The software framework for queue scheduling at the MMT Observatory (MMTO) is presented. This framework is part of the MMTO's Observatory Manager (OM) that handles queue scheduling and many other observatory-related activities. The OM is divided into four overall components: 1) the "Web Frontend", 2) the "REST API", 3) the "Web Framework", and 4) the "Scheduler Backend". This paper emphasis the Scheduler Backend, which builds on the Python Astropy/Astroplan library with several new user-defined constraints and a custom sequential scheduler. These new constraints form an integral role in capturing the scheduling policies and priorities of the MMTO. The Scheduler Backend service can be run in two modes: 1) a "dispatcher" mode where observing blocks (OB's) are ranked for a specific observing time, and 2) a "scheduler" mode where all OB's are scheduled for the duration of the queue observing run. The dispatcher can be run multiple times throughout the night, as needed. The scheduler is typically executed once daily after sunrise after all data is collected for the night. Results from the dispatcher and scheduler are posted to a centralized Redis server for real-time monitoring of computing status and to relational databases for later review. Performance and optimization issues are discussed.