Since you need to use the old-style outer join syntax, here is one way (simplified since you did not provide us with sample data and / or table creation scripts):
with assignments as (select 1 assignment_id, 1 person_id, to_date('01/08/2015', 'dd/mm/yyyy') start_date, to_date('03/08/2015', 'dd/mm/yyyy') end_date from dual union all select 2 assignment_id, 1 person_id, to_date('02/08/2015', 'dd/mm/yyyy') start_date, to_date('04/08/2015', 'dd/mm/yyyy') end_date from dual union all select 3 assignment_id, 1 person_id, to_date('06/08/2015', 'dd/mm/yyyy') start_date, to_date('10/08/2015', 'dd/mm/yyyy') end_date from dual union all select 4 assignment_id, 2 person_id, to_date('02/08/2015', 'dd/mm/yyyy') start_date, to_date('03/08/2015', 'dd/mm/yyyy') end_date from dual), employees as (select 1 person_id, to_date('01/08/2015', 'dd/mm/yyyy') start_date, to_date('03/08/2015', 'dd/mm/yyyy') end_date from dual union all select 3 person_id, to_date('01/08/2015', 'dd/mm/yyyy') start_date, to_date('03/08/2015', 'dd/mm/yyyy') end_date from dual) select * from assignments dah, employees emp where dah.person_id = emp.person_id (+) and dah.start_date <= emp.end_date (+) and dah.end_date >= emp.start_date (+); ASSIGNMENT_ID PERSON_ID START_DATE END_DATE PERSON_ID_1 START_DATE_1 END_DATE_1
Are you sure you got your outer join in the right direction? Are you sure that you are not actually using the following:
with assignments as (select 1 assignment_id, 1 person_id, to_date('01/08/2015', 'dd/mm/yyyy') start_date, to_date('03/08/2015', 'dd/mm/yyyy') end_date from dual union all select 2 assignment_id, 1 person_id, to_date('02/08/2015', 'dd/mm/yyyy') start_date, to_date('04/08/2015', 'dd/mm/yyyy') end_date from dual union all select 3 assignment_id, 1 person_id, to_date('06/08/2015', 'dd/mm/yyyy') start_date, to_date('10/08/2015', 'dd/mm/yyyy') end_date from dual union all select 4 assignment_id, 2 person_id, to_date('02/08/2015', 'dd/mm/yyyy') start_date, to_date('03/08/2015', 'dd/mm/yyyy') end_date from dual), employees as (select 1 person_id, to_date('01/08/2015', 'dd/mm/yyyy') start_date, to_date('03/08/2015', 'dd/mm/yyyy') end_date from dual union all select 3 person_id, to_date('01/08/2015', 'dd/mm/yyyy') start_date, to_date('03/08/2015', 'dd/mm/yyyy') end_date from dual) select * from assignments dah, employees emp where dah.person_id (+) = emp.person_id and dah.start_date (+) <= emp.end_date and dah.end_date (+) >= emp.start_date; ASSIGNMENT_ID PERSON_ID START_DATE END_DATE PERSON_ID_1 START_DATE_1 END_DATE_1