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Optimization of staffing using Linear programming

Dear OTA,

Please provide me a solution with detailed explanation.


The nuclear plant currently has 350 fully trained workers. They need to know how many worker are 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 Excel Solver.


Solution Summary

This step by step detailed solution uses linear programming and MS excel for solving staffing problem. Excel file is also attached for reference.