A personnel selection problem.
(a) A contractor is assembling a crew with six positions. The contractor will select the six people from among a dozen of the firm's employees who are willing to travel. Each of the dozen people who are eligible for the assignment has been ranked according to effectiveness in each of the six slots. The selection problem is to choose the six crew members from the 12 eligible employees in such a way that the crew's total effectiveness is maximized. You are given the effectiveness eij of the ith eligible employee in the jth position on the crew’s in all 72 parameters. The decision variables are
Xij- 1, 0; it is 1 if eligible employee i is chosen for the jth job on the crew, and 0 otherwise.
Formulate this problem as a zero-one programming problem. Suppose this problem was solved as a continuous or relaxed linear programming problem, that is, with the variables only constrained to be greater than or equal to zero. what evidence do you have that this problem. solved.." a continuous I P, will solve- with all variables equal to zero or one?
(b) As an added feature of this problem, The particular set of employees are well known to one another and not all of them get alone In particular employee five and employee nine, though individually valued by the company, have a to longstanding dislike for one another, a dislike that makes them ineffective when working together and disruptive of the work. of others. You still want to assemble the most effective crew hut now you need to create a crew that does not have both employees five and nine
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