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Modeling and Optimization : Staffing Levels

Scheduling staff. You are the director of the Computer Center for Gaillard College and rewponsible for scheduling the staffing of the center, which is open from *a.m. until midnight. You have monitored the usage of the center at various times of the day and determined that the following number of computer consultants are required:
Time of day Minimum # of Consultants required to be on duty
8am-noon 4
Noon-4pm 8
4pm-8pm 10
8-midnight 6
Two types of computer consultants can be hired: full-time and part-time. the full-time consultants work for eight consecutive hours in any of the following shifts: morning (8am -4pm), afternoon (noon-8pm), and evening (4pm-midnight.) Full-time consultants are paid $14 per hour.
Part-time consultants can be hired to work any of the four shifts listed in the table. Part-time consultants are paid $12 per hour. An additional requirement is that during every time period, at least one ful-time consultant must be on duty for every part-time consultant on duty.
a. Determine a minimum-cost staffing plan for the center. How many full-time and part-time consultants will be needed? What is the minimum cost?
b. After thinking about this problem for a while, you have decided to recognize meal breaks explicitly in the scheduling of full-time consultants. In particular, full-time consultants are entitled to a one-hour lunch break during their eight-hour shift. In addition, employment rules specify that the lunch break can start after three hours of work or after four hours of work, but those are the only alternatives. Parttime consultants do not receive a meal break. Under these conditions, what staffing schedule minimizes costs? What is the minimum cost?

Solution Summary

Modeling, optimization and staffing levels are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.