Senior design students are negotiating which of the four members of the team will take primary reponsibility for each of the four project tasks the team must complete. The following table shows the composite ratings (0 to 100)

they have prepared to estimate the ability of each member to manage each task.

The team wants to find a maximum total score plan that allocates exactly one task to each team member.

(a) Formulate a linear assignment problem (LP) to choose an optimal plan.

(b) Use class optimization software to compute an optimal assignment.

(c) Show that your assignment problem can be represented as a minimum total cost flow model by sketching the corresponding bipartite digraph and labeling as in Exercise 10-1.

(d) A feasible assignment must have decision variables = 0 or 1 in part (a), yet the model can be solved as a linear program.
Explain how the underlying network nature of the problem makes this possible.

Transcribed Image Text:

Task Rating Member 1 2 3 4 1234 90 2 11 77 45 69 71 50 89 3 88 90 85 93 4 40 80 65 39