Linear programming :Staffing problem
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A power plant has just announced it's opening on August 1. It's HR department has been asked to determine how many techicians need to be hired and trained during the remainder of the year.
The plant currently employs 350 fully trained technicians and projects the following personnel needs
MONTH man hours needed
August 40000
September 45000
October 35000
November 50000
December 45000
By state law, a utility employee can work no more than 130 hours/month. (slightly over one hour per day is used for check-in check-out and safety scans of employees).
Policy at this company also requires that layoffs are not acceptable in months when the plant is overstaffed. So if more trained employees are available than needed in any month each worker is still fully paid, even though he or she is not required to work the full 130 hours.
It takes one month of one-on-one classroom instruction, before a technician is permitted to work alone in the plant. Therefore the plant hires emplyees one month before they are needed. Each trainee teams up with an existing employee for training and requires 90 hours of that employees time. This implies that 90 hours less of that employee's time are available for doing actual work in the plant.
HR records indicate a turnover of trained technicians at 5% per month.
This means 5% of employees at the start of the month resign at the end of the month. A trained employee earns an average salary of $2000 (regardless of the number of hours worked, as noted earlier). Trainees are paid $900 during their one month of instruction.
(a) Formulate this staffing problem using LP.
(b) Solve the problem. How many trainees must begin each month.
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The mathematical formulation of staffing problem is given with explanations and workings. The formulation and optimal solution is available in excel file.
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