Absenteeism Prediction & Labor Force Optimization in Rail Dispatcher Scheduling Authors: Taylor Jensen & Qi Sun Advisor: Dr. Tony Craig MIT SCM ResearchFest May 22-23, 2013
31,000 Miles of Track Operates 24 hours a day, 365 days a year May 22-23, 2013 MIT SCM ResearchFest 2
Dispatcher Scheduling 270 positions must be staffed every day. Each position has unique qualification requirements. Unplanned absences complicate the scheduling task. May 22-23, 2013 MIT SCM ResearchFest 3
Research Questions 1. Is it possible to predict unplanned absences? 2. How many extra employees should BNSF have on staff? May 22-23, 2013 MIT SCM ResearchFest 4
1 st Question: Predicting Unplanned Absences Unplanned absences are highly variable. If BNSF could predict unplanned absences they could adjust training schedules and planned vacation allotments. May 22-23, 2013 MIT SCM ResearchFest 5
Modeling Unplanned Absences Four years of Data: Jan 1, 2009 – Dec 31, 2012 Count unplanned absences by shift – 4 years*365 days*3 shifts = 4,383 shifts *20% of all shifts have 3 absences, etc. May 22-23, 2013 MIT SCM ResearchFest 6
Modeling Unplanned Absences Four years of Data: Jan 1, 2009 – Dec 31, 2012 Count unplanned absences by shift – 4 years*365 days*3 shifts = 4,383 shifts *20% of all shifts have 3 absences, etc. 𝜇 𝑙 𝑓 −𝜇 𝑄 𝑌 = 𝑙 = 𝑙 ! May 22-23, 2013 MIT SCM ResearchFest 7
What influences unplanned absences? – Day of the week = 66 – Day of the month – Shift – Holidays Dummy – Football Games Variables – Hunting Season – Snowstorms – Planned Absences Evaluate using Poisson Regression May 22-23, 2013 MIT SCM ResearchFest 8
Results: Holidays Holidays = Less absences Holiday Coef. Actual Effect Std. Err. z P>z Lower 95% int Upper 95% int newyears -0.722219 -1.930722 0.209295 -3.45 0.001 -1.132429 -0.312009 presidents -0.420272 -1.122878 0.206649 -2.03 0.042 -0.825297 -0.015248 memorial -0.418113 -1.115345 0.226170 -1.85 0.065 -0.861397 0.025172 independence -0.916658 -2.448851 0.303559 -3.02 0.003 -1.511622 -0.321694 labor -0.295194 0.000000 0.221066 -1.34 0.182 -0.728476 0.138088 thanksgiving -1.171696 -3.104133 0.335387 -3.49 <.0001 -1.829043 -0.514350 thanksgivingfriday -0.330449 0.000000 0.221151 -1.49 0.135 -0.763897 0.103000 christmaseve -0.841878 -2.248154 0.260941 -3.23 0.001 -1.353313 -0.330443 christmas -0.762535 -2.035175 0.252826 -3.02 0.003 -1.258065 -0.267006 federal 0.010323 0.000000 0.101771 0.10 0.919 -0.189144 0.209790 Less than .05 = Statistically Significant May 22-23, 2013 MIT SCM ResearchFest 9
Results: Football Games & Hunting Season Football Games Parameter Coef. Std. Err. z P>z Lower 95% int Upper 95% int NFL 0.01894 0.04944 0.38 0.702 -0.077954 0.115830 Super Bowl -0.19899 0.18556 -1.07 0.284 -0.562688 0.164712 *Football Games & Hunting Season do not cause unplanned absences. Hunting Season Parameter Coef. Std. Err. z P>z Lower 95% int Upper 95% int Beg Hunt Season -0.096593 0.140805 -0.69 0.493 -0.372566 0.179380 End Hunt Season 0.217245 0.124163 1.75 0.080 -0.026110 0.460601 May 22-23, 2013 MIT SCM ResearchFest 10
Summary of Statistically Significant Factors Statistically Insignificant Parameter Avg. Effect Std. Err. z P>z Lower 95% int Upper 95% int jan 0.58494 0.13272 4.41 0.000 0.32481 0.84507 -Day of the month feb 0.67105 0.13414 5.00 0.000 0.40814 0.93396 mar 0.62630 0.12554 4.99 0.000 0.38025 0.87235 -Day of the week apr 0.65572 0.12724 5.15 0.000 0.40634 0.90510 -Hunting Season oct 0.49693 0.12498 3.98 0.000 0.25198 0.74187 dec 0.32114 0.13089 2.45 0.014 0.06460 0.57768 -Football Games shift2 0.17815 0.07013 2.54 0.011 0.04070 0.31560 shift3 0.27073 0.06340 4.27 0.000 0.14647 0.39500 -Months: snow 2.16735 0.24243 8.94 0.000 1.69220 2.64249 May, Jun, Aug, Jun, Aug, Sep, Nov newyears -1.93072 0.55983 -3.45 0.001 -3.02797 -0.83348 presidents -1.12288 0.55258 -2.03 0.042 -2.20591 -0.03985 -Planned Absences independence -2.44885 0.81188 -3.02 0.003 -4.04011 -0.85759 thanksgiving -3.10413 0.89692 -3.46 0.001 -4.86207 -1.34620 -Holidays christmas -2.03518 0.67619 -3.01 0.003 -3.36048 -0.70988 christmaseve -2.24815 0.69794 Memorial, Veterans, Labor, MLK -3.22 0.001 -3.61609 -0.88022 May 22-23, 2013 MIT SCM ResearchFest 11
