I will be giving a webinar titled “Project-Based Learning in Operations Research and Sustainability” on Wednesday at 10:00 AM EST on ORComplete.com.
To access it, check this page.
Here’s the abstract:
Operations research (O.R.) is playing an increasingly important role in addressing sustainability challenges such as green-house gas reduction and renewable energy use. In this talk, quantitative sustainability projects that can be utilized in undergraduate courses are described using the lens of descriptive, predictive, and prescriptive analytics recently espoused by the O.R. community.
I gave a similar talk at the New Jersey MAA section meeting in a “Mathematics and Planet Earth” session a couple of weeks ago.
Thanks to Ahmet from ORComplete.com for the invitation. He has been posting the videos of the webinars on youtube after the fact so you should be able to access it there later on.
Some recent and current activity in green O.R. and related areas:
- There is great initiative on “Math and Sustainability” over at the “Mathematics and Planet Earth 2013” website. The site is filled with information, lesson plans, reference material and more. Check it out!
- “Sustainable Production and Service Supply Chains” is the theme of the 2013 International Conference on Advances in Production Management Systems (APMS) held at the Penn Stater Conference Center, State College, Pennsylvania, USA, 9-12 September 2013.
- The Production and Operations Management Society now sponsors the Paul Kleindorfer Award in Sustainability. Paul Kleindorfer passed away in 2012. See this site to learn more about this impressive man.
- ACEEE has put out an energy efficiency calculator “that lets users get an idea of the costs and air quality benefits of some basic energy efficiency policies and allows them to compare those options with more piecemeal approaches to reducing air pollution”. More here.
- An energy efficiency bill passed in U.S. Story here.
Here’s a nice opportunity in the NYC area, deadline is next week:
Mathematics and Planet Earth – Mathematical Association of America, NJ Section Spring 2013 Conference
The Mathematical Association of America (MAA)-NJ Spring Meeting will have a special contributed paper session on Mathematics and Planet Earth, where participants will give a talk for about 15-20 minutes on their papers. The organizer of the session is calling for papers from graduate students, faculty members and researchers working on any topic(s) related to Mathematics and Planet Earth. All submitted papers will be reviewed by the organizers and the selection committee. Please submit a title and an abstract by February 20, 2013 to the organizer of the session – Dr. Srabasti Dutta at firstname.lastname@example.org and Dr. Patricia Kenschaft at email@example.com.
Preferences will be given to those papers that use Mathematics, show applications of Mathematics, focus on Mathematical modeling or discuss about how perhaps Mathematics can be used to solve some relevant or important questions related to Planet Earth. Topics can be on anything from complex modeling to simple issues like how hybrid cars can help the Planet Earth. Though the workshop is organized by MAA-NJ, you need not be a Mathematics professor, researcher or graduate student to present a paper. Everyone is welcome. Similarly, the talks can involve complex Mathematics and research and thus be aimed at the graduate students and researchers in the fields, or, the talks can be aimed at school teachers, undergraduate students or college faculty.
The workshop will take place during the joint Mathematical Association of America (MAA)-NJ and GSUMC (Garden State Undergraduate Mathematics Conference) spring meeting at Felician College (Lodi Campus), Lodi, New Jersey on April 13, 2013. Please pass this message to your students and colleagues.
Recently I was asked to do some calculations to determine whether it made sense for my city of New London, CT to switch from a gasoline-fueled truck fleet to one running on compressed natural gas (CNG). Could this change lower fuel costs and emissions, and have a reasonable payback period? I wrote about the GREET transportation model from Argonne national lab a while back and thought this would give me a good chance to take its fleet footprint calculator for a spin. I found it to be a flexible and relatively user-friendly tool. One of the dangers of these calculators is that the user is not always aware of the assumptions being made (see this post about the issue in LCA calculators) but in the case of GREET, many of the assumptions are clearly indicated within the calculator. Furthermore, you have the ability to alter them to suit your own situation. I did have to do a little reverse-engineering to arrive at the results I was looking for, which I describe below.
