Tag Archives: work-life balance

why women are (sort of) responsible for traffic congestion

This summer I read Traffic by Tom Vanderbilt and blogged about the OR and networks topics covered in the book. The follow-up post that I promised took nearly three months longer than I thought it would.

For those of you who are familiar with driving and traffic data, you will know that men, on average, drive more than women across all ages, and it’s not even close. Men age 55+ drive more than more than twice as many miles on average as women of the same age. On face value, it seems like men are disproportionately responsible for all the traffic congestion on the road. Tom Vanderbilt challenges this idea in Traffic, looking at why and when women drive rather than looking at how much they drive.

Both men and women drive a lot more than they did in the 1950s, leading to traffic and congestion. There are many reasons for this. Two that are often named are suburban sprawl (people living farther from where they work) and women joining the workforce. This naturally led to an increase in driving by both men and women. Let’s look a bit deeper.

Other things have changed–or not–since the 1950s. One thing that has not changed is that the women who have entered the workforce still do the lion’s share of errands, particularly those involving kids (think: “soccer moms”). In the 1950s, 40% of car trips were work trips. As of ~2010, a mere 16% of car trips were work trips. The difference is not that people aren’t working or taking public transportation to work (they are actually driving to work more!). The difference is that we’ve added many other driving trips to our schedules. And women do more of these extra errands and trips than men do.

Women do a lot of “trip chaining,” stopping at the grocery store on the way to or from work, taking Johnny to soccer practice, etc. The reason why women make such an impact on congestion is because (1) they are taking these trips during peak traffic times due to inflexible schedules, (2) they they use smaller roads less equipped for large traffic loads (these trips do not usually use the interstates), and (3) the distance between trips is significant (suburban sprawl!). Side note: We women are fairly efficient here in that we can minimize travel times by “chaining” – adding a TSP-like “tour” of errands rather than making individual trips that would take longer.

blogged about the issue of women having inflexible driving routes earlier, where I argue that dropping kids off at day care often makes taking public transportation impossible. Vanderbilt observes this, too. He also does not blame women for the extra traffic, as our travel patterns are what you would expect when considering the demands of both our families and careers. But there are implications.

In all seriousness, this post discussed traffic from the perspective of the “average” men and women. None of us are “average,” of course. The OR tie-in here is that the who, why, where, and when are important for understanding why congestion happens at certain times. The network structure is also important, as traffic network is reflected in trip chaining, and it sheds light on what parts of the network will experience the worst congestion. Vanderbilt’s writing on this topic suggests that encouraging people to contribute less to congestion is challenging, since there are many constraints on women’s driving patterns, and as a result, they might not be able to respond to incentives for reducing the amount they drive.

On a related note: for the first time in the US, the majority of licensed drivers are women.

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Federal van pools: a case of too many constraints

My husband works for the Federal government. He takes a van pool to and from his work on most days (he has a 120 mile commute round trip). The van pools are a great deal. If someone rides in a van pool, they commit to riding a certain number of days per quarter. They pay a membership fee and are reimbursed for saving gas.

In response to fraud, two significant changes were made to the van pool contracts:

  1. Van riders have to ride the van at least 50% of the working days each month (instead of each quarter).
  2. The van needs to be more than 50% full (not including the driver) at least 80% of the time.

First requirement

The first requirement is a problem. Vacations, has off-site training, goes to a conference, etc, interfere with ridership. Add two of these events together, and you end up with a severely inflexible policy. Employees who have to travel or who want to take a vacation may not be able to abide with the new requirements. Employees that travel a lot may not be the best candidates for the van pool, but employees who have one long trip ever should be able to ride the van.

Second requirement

The second change is even more restrictive. My husband’s van holds 14 people. They need to have at least 8 people ride (7 out of 13 + 1 driver) at least 4 out of 5 days in the week. It’s worth noting that small vans are going to have more of a problem with this because they typically have more variability in who shows up.

Looking at the long-term, a van needs to have at least 8 riders 80% of the time. That implies that the average number of days until the van is not “half” full needs to be 5. If we assume that each day is independent of the others, then we can model this as a geometric distribution. To get the desired average of 5, we need a “success” probability of 1/5. That is, the probability of a van being less than half full on any single day needs to be 20%. Is that realistic?

Let’s look at the 14 riders. Let’s say they each ride each day with probability p and that each day is independent. Then we can model the number of riders each day R~ Binomial(14,p). We need P(R<8) < 0.2 to meet requirement #2 (from the last paragraph). But if p=0.5 (as required), then P(R<8) = 0.605.  We need p > 0.642 to get P(R<8) < 0.2.

