Absenteeism Prediction & Labor Force Optimization in Rail ... · Four years of Data: Jan 1, 2009...
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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
Transcript of Absenteeism Prediction & Labor Force Optimization in Rail ... · Four years of Data: Jan 1, 2009...
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
May 22-23, 2013 MIT SCM ResearchFest 2
31,000 Miles of Track Operates 24 hours a day, 365 days a year
Dispatcher Scheduling
270 positions must be staffed every day.
Each position has unique qualification requirements.
Unplanned absences complicate the scheduling task.
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Research Questions
1. Is it possible to predict unplanned absences?
2. How many extra employees should BNSF have on staff?
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1st Question: Predicting Unplanned Absences
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Unplanned absences are highly variable.
If BNSF could predict unplanned absences they could adjust training schedules and planned vacation allotments.
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
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*20% of all shifts have 3 absences, etc.
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
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𝑃 𝑋 = 𝑘 =𝜆𝑘𝑒−𝜆
𝑘!
*20% of all shifts have 3 absences, etc.
What influences unplanned absences?
– Day of the week
– Day of the month
– Shift
– Holidays
– Football Games
– Hunting Season
– Snowstorms
– Planned Absences
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= 66
Dummy Variables
Evaluate using Poisson Regression
Results: Holidays
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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 -0.015248memorial -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 -0.514350thanksgivingfriday -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 -0.267006federal 0.010323 0.000000 0.101771 0.10 0.919 -0.189144 0.209790
Less than .05 = Statistically Significant
Holidays = Less absences
Results: Football Games & Hunting Season
Football Games
Hunting Season
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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
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
*Football Games & Hunting Season do not cause unplanned absences.
Summary of Statistically Significant Factors
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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
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
apr 0.65572 0.12724 5.15 0.000 0.40634 0.90510
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
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
snow 2.16735 0.24243 8.94 0.000 1.69220 2.64249
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
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
christmas -2.03518 0.67619 -3.01 0.003 -3.36048 -0.70988
christmaseve -2.24815 0.69794 -3.22 0.001 -3.61609 -0.88022
Statistically Insignificant -Day of the month -Day of the week -Hunting Season -Football Games -Months: May, Jun, Aug, Jun, Aug, Sep, Nov -Planned Absences -Holidays Memorial, Veterans, Labor, MLK
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
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2nd 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
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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
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1st Input: Regular Employee Qualifications
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The distribution of qualifications of regular employees can be modeled by a Negative Binomial distribution.
Friday 3rd Shift
2nd Input: Extra employee Qualifications
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The distribution of qualifications of extra employees can be modeled by a Negative Binomial distribution.
Friday 3rd Shift
3rd Input: Absences by shift
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The distribution of unplanned absences can be modeled by a Negative Binomial distribution.
Assignment Problem
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The mathematical formulation of our problem.
Qualification Matrix
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The qualification matrix describes who can work on which position.
Position
1 2 3 4 …. N
1 1 1 0 0 … 0
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
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
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Cost Matrix
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The cost matrix describes the corresponding cost of each single assignment.
Position
1 2 3 4 …. N
1 0 0.5 X X … X
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
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
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Solution Matrix
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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
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
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
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dEmployees 2 and 4 are absent
Solution Matrix
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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
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
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
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Extra Cost
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Extra cost always decreases as the number of extra employees increases.
Total Labor Cost
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Total labor cost always increases with more extra board employees; qualification level does not make a large difference
Total Labor Cost and Extra Cost
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Total cost always goes up even though the extra cost is going down.
Conclusion
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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
