Silo State’s Industrial Engineering faculty is moving to new offices. Professors p = 1,c, 20 will be assigned offices among the r = 1,c, 25 rooms, with unused rooms being left for graduate assistants. Walking distances dr, r  have been computed between all pairs of rooms 1r, r2.

The department head also has collected values cp, p=! the number of times per month each pair of professors 1p, p=2 collaborates in their teaching and research. Now, she would like to pick an assignment of professors to rooms that minimizes the total of collaboration traffic cp, p= # dr, r over all chosen assignments.

(a) Formulate the head’s task as a Quadratic Assignment model 11.16 , using decision variables xp, r!1 if professor p is assigned to room r and = 0 otherwise, together with the model parameters defined above.

(b) Refer to Sections 11.4 and Chapter 14 to justify solving the model heuristically using methods of this chapter because tractable exact solution is unlikely.