Thus far, I’ve assumed that each day is independent. Making that assumption will yield optimistic results. The “optimistic” results suggest that even under idealistic assumptions, the new van pool requirements will be extremely difficult to meet.

But this assumption is not valid. Riders ride less on Mondays and Fridays (40% of the work week). In practice, this means a van is likely to have at least 8 riders on three days of the week (Tue-Thu), but not four as required. For simplicity, let’s say that a van always has 8 riders on Tue-Thu (an idealistic assumption, but not too unreasonable). Let’s say that each rider takes the van with probability p = 1/3 on Mondays and Fridays (a modest change), and let’s assume that each rider and day are independent. Then the van has 8 riders with probability 0.0576 on these days. The probability that the van covers at least one Monday or Friday per week is 0.111. Therefore, under more realistic assumptions, it is even more unlikely that a van can meet assumption #2.

Vans could meet these requirements if they “overbook” and allow more riders than there are seats in the van. They will surely need to risk turning riders away to meet their requirements if more than 14 show up some day.  This may happen when gas prices change, since ridership increases when gas prices shoot up. However, my husband has noted problems meeting requirement #2 in the past couple of months when gas has been ~$4 per gallon.

Van pools and (un)intended consequences

Van pools are intended to improve the environment by encouraging car pooling. Van pools ultimately create an incentive for people to live very, very far from where they work, thus leading to more fuel usage. In the end, I do not think they save much (or any) fuel from being consumed. But this is open for debate.

On the other hand, van pools are great if your significant other wants a career. It has made our “two body problem” quite manageable. Accommodating one’s spouse’s career is rarely cited as a benefit to van pools. I am grateful that van pools exist so that both my husband and I can have careers. I hope it’s still possible for him to carpool with new rules.

Final thoughts

I applaud the Federal government for trying to crack down on fraud. But I encourage them to create rules that make it possible for riders to follow the letter of the law. And maybe someone who has taken a course on probability should look over the next set of rules and crunches some numbers.

Do you ride a van? Please correct anything I got wrong in the comments and add your two cents about how they can be improved.


five articles about women and engineering

ere are five articles about women and engineering. What do these five articles have in common? They were sent to me by men. Thanks guys!

1.Lack of Confidence Spurs Women to leave Engineering

Why do women engineering majors drop out of engineering and switch to other majors? It’s not because women lack competence, it’s because women tend to lack confidence (at least in comparison to their male peers). “As one of the most sex-segregated professions outside the military, engineering carries ingrained notions and biases about men being more naturally suited to the field, which can have self-reinforcing effects.”

A superstar women engineering faculty member whose mannerisms are similar to my own (i.e., she doesn’t ooze confidence) once told/warned me that “a lack of confidence can be interpreted as a lack of competence.”  It sounds like it’s not just the men who incorrectly infer–we women internalize this too.

This study doesn’t capture the incoming college students who are deterred for even selecting a science or engineering major, since their high school teachers keep reminding them about how tough and competitive these majors are (see article #4 below). I realize that these “missing” engineering majors are impossible to track, but I find this issue particularly relevant since I started college as a history major (I had particularly low self-confidence in high school). Luckily, I found my way to engineering.

This study has real implications for those of us who are faculty members in STEM fields. Our words and internal biases can have powerful effects. However, we’ve all had a confident alpha male bomb in our classes and have had non-confident, conscientious superstar students, so I hope we know that appearances can be misleading.

2. Engineering blogs: why women don’t go into engineering

A woman’s competence seems to be a function of what she look like and how much makeup she wears.

This blog post makes me cringe because it hits the mark. An interview with this woman engineer was posted online. The first comment about her professional interview was an inappropriate comment about the relative hotness of women in her field. Many women feel uncomfortable in engineering because a few men in engineering always seem to comment on our appearances first. (Note: I am not blaming all or even most men here). I would guess that this is mainly a maturity issue among undergraduates in engineering, which would again create a bad climate for women engineering students. I’m glad that Punk Rock OR attracts more enlightened men.

3.Why women leave the engineering field

A slew of statistical tests using NSF’s data on former engineering majors suggest some interesting findings. The first is that “women actually don’t leave jobs in science at an above average rate. The difference…comes from the engineering sector.” Why do women disproportionately leave engineering but not other scientific fields? The study’s author finds evidence to suggest that being in “a majority-male environment” leads women to leave engineering. The author claims that work-life balance benefits are nice, but they miss the mark when it comes to retaining women in engineering.

4. Working conditions drive women from engineering

Another NSF sponsored study examines why women leave engineering, and it reports similar results. They find that women don’t leave for family reasons nearly as much as we’ve been led to believe. “Nearly half of the women surveyed who left the engineering field said it was because of working conditions and issues such as a lack of career advancement and low salary.” This corroborates some of the findings in the previously listed study.

