Cost-Benefit Problems Revisited
Recall our problem from a prior class.
Example 3: Sylvia Electronics (SE) provides a call center to its customers to assist them in troubleshooting technology problems associated with SE products. Each operator at the call center works eight consecutive hours beginning at one of four shifts. The shifts and the number of operators who need to be staffed to meet call demand are shown below
Shift / Minimum Operators8am - 12 noon / 37
12 noon - 4pm / 32
4pm - 8pm / 42
8pm - 12 mid / 30
12 mid - 4am / 12
Assuming that all operators are paid the same wage, what is the fewest number of operators needed?
Example 5: Now assume that the workers must be given a one hour lunch break after 4 hours. Consider now the distribution of labor hours across the times from 8:00 am to 4:00 am. It will be assumed that the number of operators required between 4am and 5am is 0.
Are the constraints redundant? Can they be reduced to 5 constraints?
What is the cost of the lunch break?
Example 6: (Test yourself) In the SE problem, assume that lunch can be taken after 4 or 5 hours. What is the fewest number of operators needed?
(Hint: How many different types of employees start at 8am?)
Example 7: Returning to the assumptions made in Example 3, assume that operators earn $300 per shift in earning and benefits. However, part-time employees can be hired to work any of the five 4-hour shifts at $120 per shift. Determine the least cost schedule that meets the shift requirements.
Is this solution a surprise? What is left out of the model?
Assume that SE management wants at least one full-time operator for every part-time operator at any point in time. What constraints should we add?
Suppose there should be at least two full-time operators for every part-time one. What constraints should we add?