Recent Growth in the College's Enrollment Has Been Disproportional Among

Essay

Recent growth in the college's enrollment has been disproportional among her five primary departments. As a result, she is concerned about the mix of faculty and staff within each of the departments. Her concerns have been echoed in some recent staff meetings involving her department heads. This concern prompted a call to the consulting company you work for which in turn led to your assignment to investigate the Dean's problem.
Since the Dean feels the faculty mix and staff allocation is out-of-kilter across the departments, she would like an independent staffing analysis completed. She further wants this analysis completed "in the blind" with respect to her current staffing. Part of her rationale for this blind study concept is to avoid a rampant rumor mill suggesting a consulting was going to be cutting faculty and staff.Since Maxwell is primarily a teaching college, the teaching load among all the faculty is quite high. Naturally, the more senior in academic rank to receive some perks. The faculty teach courses both for students enrolled in their department's programs and to students enrolled in programs within other departments. These courses are referred to as In-Department and Out-Department courses, respectively. The number of In-Department and Out-Department courses per faculty member varies by academic rank and by the department. Within a department, the numbers are consistent among comparable faculty members.
The following data was provided by the Dean.
For the purposes of the study, the Dean suggested using an average of 3 classes per semester per student for In-Department course requirements and 2 classes per semester per student for Out-Department course requirements. The average class size is 20 students per class. For the purposes of the student, you may assume every department offers an equal share of the Out-Department course requirements across all five departments. Naturally, the Dean wants to ensure the staffing study suggests a faculty sufficient to handle to the expected number of courses offered.Through discussions with the Dean, various study goals became apparent and are listed below:

Additional data provided by the Dean pertinent to these goals is provided in the following table:

You have quickly realized that this is a multi-objective linear programming problem to find a solution that will minimize faculty salary costs and to find a solution to maximize the quality of a faculty mix. Since these are competing objectives, once determined, you will need to roll these values into a goal programming model to then interact with the Dean and arrive at a suitable faculty mix solution.
a. Formulate a MOLP for this problem.
b. Implement the MOLP in Excel and use the Risk Solver Platform (RSP) to find solutions. Report the suggested faculty and staff mix to obtain a minimum cost faculty, a maximum quality faculty, and the minimum size faculty required.c. Formulate the GP for this problem.
d. Implement the GP in Excel and solve the model using the Risk Solver Platform (RSP). Report back the suggested faculty and staff mix.
e. Examine the solution obtained in Part d. If any of the goals seem to far out of line, adjust your goal programming weights, resolve and re-examine the suggested solution.
a.Formulate a MOLP for this problem.
b.Implement the MOLP in Excel and use the Risk Solver Platform (RSP) to find solutions. Report the suggested faculty and staff mix to obtain a minimum cost faculty, a maximum quality faculty, and the minimum size faculty required.
c.Formulate the GP for this problem.
d.Implement the GP in Excel and solve the model using the Risk Solver Platform (RSP). Report back the suggested faculty and staff mix.
d. If any of the goals seem to far out of line, adjust your goal programming weights, resolve and re-examine the suggested solution.