, they are still paid but not required to work the 130 hours.

Trainees must be hired 1 month before they are needed. Each trainee teams up with a skilled worker and requires 90 hours of that employee's time. This mean the skilled worker is not available for those 90 hours during this month.

There is a turnover rate of trained workers of 5% per month. (5% of the trained employees at the start of the month resign by the end of the month) A trained worker earns an average of \$2,000 per month, regardless of the number of hours worked. Trainees are paid \$900 during their one month of instruction.

1. Formulate this staffing problem using LP.
2. Solve the problem. How many trainees must begin each month?
3. Submit the problem in POM-QM Software format.

##### Solution Summary

Descriptive answers to each question and a POM-QM .lin file with solution, which will open in the POM-QM software. Also, a screenshot of the problem setup and solved in POM-QM.

##### Solution Preview

Student, Attached is a POM-QM .lin file with your solution which will open in the POM-QM software. Also, attached is a screenshot of the problem set up and solved in POM-QM.

1. Formulate this staffing problem using LP.
Let Xi = no. of trained workers available at start of Month i
Yi= No of trainees beginning at the start of month i,
Where i=1(August), 2(September), 3(October), 4(November) and 5(December)
This problem is that of minimizing the total salaries paid to the Staff:
The full time trained workers get \$2000 while the trainee gets \$900 during the training month.

Thus, The objective function is :
Minimize Total salaries ...

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