Hamburger SV

Due to the bad performance in the season, Hamburger SV football club wants to hire up to three new players. There are five players under consideration. If player { is hired he will cost an amount of er. The potential contribution to the total strength of the team in defense, midfield, and offense is quantified by a parameter d, my, and of for each player i. Hamburger SV wants to strengthen the team in defense, midfield, and offense by the given total values D, M, and O. Players 2 and 3 must not be hired together because they are personal enemies. Players 1 and 2 have already played together and would strengthen the defense by a value of diz which is larger than di + da if both players are hired. Players 1 and 4 cannot play well together, so the midfield would only be strengthened by a value of my , which is smaller than m, + my if both players are hired. Players 3 and 5 can play well together in offense but not in defense, so the offense would be strengthened by a value of os , which is larger than of to; and the defense by a value of das which is smaller than do + d if both players are hired. Formulate an integer program for minimizing the total costs of strengthening the team in defense, midfield, and offense by the given total values D, M, and O.

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