Manager A is trying to decide which of 7 tasks he will assign to his 2 assistant

Question

Manager A is trying to decide which of 7 tasks he will assign to his 2 assistants. Naturally, each assistant would be better at some tasks than the other. The following table shows his impression of their potentials (high is good).

Manager A wants to assignthose 7 tasks to the two assistants. However, tasks 1 and 2 are major assignments and should not be assigned to the same assistant. Tasks 3 and 4 are related and should be assigned to the same assistant.

Explain why xj (j=1,...,7; xj= 0 or 1) are appropriate decision variables for this problem and Formulate an objective function to maximize the potential of the assignments.

Explanation / Answer

xi = 0 or 1 is the appropriate decision variable.

Here we can say that 1 implies the task assigned to A and 0 implies the task is assigned to B.

This type decision variable is Binary Decision Variable which is appropriate because in the case above only two assistants are there, of which one has to be assistant each of tasks.

b) Our Objective Function:

Maximize Total Potential of Assignments, Z (say) = 9*x1 + 7*x2 + 8*x3 + 5*x4 + 7*x5 + 6*x6 + 4*x7 + 8*(1-x1) + 9*(1-x2) + 7*(1-x3) + 7*(1-x4) + 8*(1-x5) + 4*(1-x6) + 5*(1-x7)

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