5. Girls go Geek…Again

In 1967, the fashion magazine Cosmopolitan featured an article that urged women to become computer scientists. Yes, this is for real. You should really check this blog post out of only for this pictures. In 1987, 42% of software developers were women. However, women computer science majors dropped from 37% in 1984 to 20% in 2006. In the past couple of years, women CS majors have risen at some of the top universities. This blog post by Fog Creek Software delves into the mystery of why the number of women CS majors has ebbed and flowed. My husband (a programmer) found this part of the blog post relevant and actionable:

[O]ne of the things that happens is that women don’t even think they’re qualified for [a computer science position] because it’s advertised in competitive language. The language of competition not only doesn’t appeal to many women, it actually puts them off. Google advertises their Summer of Code with very competitive language. In 2006, GNOME received almost two hundred GSoC applicants – all male. When GNOME advertised an identical program for women, but emphasizing the opportunities for mentorship and learning, they received over a hundred highly qualified female applicants for the three spots they were able to fund.

I have written about women trailblazers in computing once or twice before. I am still floored by how many women worked for the Bell Labs data center in the 1960s. These retro pictures of computing (1940s – 1960s) also feature women. It’s too bad that when we think of computer scientists, we tend to think of men. Apparently, women have always been an integral part of computer science.

Retro women of computing

All articles and links were sent to me be men. Hat tips to Hemanshu Kaul, Red Dave, Aaron Ball, and Christopher Felton.


what operations research has taught me about parenthood

In anticipation of the birth of my third child, I am writing a post about all the ways in which operations research has enriched my views on parenthood and maintain balance.

  • Value focused thinking has helped me to focus on raising independent and intelligent daughters, rather than doing things the convenient, short-sighted way.  It helps me to pick and choose the good habits I want to establish (like regular bedtimes, regular naps, and good manners), even if they’re inconvenient in the short term.
  • I don’t claim to never indulge a little.  Of course I do things for convenience!  OR has helped me to realize that every day I solve a knapsack problem, where the constraint is time.  I have to make only a small subset of my to-do-list a real priority, otherwise my day’s schedule would be over-constrained and infeasible.  Early on, I learned that I could not afford to buy into a “parenting philosophy” or my schedule would be over-constrained and I’d go crazy (I’m not saying that it can’t be done, because I’ve seen it happen, but it’s just not for me).  Basic knowledge of OR prevented me from beating myself up over this.
  • I optimally schedule my children’s vaccinations using discrete optimization methods (a video on this is here, where I have a brief cameo)
  • A little bit of knowledge about scheduling and critical paths goes a long way toward creating a more efficient daily schedule, although to be honest, my husband doesn’t appreciate my attempts to optimize his schedule.
  • Sadly, there are few algorithms that can be used for raising children.  But I still try.  The one meta-algorithm I use is a daily schedule (see last bullet). I step through this algorithm daily. However, there are a number of infant sleep algorithms that can be used with good success (although your mileage may vary).  I have found potty-training algorithms useless.
  • OR has helped me to understand why my daughters will probably not be as tall as I am.  It’s simply regression to the mean–I am five inches taller than the average American woman, and odds are, they will be tall but slightly less so than their mother.  But you never know why kind of draw they pulled.
  • And most importantly, OR has helped me to realize that parenthood is not an optimization problem, its a feasibility problem.  There are many ways to be a good parent.

What am I missing?

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what operations research has taught me about having a baby

After having my third baby last week, I am writing a post on how OR has helped me navigate pregnancy, labor, and birth.  Here is a few ways that OR has enhanced my experiences with having babies.

A solid OR background gave me the necessary knowledge about statistics to wade through all of the pregnancy advice out there and keep my perspective.  Much of the advice is silly and not evidence-based (like keeping your heart rate < 140 bpm, not lying on your back in a low-risk pregnancy, omitting all caffeine, avoiding certain foods, etc.).  Yet some of the best pregnancy advice (like eating your vegetables and staying active) is rarely verbalized.

A solid OR background also means that my educational background alone makes me a likely candidate to avoid most pregnancy complications (education of the mother is almost always a statistically significant factor that is negatively correlated with most adverse pregnancy outcomes).

I know that pregnancy statistics based on aggregate data are almost useless when on my third pregnancy. It’s all about correlation at this point.

After having two labors shorter than average, my midwife told me not to necessarily expect an even shorter labor.  After some discussion, I realized she was explaining that anecdotally, she has observed that most women experience regression to the mean after very short labors.  That makes sense.  If I had a good draw the last time, the odds are, I won’t get as good of a draw this time.  In general, buying into the Flaw of Averages is a bad idea for preparing for labor.  Few labors are “average.” However, I don’t have a good approach for managing the anxiety that comes along with having to prepare for a myriad of labor realizations. (I ended up having my shortest labor this time).

