For Network representation, consider Professors as the Sources/ Supply and Cours

Question

For Network representation, consider Professors as the Sources/ Supply and Courses as the Destination/ Demand

Draw lines between A&UG, A&MBA, A&MS, A&Ph.D. , B&UG, B&MBA, B&MS, B&Ph.D., C&UG, C&MBA, C&MS, D&UG, D&MBA, D&MS, D&Ph.D. (note there is no line between C and Ph.D.) These lines are branches of the network having values of student evaluations as the flows between the nodes representing sources and destinations.

For linear programming formulation define decision variables as binary Xij taking the value 1 if ith Professor is assinged to jth course otherwise it takes the value zero. X34=0 because Professor C(3) can not take Ph.D.(4)

Similarly the parameters student evaluation are represented as Cij for ith Professor taking jth course.

Objective is to have Maximum scores of students evaluation as Z = Sigma(i,j)CijXij

Constraints are in terms of one Professor for one course and as mentioned above X34=0

Therefore, Sigma(i)Xij = 1 for all j=1,2,3,4      and Sigma(j)Xij = 1 for all i=1,2,3,4 and Xij = 0 or 1

Formulation and solution using excel solver is as follows:

Objective is to Maximize CijXij is the SumProduct of matrices representing student evaluations and decision variables.

Changing cells are Xij matrix and constraints are as mentioned above.

Optimal solution using excel solver is as follows:

Evaluation matrix--Cij UG MBA MS Ph.D. A 4.5 4.8 4.4 4.2 B 4.2 4.3 3.9 4.6 C 4.7 4.1 4.3 0 D 4.9 4 4.7 4.4 Decision Variable matrix--Xij UG MBA MS Ph.D. Sum Sign RHS A 1 1 = 1 B 1 1 = 1 C 1 0 1 = 1 D 1 1 = 1 Sum 1 1 1 1 Sign = = = = RHS 1 1 1 1 Objective-Maximize CijXij (SumProduct)= 18.8

Explanation / Answer

1. Analytics department chair will be scheduling faculty to teach courses during the coming fall semester. Four core courses need to be covered. The four courses are at the UG MBA, MS, and Ph.D. levels. Four professors will be assigned to the courses, with each professor receiving one of the courses. Student evaluations of professors are available from previous semesters. Based on a rating scale of 1 to 5, the average student evaluations for each professor are shown in the following table. Professor C does not have a Ph.D and cannot be assigned to teach the Ph.D. level course. If the department chair makes teaching assignments based on maximizing the student evaluation ratings over all four courses, what staff assignments should be made? Course Professor UG MBAMSPh.D 4.5 4.8 4.4 4.2 4.24.33.94.6 4.3 4.94.0 4.7 4.4 4.7 4.1 a) Develop a network representation of this problem b) Formulate a linear programming model for this problem c) Solve the problem by using Excel Solver (Hand-in the value and formulas printouts for the problem)

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