Question

Consider an assignment problem to assign 2? people to do ? jobs (2? ≥ ?). Each job must be assigned to exactly one person. The first ? people (i.e., persons 1,2, ⋯ , ?) are female and the rest (i.e., persons ? + 1, ? + 2, ⋯ ,2?) are male. It costs ??? to assign person ? to do job ? (? = 1, ⋯ ,2?;? = 1, ⋯ , ?). In addition, it is required that the difference between the numbers of male and female employees must be less than or equal to a constant ?. Formulate an integer linear model to minimize the total cost of the assignment.

Answer 1