I have found Bayes rule to be extremely helpful for managing prenatal anxiety.  Many screening tests are performed during pregnancy.  The one that perhaps causes the most anxiety in expectant moms is the quad screening test, which attempts to screen for Downs syndrome and spina bifida.  Given that the test comes back positive, for example, a baby has about a 3% chance of having Downs Syndrome (although I recently learned that these odds vary according to the age of the mother).  My quad screen tests came back negative for all three pregnancies, but I was prepared not to panic just in case.  A similar screening test is done for gestational diabetes.  I had a false positive once and took the dreaded three hour glucose test.  That was no fun, but again, I knew not to worry.

My last two deliveries took place at the tail end of a brief surge in births at the hospital (births should be a Poisson process–see my post on the exponential distribution).  This meant that all of the recovery rooms in the hospital were occupied by the time I needed one (!)   Luckily, I was able to get into a room both times, although this time, I am indebted to two kind nurses who pulled a few strings for me.  My hospital stay illustrates that hospitals still need lots of OR for planning hospital beds.  (My hospital stay also suggests that OR could be used to schedule meal deliveries, schedule infant inspections, and organize hospital discharges).

With regard to hospital discharges, the bottleneck in the process is waiting for someone with a wheelchair to take me and baby to the car after discharge.  This was also true three years ago after my last birth.  I would have thought that the bottleneck would be scheduling the “important” stuff, like the pediatrician’s checkup of the baby and the nurse’s checkup of me.  Despite being tired after having a baby, I couldn’t help but start to model the hospital system and mentally note where they need to make improvements.

I have avoided amniocentesis for all of my pregnancies, but if I was offered amniocentesis, I would use a decision tree with my personalized economic model to make the decision.

And most importantly, decision analysis methods confirm that it was a good idea for me to be fruitful and multiply.


    more men attended the work-life balance session than women attended the social networking session

    I am not an expert on the status of men and women in OR/MS, but I have two observations to offer.

    1.  I was surprised to see that no women attended the social networking session at INFORMS (three women were on the panel).

    2.  I was surprised to see that several men attended the work-life balance session at INFORMS.  Better yet, they even asked questions.

    One step backward and one step forward. Certainly, there are gender disparities in blog readership (more men read blogs, particularly technical blogs), blog commenting (I’d wager than men are more likely to leave comments), twitter participation (more women tweet).  This might translate into disparities of who feels comfortable attending a social networking panel. (Note: by disparities, I literally mean differences, with no judgment attached).  I wonder about disparities because quite a few women asked me about the session during the conference (I received more inquiries from women than men) so I know that they were interested but didn’t show up. I don’t have a way to draw conclusions from my small sample of observations.

    I’ll stop there before I put my foot in my mouth.  What do you think?

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    External links:

    The social networking panelists at INFORMS

    The social networking panelists at INFORMS courtesy of Anna Nagurney


    Emily Stoll on using math/OR in the real world

    Emily Stoll from Johns Hopkins Applied Physics Laboratory gave  a talk on balancing life and work as part of the Women in Math program.  She offered several lessons that she has learned along the way.

    Stoll has a degree in civil engineering, a degree in applied math, and an MBA.  She talked about all of the different things you can do with an applied math degree.  Most of her work involves homeland security applications.  As a mathematical analyst, she analyzed submarine data using the Chi-squared test, Kolmogorov-Smirnov test, Fault tree analysis, and other statistical tests.    She used design of experiments as well as modeling and simulation to improve port security.  Her research on receiver operating (ROC) curves for IED detection was featured in the TSA’s blog.

    One of the more interesting projects Stoll was involved with is the US NavyMarine Mammals” program. She helped to optimize the location of dolphins and sea lions to interdict dangerous materials (such as mines) and for swimmer defense.  Amazingly, the US Navy has been using the marine mammals program since the Vietnam War era.

    All of Stoll’s work requires the use of statistics.  It’s nice to know that the tools I teach students in STAT 541 (an introductory statistics course for engineers) are widely used in industry, even by mathematicians and engineers who don’t consider themselves to be statisticians.

    Stoll’s excellent life lessons include:

    • Take your time to think about a job offer before accepting
    • Know what you want before you go after it.
    • Build and use your network.
    • Very few decisions in life are Life Decisions.
    • Sometimes you have to take a risk.
    • You can do it all, just not at the same time.
    • Do what works for you.
    • Realize that it can be done.
    • Realize that you will need help.
    • Realize that almost every other woman in your position are struggling with the same decisions.
    • Figure out what is important to you and make that your priority.