The calculator, part of which is shown in the screen shot above, can be run using one of two methods. I used method two, for when you already know the fuel consumption of your fleet. In method one, you specify the size of the fleet by vehicle and fuel types, selecting from the following lists:
- School Bus
- Transit Bus
- Shuttle/Paratransit Bus
- Waste Hauler
- Street Sweeper
- Delivery Step Van
- Transport/Freight Truck
- Medium/Heavy Duty Pickup Truck
- Maintenance Utility Vehicle
- Diesel HEV
- Biodiesel (B20)
- Biodiesel (B100)
- Ethanol (E85)
- Compressed Natural Gas (CNG)
- Liquefied Natural Gas (LNG)
- Liquefied Petroleum Gas/ Propane (LPG)
- Gaseous Hydrogen (G.H2)
- Liquid Hydrogen (L.H2)
So for instance, you could enter five school buses running on diesel, a street sweeper on B20, delivery van on CNG, etc. The GREET calculator has average mileages and fuel economies for each vehicle-fuel pair, which it can then use together with your inputted fleet information to generate overall fuel usage. All of the mileage and fuel economy numbers are estimates, assumptions the calculator is making for your fleet. But these are editable by the user. So if you know your school buses average 6,000 miles per year instead of the default 12,000, you can simply change that value. Ideally, you would have the fuel usage information, as my city fortunately does, and you would be able to skip all of this and use Method two. But, the functionality of Method one allows you to conduct some what-if explorations, to see what kind of fuel usage and emissions you might rack up should you decide, for example, to add a street sweeper to your fleet. Or suppose you are starting a brand new campus from scratch and want to explore various combinations of vehicles.
Our situation was quite simple: compare a small gasoline-fueled fleet with an equivalent (in terms of mileage) CNG fleet on fuel usage and emissions. I could easily enter the fuel usage (roughly 3,000 gallons of gasoline annually) into the calculator. GREET then output petroleum usage of 67.8 barrels of oil and 37.6 short tons of GHG emissions. To find the equivalent amount of CNG, I had to work backwards since the calculator does not have a direct conversion capability, though perhaps this is present in another of the Argonne tools. The fuel use block in the calculator has a “gasoline gallon equivalent” line at the bottom. So a crude way to achieve the conversion is to enter numbers in the desired fuel column (vehicle type does not matter) until the gasoline equivalents match. In my case, a few tries got me fairly close with 360,000 cubic feet of CNG (see screen shot below).
To get a more accurate value, I drilled down into the calculations for the gasoline-equivalent row. The conversion is fairly straightforward and can be extracted from the calculator with a small amount of trace-back through cell formulas. Essentially the different fuel types start off as apples and oranges, but can be compared by converting them into energy in units of Btu’s. This is achieved by GREET using the lower heat values (LHV), and it indicates values of 0.983 Btu per cubic feet of CNG, and about 115,000 Btu per gallon of gasoline. This assumes the gasoline is 50% conventional / 50% reformulated or low sulfur and that CNG is sourced in North America with a breakdown of 77% conventional and 23% shale (which can be extracted using fracking). Again, these assumptions are indicated in the calculator and you could adjust them as needed. I included a partial screen shot below showing the CNG assumptions; you can also see many of the others. Depending on your scenario, changes in assumptions may or may not make a difference. But you would need to determine that, rather than just going with what the default settings tell you.
Putting the LHV’s together results in the following conversion formula, which is what GREET used in this case:
That is about 116.832 cubic feet of CNG per gallon of gasoline. For the fleet I was looking at, that translates to approximately 357,506 cubic feet annually. Now that the equivalent amounts of both fuels are known, then given the unit price of each, a fuel cost comparison can be made.
