My mother has Alzheimer's, more on the severe case. She walked out of the house the other night and neither my father or I knew. Any suggestions?

All I did was fix several 'dummy' handles to the inside of the door, and my husband never managed to find the real one! you could put some on the hinge side as well ......

"10 Lifesaving Location Devices for Dementia Patients" ... see ...
https://www.alzheimers.net/8-8-14-location-devices-dementia

Someone NOW Needs to Take the Bull by the Horns, She will get Worse...Discuss Care at Home or a facility Best from the Rest.

I've read (didn’t need to use) if you put a lock higher than normal, they don’t think to look up. We were going to do this on all the outer doors but my stepfather never wandered

There are door alarms that can be purchased. I picked mine up at a Home Depot.
However, what I found most useful were sleigh bells.
Dad had an antique ring of sleigh bells (from somewhere in his past) that I looped over the door.
He didn’t question it and my mother could hear those bells if Dad tried to open the door.

Bless you and good luck. The road you are on is not easy. Been there twice!

If feasible, install a lock that requires a key to open from inside the house and then keep the key with you. I do that at our house because my husband sometimes wants to leave at night.

Zmodo motion detection camera costs $30 @ Walmart.com. No monthly charge. Download app on your phone or as many phones as you like, and when motion is detected your phone will alert you. This had been great for my dad with dementia.

Ring Door Bell.

Moms door had a round knob. So I bought baby covers. They just go around and around. Theres a way to open the door but Mom never found it. My cousin put dead bolt key locks on his doors. His Dad was never alone. After he passed, cousin had locks removed. Had to do with the fire code.

There are basically reverse alarm type systems that have an "eye" that will alert you when someone walks by it so when someone goes through the door for instance you can get an alert on your phone and other devices. There is also at least one system that incorporates a bunch of things including an easy to use computer screen type thing that enables all kinds of access but I think that's more for elders still living on their own who need some supervision just not necessarily hands on but it has a monthly charge and I don't think it's inexpensive. Some of the other devices that you can monitor through your phone don't need a monthly fee. We have a camera that looks at moms parking area that detects motion and sends an alert so we can look to see who has driven in or out it would work on the front door too, I got it pretty inexpensively from Amazon. We also recently installed a Ring doorbell, they have several types of devices I think, and it sends an alert when it detects motion in front of it and anytime the door is opened and a different alert when someone rings the doorbell. That would work well for your purposes too, it's more expensive but also allows us to communicate with someone at the door. You can purchase cloud storage for both of those I think for a monthly fee but you don't need that to have it work, especially for your purposes I would think. Our camera over mom's "medicine" table stores 24 hrs worth of clips taken whenever it senses motion and we can watch it live anytime, I don't have alerts on that.

I purchased an inexpensive alarm system for our house. It works. It has wireless switches at the doors and a central unit that just plugs into a wall outlet and I also ordered a pager that goes with it. It is a local pager that I wore around the house. No service company involved. It worked for us. but you have to live in the house for you to be contacted. It has a list of other attachments that can be added to it, like mats and motion sensors.
I also installed some little flip locks on the doors and Luz never figured out how to use them.

Medical supply stores have products that you can place in the bed, a light layer, that nobody can feel as uncomfortable, and even on chairs, if there is a recliner or lift chair for your LO, that will ring an alarm when someone tries to move out of the bed or the chair. Problem is, they are very sensitive things, so they may ring the alarm more than you want.

I don't know if anyone has this product, but someone should. If you can place an area rug on both sides of the bed, a thin one, one that nobody would trip over (tape it to the tile or carpet, whatever), and place a alarm based thin liner under it.......that would always let you know when your LO got out of bed once you were off on your own in bed.

Here are articles about wandering: 
https://www.agingcare.com/articles/products-and-strategies-for-managing-dementia-wandering-142801.htm
(Please note that I do not think the suggestion of locks on the outside doors is appropriate.)

https://www.agingcare.com/articles/wandering-alzheimers-patients-142875.htm

Visual deterrents such as STOP SIGNS that hang ACROSS DOORWAYS and Black or DARK MATS on the floor that are interpreted as "BLACK HOLES" are a couple of ways to minimize wandering of people with Alzheimer's and Dementia.

Here are some websites (Copy & Paste URL to your browser.) of Stop Signs made especially as visual deterrent for wandering. Many of the signs are attached with Velcro-like fasteners so that you can take them off anytime you want to.  The sign will need to be removed prior to your loved one going out the door. 

https://www.webmd.com/brain/10-ways-to-prevent-wandering#

https://www.alzstore.com/stop-sign-banner-p/0134.htm

https://www.caregiverproducts.com/posey-stop-sign-door-banner.html

https://www.mindcarestore.com/stop-sign-banner-p/mc-0134.htm

https://www.alzstore.com/alzheimers-dementia-wandering-s/1828.htm

“Locator Services for Wandering Alzheimer's and Dementia Patients” Several companies offer (for a small monthly or annual fee) “medical alert systems” for dementia patients with or without GPS. 
This website offers a list of 10 Lifesaving Location Devices for Dementia Patients:
https://www.alzheimers.net/8-8-14-location-devices-dementia/

You could buy some "open door indicators?" similar to those used by business, that sound whenever the door is opened.

Good Luck with finding an option that works for your family. {{{HUGS}}}

You can do a security system that chimes when doors are opened.

If you or someone you know is clever you can do this yourself for pennies on the dollar of having it done. Everything is remote now a days and that simplifies it tremendously.

I have 2 keypads, 1 near the bedrooms so it can be heard at night.

Aznbobbo, that is scary when a love one wanders away from home, thank goodness a neighbour found her.

Here is simple suggestion. Put black rugs in front of the exterior doors, on the inside floor. To Mom, those black rugs may look like a dark hole in the floor, thus she may be afraid to step on it. This may or may not work. It's the less expensive thing to try.