“Wins above replacement,” or WAR, is a complex statistical measure of a major league baseball player’s performance that sums up a player’s total contribution to a team using various offensive and defensive statistics. It reflects the number of additional wins a team has gained with a player relative to the number of expected wins with a replacement level player at a minimal cost. The highest WAR measure for a player last season was 10.0. The Sox’s general manager is evaluating 10 free agent players to possibly sign to contracts for next season. Following are the WAR measures (from last season), contract demands, and ages of these players.

Player WAR Contract $

(millions)

Contract Years Age Mike Bass 4.6 2.1 1 25 Josh Donald, p 3.7 10.0 1 28 Miguel Gomez 5.9 17.4 2 31 Carlos Cabrera 9.1 24.0 5 32 Matt Carper, p 7.2 18.0 3 34 Evan Longier 4.3 4.3 1 27 Paul Goldsmith 2.7 3.1 1 36 Joey Veto 5.2 16.5 3 29 Robinson Canoe 8.1 24.0 6 28 Matt Fists, p 7.5 9.3 2 31 For those players bargaining for multiyear contracts, the dollar values are spread equally over the years of the contract. The general manager has some specific guidelines for signing new players.

Donald, Carper, and Fists are pitchers and the general manager wants to sign at least one pitcher.

He wants to limit the contracts’ dollars for next season to $34 million, and the overall value of the contracts to not exceed $55 million in order to remain under the league salary cap (and not be taxed for exceeding the cap). He does not want the average contract length to exceed 2.5 years, and he wants the average age of the players he signs to be 31 years or less.

Formulate and solve an integer programming model to determine which players the general manager should sign to contracts in order to maximize the overall WAR of the players.

 LO.1