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8-37 Every year the U.S. Navy must plan the reassignment of thousands of sailors finishing one tour of duty in specialties i=1,,300 and preparing for their next one, k. The reassignment may also require a move of the sailor and his or her dependents from present base location j=1,,25 to a new base . To plan the move, personnel staff estimate numbers si,j of sailors at base j in specialty i who are ready for reassignment, dk, of sailors needed at base in specialty k, as well as average costs cj,l of moving a sailor and dependents from base j to base . Training is required for the new position if it involves a different specialty than the present one, and capacity limits uk at training schools limit the number that can be trained for any specialty k during the year. One Navy objective in planning reassignment is to keep total relocation costs as low as possible. However, other considerations arise from the fact that full staffing levels dk, can almost never all be met. Naturally, the Atlantic fleet (bases j,=1,,15) wishes to maximize the fraction of its slots actually filled, and the Pacific fleet (bases j,=16,,25 prefers to maximize the fraction of its needs accommodated. Formulate a 3-objective LP model to aid the Navy in planning reassignments using the decision variables xi,j,k,l number of sailors presently in specialty i at base j reassigned to specialty k at location 8-37 Every year the U.S. Navy must plan the reassignment of thousands of sailors finishing one tour of duty in specialties i=1,,300 and preparing for their next one, k. The reassignment may also require a move of the sailor and his or her dependents from present base location j=1,,25 to a new base . To plan the move, personnel staff estimate numbers si,j of sailors at base j in specialty i who are ready for reassignment, dk, of sailors needed at base in specialty k, as well as average costs cj,l of moving a sailor and dependents from base j to base . Training is required for the new position if it involves a different specialty than the present one, and capacity limits uk at training schools limit the number that can be trained for any specialty k during the year. One Navy objective in planning reassignment is to keep total relocation costs as low as possible. However, other considerations arise from the fact that full staffing levels dk, can almost never all be met. Naturally, the Atlantic fleet (bases j,=1,,15) wishes to maximize the fraction of its slots actually filled, and the Pacific fleet (bases j,=16,,25 prefers to maximize the fraction of its needs accommodated. Formulate a 3-objective LP model to aid the Navy in planning reassignments using the decision variables xi,j,k,l number of sailors presently in specialty i at base j reassigned to specialty k at location

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