horizon lines, inc. is the nation's leading domestic ocean shipping and integrated logistics company. the company owns or leases a fleet of 20 u.s.-flag containerships and operates five port terminals linking the continental united states with alaska, hawaii, guam, micronesia and puerto rico.horizon lines, inc. is the nation's leading domestic ocean shipping and integrated logistics company. the company owns or leases a fleet of 20 u.s.-flag containerships and operates five port terminals linking the continental united states with alaska, hawaii, guam, micronesia and puerto rico. the company also manages a domestic and overseas service partner network and provides integrated, reliable and cost competitive logistics solutions.