There are lots of alternatives for Jenkins as a CI builder but I haven't found many for Jenkins as a web-based cron with a nice UI that keeps track of history, has tons of options for notifications on failures, and quickly allows re-building (even with user-supplied parameters!)

We use Jenkins for running backup jobs, periodically updating data, and building quick little jobs for support staff to run--infrequently enough that they don't warrant adding to our admin app but frequently enough that bothering at developer adds up.

For periodic admin tasks, you might consider giving Ansible AWX a try (https://github.com/ansible/awx). It is a web interface for managing Ansible playbooks, and lets you configure jobs that another user can then execute and provide parameters. It keeps track of all run results, has a fair number of supported integrations for notifications, and can schedule runs.

I work for Red Hat, and AWX is the upstream community project for Ansible Tower, which we provide support for. AWX is one of our newer open source projects (we open sourced it after acquiring Ansible), so you'll sometimes have better luck searching for information on "Ansible Tower".