When I was doing the rough trial and error fuel calculation before, I left both the CNG and gasoline fuel consumptions in the spreadsheet. Now with a precise value for the CNG amount from my formula above, I delete the gasoline to see the consequences of a CNG-only fleet. The calculator reports 0.4 barrels of oil and 33.8 short tons of GHG emissions. Why is there still petroleum usage even though we have switched to CNG? GREET calculates emissions and petroleum usage in a well-to-wheels (WTW) manner, so it is including the life-cycle of the fuel from the time it is extracted through transport to when it is consumed by the vehicle. Of course it does take some form of energy to get even a clean fuel from well to wheels.
I also drilled down into this emissions calculation and it is similar to the fuel equivalence one, but adds the additional emissions factor corresponding to each fuel. This is the key factor underlying sustainability arguments. CNG is generally considered a more environmentally friendly fuel than gasoline because it produces fewer emissions. So this emissions factor, which GREET provides in units of grams per Btu, should be lower for CNG compared to gasoline. Or should it? The table below lists the factors used by GREET:
Notice how source location of the CNG makes the difference between whether it is environmentally favorable to gasoline or not (at least in terms of CO2 emissions). This is a US-based tool; hence the non-North-American (NNA) CNG takes an environmental hit, which I am guessing is due to transport emissions. In our case I assumed North American (NA) CNG, resulting in a 10% emissions reduction for our fleet as compared to gasoline. The calculation for North American CNG, for instance, would be:
It is interesting to see the emissions factors for various fuel types in the table from the GREET calculator above. For instance, notice how CNG sourced from landfill gas (LFG) has a negative factor for the upstream portion of GHGs because using this source as fuel prevents emissions from entering the atmosphere that otherwise would have. There are still associated emissions at the tailpipe as the fuel is burned, but the net effect is very small (factor of 0.018) compared to most of the other fuels.
What would happen next is a look at the cost side of the problem. Find the prices of each fuel and the replacement CNG vehicles. Determine the annual fuel savings and then the payback period for the new fleet. This is tricky as the fuel prices can be highly variable, but you can use estimates from the EIA or elsewhere and run a few different scenarios to get a sense of what might happen. I did a quick and dirty check and found these fuel prices:
- Gasoline: $3.50 / gallon in New England as of 1/21/13 (via this EIA page)
- CNG: $2.12 / gasoline gallon equivalent (GGE) in U.S. as of Oct. 2012 (via this EERE page)
Note that the GGE units save one the trouble of converting cubic feet of CNG to equivalent Btu’s, something I did above. Still, when it comes time to budget or order, you’d need to know how much fuel is needed. Be aware that these numbers are rough estimates and don’t even match up completely in terms of date and location, but qualitatively you can see a pretty large price difference. And if you look at the web page the CNG price came from, you can see from the price plot that CNG has not exceeded $2.50 / GGE going back to 2000.
The following table summarizes the results for our example:
Estimated Fuel Cost
CO2 Emissions (short tons of CO-2 equivalent GHG’s)
% Change in CO2 Emissions Relative to Gasoline
|CNG – non-North American||357,506 ft3||38.16||1.5%|
|CNG – North American||357,506 ft3||$6,487||33.84||-10.0%|
The savings are there fuel-wise, on the order of $4K per year, though that is spread over several vehicles. So it would take some time to recoup the capital expense of investing in the new vehicles. (This provides a nice opportunity to utilize the capital budgeting problem, found in many undergrad O.R. texts.) More realistically, vehicles nearing end of use would be replaced with comparable CNG vehicles (and the equipment replacement problem comes in for that). On the emissions side, the switch to (native) CNG leads to a decent reduction, as was pointed out above.
To tie in more directly with O.R., consider the decision problem of what kind of fuel-type vehicles your fleet should contain. GREET provides information in the form of energy usage (lower heat values) and emissions on a wide array of types, under many different assumptions (e.g. sourcing). It can form the back end of a decision support tool using an integer program optimization, the decision variables being how many of each type of vehicle to obtain. You would most likely add in tables to calculate costs, which might be the (or an) objective. Constraints could ensure you have enough of each type of vehicle to accomplish required tasks (e.g. trash hauling, landscaping, etc.), are not consuming more a type of fuel than is available (e.g. via electric charging stations), and more.
