1. Scheduling for Trinity School at Meadow View
Problem Definition & Possible Solution Approaches
Fall 2016
Mary Barthelson
Marissa Brienza
Zachary Nuzzo

2. Introduction Don’t Rock the Boat
Begin with the schedule of the previous semester and make the minimum necessary modifications to accommodate faculty requests
Trinity School at Meadow View is a local, private school with grades 7-12 that currently schedules students and teachers to classrooms and time periods by hand
This is a time intensive process that typically takes a number of days to complete

3. Problem Description
Trinity School at Meadow View is seeking a tool to schedule students and teachers to classrooms and time periods given a set of specific constraints
A balance must be struck between an optimal solution and one that solves quickly
An optimal schedule would solve in a nondeterministic polynomial amount of time
Finding an optimal solution can become inefficient if the size of the problem grows to large
Balance may be achieved by using heuristics to generate a number of feasible schedules

4. Problem Constraints Not every classroom can fit every student section
Course specific classrooms
One section per grade per gender
Specific hours of teacher availability
Different requirements for high school vs. middle school students
Separate requirements for male vs. female students
Different intricacies for the Fall and Spring semesters
Problem must solve in an acceptable amount of time
Not example needed
For example, Drama needs all of Commons and Bio/Chem can only be taught in two classrooms
For example, 7th grade Girls History or 10th Grade Boys Biology
Some teachers have extracurricular duties like supervising lunch so they cannot teach then, some are part-time and only teach two periods, some require free periods together
High schoolers and middle schoolers have different lunch periods
10th and 9th grade girls take music together
In the fall, no music scheduling needs

5. Data Sources Delivered in an Excel Workbook:
Teacher Course Assignments
Room Capacities
Course-Specific Rooms
Spring Semester Course Requirements by Grade
Fall Semester Course Requirements by Grade
Number of Students by Grade and Gender

6. Project Approach

7. Solution Options Integer Programming (IP)
Use of this approach will solve the problem optimally, but as the problem size increases it is not guaranteed that the IP will solve in a reasonable amount of time.
Heuristics
This technique will generate feasible solutions in a reasonable amount of time. Implementation of a heuristic algorithm is more an involved than an IP.
Constraint Satisfiability Algorithms (CSP)
This approach focuses on assigning variable values based on a set of constraints (no objective function) to produce a feasible schedule. Implementation of a CSP algorithm is more an involved than an IP.

8. Solution Implementation
Microsoft Access for User Interface
Excel VBA or Python for Algorithm
Excel for Final Schedule
Restrictions:
Limited software options
Available at Trinity: Access/Excel & MatLab
Free, Open-Source Software
No access to a commercial-grade solver (i.e. CPLEX)
Tool needs to be built for a non-technical audience

9. Proposal Outline 1. Introduction 2. Approach 3. Project Plan
a. Background
b. Problem Statement
c. Scope
d. Data Sources
2. Approach
a. Requirements
b. Analysis of Alternative Approaches
i. IP
ii. Heuristics
iii. Satisfiability Algorithms
c. Success Criteria
3. Project Plan
a. Schedule
b. List of Deliverables