PROBLEM 3: Network Models

The coach of a swimming team must select swimmers for a relay team taking part in the 200 metre mixed medley for the next Junior Olympic Games. Since most of the best swimmers are the fastest in more than one event, it is not clear which swimmer should be assigned to each of the four strokes. The fastest swimmers and the best times (in seconds) obtained by each swimmer for each of the strokes (over a distance of 50 metres) are given in the following table.

Question 1:

Draw a network to represent this situation as an assignment problem in which each swimmer is assigned to exactly one stroke and each stroke is done by exactly one swimmer. You may add dummy demand nodes to make sure that the requirement of an assignment problem is met.

Question 2:

Provide the mathematical formulation based on the network model in Question 1 above in order to select the swimmers for the relay team. Define the variables, objective function, and the constraints. Provide a feasible, i.e., not necessarily optimal, solution and calculate the value of the objective function for this solution.