GREET focuses on vehicles, but a fairly similar problem exists for heating air and water. We ran a capstone project in 2011 in which our students studied alternate fuel types for the boiler plant using mixed integer programming including elements of the capital budgeting problem. Similar emissions and energy factors played a role, though the higher heat value (HHV) is used instead of the lower heat value in the case of a boiler. And there are calculators to handle this kind of work, such as the Clean Air – Cool Planet calculator. You can go further and combine the energy usage and emissions of not only vehicles and boiler plants, but also buildings (see some of the tools from the EPA’s Energy Star program), industrial facilities, etc. and so look at virtually all aspects of a city or town. The organization ICLEI provides tools for doing this type of work.
But to get a good handle on vehicle fleets the GREET calculator it is an effective way to go. It provides a central location for much of the data you need to perform vehicle comparisons, and then uses that data combined with your input to provide vehicle fuel use and emissions. It lays its assumptions out clearly and it is easy for the user to change them. And it is transparent enough to allow you to reverse engineer its calculations should you want to take things a step or two further. So it is clearly a practical tool, but it also is a great learning tool, one that can be a great starting point for a project-based assignment in O.R. and sustainability. I plan to put something together in the future. If you do, let me know.
A number of interesting green O.R. items have come up lately:
- Smart meter data is available from Pacific Gas & Electric (California). There is a webinar today (Oct 26) at 2 PM EST about it. To access the data, submit a proposal. [via ENRE]
- Quantitative methods in Smart Grids – 2 faculty openings at Lehigh University. [via ENRE]
- Teaching green O.R. – Case Article in INFORMS Transactions on Education – Embedding a Sustainability Module Into Quantitative Business Courses by Susan Cholette and Theresa Roeder. About GHG emission auditing for a supply chain. Free online access. Article comes with their teaching materials attached.
- The ACEEE has a white paper about whether Jevons’ Paradox (aka the rebound effect) is real. See this greenOR post about OR and Jevons paradox.
- Read about how a brewery is using microbes to turn its waste water into methane, which is then used to run a GE turbine generating electricity.
- Coursera has an “Introduction to Sustainability” course taught by Jonathan Tomkin of University of Illinois Urbana-Chamagne. It uses his textbook (available online). I wrote about a sustainability course here.
- The computational sustainability folks now have a blog.
- Journal name change – the Environmentalist is now Environment Systems and Decisions.
- “The NSF SEES program is offering funding for NSF Science, Engineering and Education for Sustainability Fellows. http://www.nsf.gov/funding/pgm_summ.jsp?pims_id=504673 The due date is Nov. 26. The program provides up to 3 years of funding at about 80K per year. It is for people who have worked for less than 3 years in a post-phd job.” [via ENRE]
- Post-Doc opportunity in wind energy optimization, control and markets at Johns Hopkins. [via ENRE]
Apologies for the diminished rate of postings recently. I am trying to get the word out about the smaller updates and items via twitter instead of through the blog, so be sure to check out my or4green feed over there. I still intend to keep putting longer pieces on this blog. Here is a new one:
Back in April, I attended a Green Campus Conference in Connecticut. It was an interesting meeting. A frequently repeated statement was that Connecticut is aiming to become the most energy efficient state in the Union. There are rankings and the last time I checked it was third (see this post). So, many of the talks at the conference were geared towards increasing energy efficiency on college campuses.
The knee-jerk question that comes to mind for me when I hear about energy efficiency is: “What about Jevons’ paradox?” That is, as energy efficiency increases, whatever the energy was being used to obtain (cooling, heating, production, etc.) can now be now be obtained using less energy. So from a sustainability perspective, that’s good – less energy means fewer emissions, and lower general life cycle impact (e.g. production and transportation of fuel, equipment, etc.). But looked at in reverse, you could decide to keep your energy use constant, and utilize the efficiency gains to bring greater cooling, heating, production, etc. Therein lies Jevons’ paradox – energy efficiency in the latter case has not led to reduced energy usage. The environmental impact is neutral – no more energy is being consumed – but the opportunity for energy efficiency to reduce environmental impact was not utilized. Note we have assumed the unit cost of energy remains the same.
