Solving UW Math Summer Scheduling Problem
Scheduling non-major summer courses for MATH 381 group project at UW.
Abstract
Based on our interview with Sarah Garner, director of the Math Department’s Advising office, we will address the decision problem of finding an appropriate number of sections of each course in the 100 to 300 level category. The threshold for opening a section, having at least 10 out of 35 student enrollments. In this paper, we first present the problem description and its impacts. Then, we model the problem and solve it with the linear programming, simulation and statistical analysis. Finally, with limited resources, such as required number of students for a open class, we offer appropriate time schedules of sections for 9 non-major service courses based on historical data.
Keywords: Mathematical model; Monte Carlo Simulation; Statistical Analysis; Linear Pro-gramming; Course schedule
Team members Info
- Yanmeng (Anny) Kong @AnnyKong
- Linni Cai @LINNI2017
Scripts Info
- Stage I: Python scripts for Linear Programming, reading data, and tables.
- Stage II: R scripts for Monte Carlo Simulation, diagrams and priority queue.
Read csv data - Stage I
- read csv
- generate a dictionary for storing all necessary data
Generate customized table - Stage I
An example of Math 120 table would look like the following:
Math 120
year Percent. Enrollment sec 1 Percent. Enrollment sec 2 Percent. Enrollment sec 3
------ --------------------------- --------------------------- ---------------------------
2008 57.14(1050✓) 71.43(940✓) 77.14(1200✓)
2009 72.00(1050✓) 88.00(940✗) 104.00(1200✗)
2010 60.00(1200✓) 74.29(1050✓)
2011 85.71(1050✗) 97.14(1200✗)
2012 42.86(1050✗) 74.29(1200✓) 80.00(940✓)
2013 62.86(1050✓) 63.33(1200✓)
2014 28.57(1050✗) 74.29(1200✓)
2015 91.43(1200✗)
2016 85.71(1200✗)
2017 88.57(1200✗)
2018 100.00(1200✗)
Notes:
-
- check mark(✓) if the percentage within the preferred range (57% - 80%)
- cross mark(✗) otherwise
(1050✓)means- the class was scheduled at 1050am;
- and the percentage of enrollment is in the preferred range.
Output files - Stage I (better open with firefox)
-
data.jsongivescourse num -> year -> percentage of enrollmentwhich is dict -> dict-> list
- i.e.
-
data2.jsongivescourse num -> year -> time -> percentage of enrollmentwhich is dict -> dict -> dict -> list
- i.e.
Command line Outputs - Stage I
- i.e.
Math 124 year Percent. Enrollment sec 1 Percent. Enrollment sec 2 Percent. Enrollment sec 3 Percent. Enrollment sec 4 ------ --------------------------- --------------------------- --------------------------- --------------------------- 2008 51.42857143(✗) 62.85714286(✓) 77.14285714(✓) 2009 40(✗) 62.85714286(✓) 71.42857143(✓) 85.71428571(✗) 2010 57.14285714(✓) 71.42857143(✓) 74.28571429(✓) 94.28571429(✗) 2011 53.33333333(✗) 70(✓) 76.66666667(✓) 80(✓) 2012 77.14285714(✓) 85.71428571(✗) 91.42857143(✗) 100(✗) 2013 25.71428571(✗) 54.28571429(✗) 57.14285714(✓) 71.42857143(✓) 2014 34.28571429(✗) 48.57142857(✗) 65.71428571(✓) 88.57142857(✗) 2015 46.66666667(✗) 73.33333333(✓) 76.66666667(✓) 76.66666667(✓) 2016 80(✓) 85.71428571(✗) 88.57142857(✗) 2017 45.71428571(✗) 82.85714286(✗) 85.71428571(✗) 2018 51.42857143(✗) 57.14285714(✓) 57.14285714(✓) - i.e.
Math 124 year Percent. Enrollment sec 1 Percent. Enrollment sec 2 Percent. Enrollment sec 3 Percent. Enrollment sec 4 ------ --------------------------- --------------------------- --------------------------- --------------------------- 2008 51.43(110✗) 62.86(940✓) 77.14(1200✓) 2009 40.00(110✗) 62.86(940✓) 71.43(1200✓) 85.71(1050✗) 2010 57.14(1050✓) 71.43(940✓) 74.29(1200✓) 94.29(110✗) 2011 53.33(110✗) 70.00(940✓) 76.67(1050✓) 80.00(1200✓) 2012 77.14(110✓) 85.71(1050✗) 91.43(1200✗) 100.00(940✗) 2013 25.71(110✗) 54.29(1050✗) 57.14(1200✓) 71.43(940✓) 2014 34.29(940✗) 48.57(1050✗) 65.71(110✓) 88.57(1200✗) 2015 46.67(110✗) 73.33(940✓) 76.67(1050✓) 76.67(1200✓) 2016 80.00(1050✓) 85.71(110✗) 88.57(940✗) 2017 45.71(110✗) 82.86(1050✗) 85.71(940✗) 2018 51.43(1200✗) 57.14(940✓) 57.14(1050✓)
Final Result - Stage I
Command line Outputs - Stage II
Annual Total Enrollment
Past Data Summary of MATH 324
Monte Carlo Simulation
Priority Queue - Stage II (example)
[1] 324
[1] "Priority Queue:"
Section > 0.8 LB > 0.8 UB 0.57~0.8 LB 0.57~0.8 UB > 0.57 LB > 0.57 UB
5 1200 0.16208565 0.21687935 0.7571027 0.8698258 0.938973 1.063952
3 940 0.01779317 0.03928358 0.9118470 1.0350786 0.938004 1.062921
1 110 0.01698406 0.03809602 0.9137841 1.0371414 0.938973 1.063952
Final Result - stage II (example)
Prediction of MATH 324 in 2019
Section Number
1 110 1
2 220 1
3 940 1
4 1050 0
5 1200 1
Result Validation - stage II (examples)
Prediction of MATH 324 in 2018:
Section Number
1 110 1
2 220 0
3 940 1
4 1050 0
5 1200 1
Real of MATH 324 in 2018:
Section Number
1 110 1
2 220 0
3 940 1
4 1050 0
5 1200 1
[1] "Comparison of MATH 324"
[1] "110 : has the same number"
[1] "220 : has no past data"
[1] "940 : has the same number"
[1] "1050 : has no past data"
[1] "1200 : has the same number"
Prediction of MATH 308 in 2018:
Section Number
1 110 0
2 220 2
3 940 1
4 1050 1
5 1200 2
Real of MATH 308 in 2018:
Section Number
1 110 0
2 220 1
3 940 1
4 1050 1
5 1200 1
[1] "Comparison of MATH 308"
[1] "110 : has no past data"
[1] "220 : recommend to increase 1 section(s)"
[1] "940 : has the same number"
[1] "1050 : has the same number"
[1] "1200 : recommend to increase 1 section(s)"
Details can be referred from the paper.