Narrative:

Aircraft X was departing on a westbound heading eventually wanting to turn south to go out our south departure gate. I had numerous aircraft inbound from the southwest on our RNAV arrival. The first in line was the citation who was landing ZZZ which is 5 miles northwest of ZZZ1. The plan was to keep the citation eastbound in the ZZZ1 flow and turn him northbound once east of ZZZ1 to set them up for final at ZZZ. I told them my plan and few moments later they requested to turn because if they went east of ZZZ1 they would run into a minimum fuel situation. I then turned them north heading 340 and turned aircraft X south heading 250 to get them ready for a turn south in front of the next aircraft on the RNAV arrival. I couldn't turn them south immediately due to the aircraft Y VFR overflight at 6;500 [feet] south of the airport heading west northwest bound. I saw that my initial heading for aircraft X was bad and would conflict with the citation; so I corrected to a 210 [heading] which was going to tighten things up even more with the VFR overflight. I then decided to give aircraft X a hard left turn heading 100 to avoid everybody. As the citation was descending and aircraft X was turning and climbing; I believe they passed around 2 miles on non-converging courses around 6;000 feet and the same for aircraft X and aircraft Y at around 6;500 feet. Aircraft X advised they received an RA on both the citation and aircraft Y. The citation also advised they received an RA on aircraft X.the citation's request to turn north due to low fuel threw me off. I was getting pinched from a few different directions. It was busy. The heat had all the aircraft preforming slower than usual and I thought I had more time to make my initial plan work than what I did. We were split north and south. I believe we definitely needed final open but due to low staffing it wasn't. It's [event] week so our west side airspace had our supervisor's attention due to its traffic volume and complexity. I am sick to my stomach about this one. I am not very happy about my decision making. I know I could have and can do a lot better. I also feel like extremely low staffing with no end in sight coupled with 6 day work weeks for the last 3 years and most likely for the rest of my career is severely increasing burn out amongst the controllers here and devastating their morale. There are multiple days throughout the week that we cannot staff the facility to our minimum number of people with everyone here working mandatory overtime and this happens on a weekly basis but our facility is somehow still above the national average and is eligible to still lose fully certified controllers to facility transfers. Something is seriously broken with this system and I'm afraid it's not going to be addressed until something tragic takes place to get FAA to pay attention.

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Original NASA ASRS Text

Title: A TRACON Controller reported vectoring an arriving aircraft which was approaching minimum fuel into confliction with a departing aircraft and a VFR enroute aircraft causing two of the aircraft to respond to RA's.

Narrative: Aircraft X was departing on a westbound heading eventually wanting to turn south to go out our south departure gate. I had numerous aircraft inbound from the southwest on our RNAV arrival. The first in line was the Citation who was landing ZZZ which is 5 miles northwest of ZZZ1. The plan was to keep the Citation eastbound in the ZZZ1 flow and turn him northbound once east of ZZZ1 to set them up for final at ZZZ. I told them my plan and few moments later they requested to turn because if they went east of ZZZ1 they would run into a minimum fuel situation. I then turned them north heading 340 and turned Aircraft X south heading 250 to get them ready for a turn south in front of the next aircraft on the RNAV arrival. I couldn't turn them south immediately due to the Aircraft Y VFR overflight at 6;500 [feet] south of the airport heading west northwest bound. I saw that my initial heading for Aircraft X was bad and would conflict with the Citation; so I corrected to a 210 [heading] which was going to tighten things up even more with the VFR overflight. I then decided to give Aircraft X a hard left turn heading 100 to avoid everybody. As the Citation was descending and Aircraft X was turning and climbing; I believe they passed around 2 miles on non-converging courses around 6;000 feet and the same for Aircraft X and Aircraft Y at around 6;500 feet. Aircraft X advised they received an RA on both the Citation and Aircraft Y. The Citation also advised they received an RA on Aircraft X.The Citation's request to turn north due to low fuel threw me off. I was getting pinched from a few different directions. It was busy. The heat had all the aircraft preforming slower than usual and I thought I had more time to make my initial plan work than what I did. We were split north and south. I believe we definitely needed final open but due to low staffing it wasn't. It's [Event] week so our west side airspace had our Supervisor's attention due to its traffic volume and complexity. I am sick to my stomach about this one. I am not very happy about my decision making. I know I could have and can do a lot better. I also feel like extremely low staffing with no end in sight coupled with 6 day work weeks for the last 3 years and most likely for the rest of my career is severely increasing burn out amongst the controllers here and devastating their morale. There are multiple days throughout the week that we cannot staff the facility to our minimum number of people with everyone here working mandatory overtime and this happens on a weekly basis but our facility is somehow still above the national average and is eligible to still lose fully certified controllers to facility transfers. Something is seriously broken with this system and I'm afraid it's not going to be addressed until something tragic takes place to get FAA to pay attention.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.