How Useful are these Results? Model has very weak predictive capability (McFadden R-squared value of .018) Conclusion: We can identify factors that influence unplanned absences, but we cannot predict how many unplanned absences will occur May 22-23, 2013 MIT SCM ResearchFest 12
2 nd Question What is the appropriate number of extra employees? – Each position has unique qualifications – Extra employees earn a full-time salary even if they don't have an assignment every day – Extra cost to move employees from their regular position – Must pay overtime to call employees from home May 22-23, 2013 MIT SCM ResearchFest 13
Monte Carlo Simulation Explore the relationship among overtime, qualifications, and total labor cost. Steps – Set a number of extra board employees – Generate qualifications of regular employees from a probability distribution – Generate qualifications of extra employees from a probability distribution – Generate unplanned absences from a probability distribution – Use an optimization solver to find the minimum cost – Run 10,000 iterations to find the expected cost given the defined parameters May 22-23, 2013 MIT SCM ResearchFest 14
1st Input: Regular Employee Qualifications The distribution of qualifications of regular employees can be modeled by a Negative Binomial distribution. Friday 3 rd Shift May 22-23, 2013 MIT SCM ResearchFest 15
2nd Input: Extra employee Qualifications The distribution of qualifications of extra employees can be modeled by a Negative Binomial distribution. Friday 3 rd Shift May 22-23, 2013 MIT SCM ResearchFest 16
3 rd Input: Absences by shift The distribution of unplanned absences can be modeled by a Negative Binomial distribution. May 22-23, 2013 MIT SCM ResearchFest 17
Assignment Problem The mathematical formulation of our problem. May 24-25, 2011 MIT SCM ResearchFest 18
Qualification Matrix The qualification matrix describes who can work on which position. Position 1 2 3 4 …. N … 1 1 1 0 0 0 Incumbent Employee … 2 0 1 0 1 1 … 3 0 0 1 0 0 … 4 1 0 0 1 0 … … … … … … …. … N 1 0 1 1 1 … N+1 1 0 0 0 0 Extra Board … N+2 0 0 1 1 0 …. … … … … … … … N+E 1 0 0 1 0 Employee from Home N+E+1 1 1 1 1 … 1 May 24-25, 2011 MIT SCM ResearchFest 19
Cost Matrix The cost matrix describes the corresponding cost of each single assignment. Position 1 2 3 4 …. N … 1 0 0.5 X X X Incumbent Employee … 2 X 0 X 0.5 0.5 … 3 X X 0 X X … 4 0.5 X X 0 X … … … … … … …. … N 0.5 0 0.5 0.5 0 … N+1 0 X X X X Extra Board … N+2 X X 0 0 X …. … … … … … … … N+E 0 X X 0 X Employee from Home N+E+1 1.5 1.5 1.5 1.5 1.5 1.5 May 24-25, 2011 MIT SCM ResearchFest 20
Solution Matrix The inputs are entered into a matrix and a solver finds the best solution. Running many iterations produces an expected cost. Position 1 2 3 4 …. N Employees 2 and … 1 1 0 0 0 0 Incumbent Employee 4 are absent … 2 0 0 0 0 0 … 3 0 0 1 0 0 … 4 0 0 0 0 0 …. … … … … … … … N 0 0 0 0 1 … N+1 0 1 0 0 0 Extra Board … N+2 0 0 0 0 0 …. … … … … … … … N+E 0 0 0 0 0 Employee from Home N+E+1 0 0 0 1 0 0 May 22-23, 2013 MIT SCM ResearchFest 21
Solution Matrix The inputs are entered into a matrix and a solver finds the best solution. Running many iterations produces an expected cost. Position 1 2 3 4 …. N … 1 1 0 0 0 0 Incumbent Employee … 2 0 0 0 0 0 … 3 0 0 1 0 0 … 4 0 0 0 0 0 …. … … … … … … … N 0 0 0 0 1 … N+1 0 1 0 0 0 Extra Board … N+2 0 0 0 0 0 …. … … … … … … … N+E 0 0 0 0 0 Employee from Home N+E+1 0 0 0 1 0 0 May 22-23, 2013 MIT SCM ResearchFest 22
Extra Cost Extra cost always decreases as the number of extra employees increases. May 22-23, 2013 MIT SCM ResearchFest 23
Total Labor Cost Total labor cost always increases with more extra board employees; qualification level does not make a large difference May 22-23, 2013 MIT SCM ResearchFest 24
Total Labor Cost and Extra Cost Total cost always goes up even though the extra cost is going down. May 22-23, 2013 MIT SCM ResearchFest 25
Conclusion The savings in overtime costs from having extra employees does not offset the fixed cost of extra employees. However, there are other important considerations, such as: -Employee morale -Union agreements -Training and Qualification requirements May 22-23, 2013 MIT SCM ResearchFest 26
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