As I listened to the speakers talk about various ways to implement and finance energy efficiency on college campuses, I began to think Jevons’ paradox would not really be an issue in most of their cases. To see why, let’s look it at from an operations research perspective. We’ll use a very simple example to get the point across in which we only consider energy used to cool a building (home, campus building). The formulation follows:
x = energy used for cooling, in units of kilowatt-hours (kWh)
p = measure of energy efficiency in units of cooling level per kWh
L = p * x = cooling level
c = per unit energy cost (in $ per kWh)
C = c* x = total energy cost (in $)
B = budget (in $), total energy cost will be constrained to be less than B
m = per unit level of emissions (in lbs CO2 per kWh)
E = m * x = total emissions (in lbs CO2)
c x <= B — budget constraint
1 <= p x <= 10 — assume the comfort level must be between 1 and 10 (think levels on the AC unit)
Min C = c x — Cost
Max L = p x — Comfort
Min E = m x — Emissions
Now we will look at a few different scenarios. The guiding question is: as p (energy efficiency) increases, does energy consumption decrease? If so, does it decrease as much as it possibly could? Then note that environmental impact directly tracks energy consumption in this model.
Scenario 1 – Homeowner – would like to maximize comfort, but is constrained by a budget
Max p x
st c x <= B
1 <= p x <= 10
The scenario description implies that the budget is the binding constraint, which means the optimal solution is x = B/c.
If p increases, x stays fixed (assuming cost remains the binding constraint as p increases, which it will as long as p < 10 (c/B)). So energy consumption does not decrease as may have been intended – Jevons’ paradox is in effect. The efficiency gains have been used to increase comfort.
Scenario 2 – College campus – also constrained by a budget, wants comfort set at some reasonable level (we’ll say 5), but not necessarily to maximize it. So since comfort need not be maximized, it seems plausible that campus officials would want to try to minimize cost (or emissions or a combination of the two but let’s start with cost)
Min c x
st c x <= B
p x = 5
By inspection we see that the comfort constraint forces the solution x = 5 / p (assuming this is within budget, which we will assume).
So if p increases, clearly x decreases. In other words, in this scenario, increased energy efficiency leads to reduced energy consumption, and it is because the amount of what is being obtained with the energy is held constant.
Other scenarios – Given the three objectives, another natural way to look at this situation is as a multiple-objective linear program (MOLP). So far, we saw that when max cooling was the objective, Jevons’ paradox was in full effect. When cooling was constrained and min cost was the objective, Jevons’ paradox was not in effect at all. In the trade-off space explored by MOLP, you can probably guess what happens. The energy efficiency gains are split – less energy is consumed, though not as little as would be possible, because some of those gains are used to increase cooling without increasing energy use. Another variation would be to convert the cooling hard constraint in the campus scenario to a goal and solve the goal program. And of course, the setting can be changed to another type of energy use, such as heating, electricity, transportation, etc.
Coming back to my original question at the conference, I think the speakers were primarily in the college campus scenario. Most likely, they are already keeping their buildings at a comfortable level of heating or cooling, so any energy efficiency gains allow them to consume less energy, spend less money, and pollute less. In the transition from trying to maximize whatever quantity the energy is being used for (e.g. comfort), to not needing or not wanting to do so, Jevons’ paradox switches off. Campus electricity could be a little more complicated. Most likely individual buildings, labs, or dorm rooms for that matter do not have their own electricity bills. But if they did, I can imagine the paradox coming into effect. For example, a high energy lab that might have had to limit its operations due to high electricity costs, might consume more as energy efficiency increases.
In all, it was an interesting meeting. Thanks to Bill Leahy, Director of the Institute for Sustainable Energy at Eastern Connecticut State University for organizing it. For more information about the conference, go to the conference web site.