The Silo State IE faculty is dividing its 12 members into 4 teams of 3 to develop
Question:
The Silo State IE faculty is dividing its 12 members into 4 teams of 3 to develop ideas for a long-term strategic plan. Like all faculties, the professors are not all equally compatible with each other. The table below provides a compatibility score (0 bad to 100 good) for each possible pair.
(a) Formulate this team formation task as a binary ILP over professors i = 1c, 12, and decision variables xj = 1 if possible 3-prof team Tj ! 5i1, i2, i36 is included in the plan, and = 0 otherwise. The faculty seeks a maximum total compatibility collection of the 4 chosen teams, where the compatibility value of each possible team Tj denoted hj, is the sum of the 3 table values above for pairs of its members.
(b) How many columns (distinct teams) would the full formulation of
(a) include?
(c) Discuss the challenges in direct solution of the full model, especially if the faculty became much larger.
(d) Explain the possible advantages of approaching the faculty’s task indirectly with Delayed Column Generation Algorithm 13A, starting with a partial master problem including just the columns for teams of profs 1–3, 4–6, 7–9, and 10–12.
(e) Use class optimization software to compute primal and dual optimal solutions to the LP relaxation of this first partial problem.
(f) Outline an adhoc column generation subproblem using the dual LP optimum of
(e) to produce additional columns that could improve the solution.
(g) Manually apply your subproblem design of
(f) to generate 3 new columns likely to improve the solution of (e), and justify your choices in terms of reduced objective values.
(h) Add your new columns of (g) to the partial problem and re-solve its LP relaxation.
Did the solution improve? Why or why not?
(i) Do you think your solution of (h) is close to optimal? Explain.
Step by Step Answer:
