0:00

[BLANK_AUDIO].

Â So, our guest today is Don Loriad.

Â Don is an environmental engineer and a Professor Emeritus at the

Â University of North Carolina, in the

Â department of Environmental Sciences and Engineering.

Â Don spent his career working on environmental problems and

Â specifically, on water and sanitation problems in developing countries.

Â Don's been my friend and colleague for over 30 years and most of what

Â I know about piped water and sanitation

Â systems in developing countries, I learned from Don.

Â So, Don, thank you so much for coming today.

Â It's a pleasure to have you here.

Â >> What a, what a gracious interview.

Â I wish it were true.

Â My mother would love to hear that.

Â [LAUGH]

Â >> Let me, let me start and ask you, as we're going to, we're

Â going to talk about estimating the cost of piped water and sanitation systems today.

Â Are there any principles or characteristics that our students should

Â think about, before they actually get into the cost estimation task?

Â >> indeed, Dale.

Â There're few things that, that come to mind.

Â 1:33

And a, and a mathematical form.

Â So I think those four issues are really important, okay?

Â The nature of the system, the dependent variable, the

Â set of explanatory variables, and the mathematical formula for [CROSSTALK].

Â >> So why don't you start, with that list of four and tell us about.

Â >> Well let me start with the nature of the system.

Â The nature of the system, oftentimes, is something that the modeler may not have

Â a lot of control over, because the the cost modeler needs a set of data.

Â But I generally think of systems falling into just two categories.

Â Water and sanitation systems the first category being entire integrated systems.

Â An example of which would be if we

Â have total cost, construction cost data that includes a

Â water intake, a transmission main, a pumping station, a

Â treatment plant, elevated storage tanks in, in addition to.

Â >> So this'll be like a green field site right, I mean yeah.

Â >> So.

Â >> Yeah, yeah.

Â >> So that would, that would require one kind of mathematical

Â model if we had data on total costs of these integrated systems.

Â And the other, much more common situation is,

Â when we have data for individual components of systems.

Â So we have data for intakes, or we have data for pumping

Â stations, or we have data for treatment plants, or networks, or elevated tanks.

Â And it's really the latter category.

Â The, the separate the, the separate components of systems that

Â are almost universally the subject of cost modelling in the literature.

Â And as a matter of fact, it's easier to

Â get data for those components and the models that are

Â postulated tend to fit the data much better, much better

Â fits than when we tried to model totally integrated systems.

Â >> Well should, should we go component by component

Â and talk about how to model this, I mean.

Â I guess a big component is the pipe networks, right I mean so.

Â >> Sure, we can start with the networks.

Â And, interestingly, they are they tend to be the the most difficult.

Â I'm going to look at my notes here.

Â I pulled together some ideas and I want to make sure I kind of stay on message.

Â >> Sure.

Â >> With those.

Â So,

Â 4:02

It's pretty easy to find construction cost data for pipes.

Â That's because most pipe networks are built

Â by the public sector, and the projects are

Â put out for bid, and the contractors are

Â asked to break down their proposal, their bid.

Â proposal.

Â By types of pipe.

Â The materials of construction that could be ducked

Â to iron pipe, for example, vis-a-vis PVC pipe.

Â And then for each of those different materials the

Â contractors will list we're going to have so many.

Â Lineal meters, what with pipe length.

Â Of let's say 2, 2-inch diameter pipe, I'll use inches rather than metric.

Â They just.

Â >> Yeah, that's fine.

Â >> Easier for me.

Â So many meters of 4-inch pipe, 6-inch pipe, 8-inch pipe.

Â So we tend to have from contractors pretty good bid information.

Â Pipes of different materials, the diameters of

Â the pipes, and the lengths of those pipes.

Â And that kind of information makes it pretty easy to

Â develop a cost equation for a pipe of a certain material.

Â For example, let's, let's think about PVC pipe.

Â Lots of developing countries manufacture their own PVC pipe.

Â Ductile iron is typically imported.

Â But if they're manufacturing this pipe for themselves, then.

Â Let's, let's think about PVC pipe, and assume that in a in a bid proposal

Â form a contractor, we have information for

Â PVC pipe of different diameters and different lengths.

Â And the question I hear you asking is, how are we going to develop a

Â cost equation for that, how are we going to develop a cost model for that?

Â Okay.

Â And what I, and, that model's in the first slide, slide one, figure one.

Â 6:00

The dependent variable, interestingly, is not total cost.

Â If we, but rather, cost per unit length.

Â Cost per meter of length.

Â So if we have, if we were to think of, let's say three columns of data.

Â We have a column of data of cost.

Â Next column of, of data will be the diameters, different diameters.

Â Next column will be the different lengths of pipe.

Â If we divide costs, total costs, by length we have costs per unit length.

Â That's the dependent variable that works best for me, and

Â that leaves only on the right hand side of the equation.

Â A single explanatory variable which is the diameter of the pipe.

Â And the mathematical form of the equation that tends

Â to fit the data best is a log linear equation.

Â That is what we typically call a power function.

Â So the equation that is shown in figure one.

Â It's going to be cost per unit length is equal to some parameter, I

Â call it alpha in, in figure one, times the diameter D raised to some

Â exponent beta and, in order to fit that kind of a model to these raw data.

Â We have to take the log transform of cost

Â per unit length, and the log transform of diameter.

Â What comes out from, falls out from ordinary Lee squares are the parameters

Â that of best, best fit for alpha and beta, the two statistical parameters.

Â Okay?

Â >> And so is that the cost for purchasing

Â the pipe or the installing the pipe or both?

Â >> Great question, Dale.

Â Typically the data that that are, are available from contractors in their bids.

Â The contract documents call for the contractor to both

Â furnish and install, okay, so it will cover furnishing install.

Â That's a complete operating installation so if you think about,

Â what is the install part, there are lots of different.

Â Components, I mean after all you'll have to open up a trench,

Â and you'll have to get people down into the trench to fit the

Â pipe together, you have to back fill the trench there's paving, you

Â have to control traffic, so there are lots of different components with that.

Â But, typically this model, the log linear model.

Â For a pipe that goes into a

Â network covering both furnishing and installing, alright?

Â Is this power function that we talked about and almost universally

Â Dale, the value of beta lies between one and two, okay?

Â >> Is that the same for water systems and for sewer lines?

Â >> Not at all.

Â >> You're talking about water lines now.

Â >> I'm talking about water lines, okay?

Â If we get into sewers, sewers are complicated, that's for sure.

Â Let's stay on the water bit just a little bit.

Â 9:08

Of the cost calculus, is pretty easy because

Â pipe is pretty easy to manufacturer and it's the,

Â the, the furnishing part is mostly a matter

Â of what is the cost of making the pipe.

Â It's manufacturing time.

Â Not entirely.

Â Because I could tell you a story, if we have time for it, about

Â there is transportation and sometimes transportation can

Â really dominate the costs of the furniture supply.

Â >> I think you've told me that story, about Yemen, yeah?

Â >> Yemen, Yemen.

Â >> Why don't you tell our students, yeah.

Â >> Well, Yemen was a fascinating situation.

Â For years, I think it's fair to say for decades,

Â I would go into developing countries whether in Latin America or

Â South East Asia or Africa or wherever and one of it,

Â since I was doing a lot of work on pipe networks.

Â They are really hard to design.

Â They're hard to estimate their costs, and

Â immediately I would do these cost equations.

Â So, I'm doing cost equation, and I find

Â out the value of betas between one and two.

Â I go to Yemen and I find out the value of beta is less than one.

Â And I say, immediately gets my attention, and I say, what's going on here?

Â With this value of beta less than one.

Â All over the world, different continents I'm finding betas between

Â one or two, and here it is, less than one.

Â So I immediately think of, yeah, I either have a bunch of

Â bad data, so erroneous bids from contractors, or there's fraud going on.

Â Wonder what in the world is going on here, so I start

Â asking a bunch of questions only to learn I was working in Sana.

Â Which is the capital city of Yemen, sometimes called North Yemen.

Â 10:42

That the pipe is, is all imported pipe and it came into the port city of Hodeidah

Â on the Red Sea and then it had to

Â be transported on flatbed trucks for hundreds of miles.

Â And of course the cost of transportation almost,

Â almost swamped the cost of, of furnishing the pipe.

Â And because the transport makes no distinction among pipes of

Â different diameters, it made that exponent of B, less than one.

Â Large, large economies of scale.

Â It, the transport [UNKNOWN] cost was essentially a fixed setup cost, okay?

Â >> Mm-Hm.

Â >> But why is beta usually used between one and two?

Â Because on the, if it, if it were only the furnishing

Â the, the cost of pipe, the exponent of beta would be two.

Â It'd be very easy to show that.

Â It would depend on the materials.

Â The, either the weight or the volume of the materials.

Â The PVC that went into the pipe.

Â 11:38

But once we get into the construction cost, the installation

Â cost, opening up the trenches, putting the pipe in the trench,

Â putting workers down in the trench, back filling the trench,

Â controlling the traffic, buying the land, almost all of those costs.

Â Are independent of the diameter of the pipe.

Â They, too, look like fixed costs because you have to open up,

Â for example, a trench, trench of certain width for people to be

Â able to jump down into that trench to put the pipes together,

Â with the pipe is, whether the pipe is two inches in diameter.

Â Or ten inches in diameter.

Â If you get into really large diameter pipe, 36, 48 inches, 60

Â inch diameter pipe, then the size of the trench it is in fact

Â dictated by the size of the pipe, but that's uncommon for most

Â water distribution networks in cities [INAUDIBLE]

Â you don't get into pipes that size.

Â So, those costs, the installation costs, are really

Â treated as a fixed charge, along with the

Â transportation cost and that's what tends to pull

Â the exponent of data down from somewhere between.

Â What it would be, too, if it was

Â only furnishing, but to the furnishing and then stop.

Â Okay, that make sense?

Â >> Yup, Yup.

Â >> Now you had asked me about sewers?

Â >> huh.

Â 13:38

What this means is that for piped water networks, piped water

Â systems, the pipes can actually follow the contour of the ground.

Â So if the ground goes up, if it rises, the pipe is

Â still buried maybe a couple of meters below the surface of the ground.

Â So, if the ground is undulating, the pipe is

Â the depth of the trench and this makes it.

Â These models fit the data very well.

Â That's not the case with sewers.

Â Sewers are running downhill.

Â So if we get into hilly terrain.

Â I'm thinking right now of a city like Tegucigalpa, the capital city of, of,

Â of Honduras, that essentially lies in bowl,

Â with large mountains shooting up all around it.

Â The same is true of Quito, Ecuador, for example.

Â Undulating ground.

Â So, the, you can't always find ground that

Â wants to run downhill in such hilly terrain.

Â So that, sometimes, if you are in, on a

Â street where in fact the street is running downhill

Â and the, and the, the sewer is sloping down,

Â 14:45

It's going to get deeper and deeper in the ground.

Â And then if the ground starts to rise it gets very deep

Â in the ground, right, and that gets to be very expensive construction.

Â And if the depth of the trench gets to be something like five or six meters.

Â Then to construct a trench with straight sides such that the walls are

Â not going to collapse on the workmen when they get down in the trench and kill them.

Â You get into the construction of having to install sheeting, what's called sheeting.

Â It can be wood sheeting, it can be

Â steel sheeting, but these are either planks of wood

Â or, or, or planks of or sheets of steel

Â that buttress the walls that keep them from collapsing.

Â They have bracing.

Â Very, very expensive construction.

Â And for this reason Dale, the cost of a sewer

Â system is much more dependent on typography than a water system.

Â So it's pretty easy to model the cost of a water pipe network.

Â Very, very difficult to model the cost of a sewer network.

Â >> So can we go back then to the modeling of the water system for a minute?

Â >> Yeah.

Â >> So, you were talking about contractors putting bidding documents and I

Â guess that's the data set you'd use to estimate the cost function.

Â Can you tell us a little bit about what kind of data

Â sets you need and sort of the size of the data sets?

Â I mean, how many kinds, our students are trying to estimate a water cost function.

Â >> Right.

Â >> So, what should they be looking for in terms of datasets?

Â 16:25

>> Okay.

Â Since water networks are mostly constructed in

Â the, in the public sector, not entirely.

Â Let me digress for just a minute.

Â Think about.

Â Private estates.

Â You and I were working in the Philippines some time

Â ago, and there were lots of gated communities, private estates.

Â Where it was the developer who constructed both the water and, and the sewer system.

Â Those data are typically hard to get because

Â it's a private enterprise that has developed those communities.

Â But for most water supply networks, they're constructed in the public sector.

Â And the public sector requires there's a net advertisement for the project, it is

Â publicly bid, then there is a formal bid opening by all the contractors who submit.

Â Who submit their bids, and those documents are in the

Â public sector, so the public sector will make them available

Â for people who ask for them, and what students should

Â be aware of is that you don't only have to find.

Â The lowest bid, the successful bidder, he may

Â have had the overall lowest cost, but all

Â of these contractors are going to have bid

Â prices that are usually fairly close to each other.

Â So, don't turn up your noses at.

Â Unsuccessful bidders who didn't get the job.

Â Those cost data, also, are relevant.

Â And what students might want to do is if there were a single project, for example,

Â where there were, let's say, four or five or six different bidders on that project.

Â And there was a large component of a piped water supply system.

Â The students might want to look at, at all of the all of the different bids.

Â The costs of them.

Â That raises an interesting question, Dale.

Â For, my wheels are turning here as you ask these questions.

Â But.

Â Let's assume that there were five different

Â bidders for the same project and the students

Â found cost data for each of those separate in the contractors in their bid documents.

Â 18:33

How would they use the data for developing a cost equation?

Â I've already suggested that the cost equation is cost per unit

Â length as a function of diameter on the right hand side.

Â A single explanatory variable.

Â And you're going to actually use the log transforms of those data.

Â But now we have five or six different sources of data.

Â What would you do?

Â What would I do?

Â I would probably include dummy variables.

Â I would pool all of the data, right?

Â And I would have, if there were five different contractors that

Â had submitted bills submitted proposals, I would probably

Â pool all of the cost data for all five contractors and that

Â implies the need to include four dummy variables always.

Â These are, there are five categories.

Â The number of dummy variables is one less than the, than the category.

Â The baseline category is some one of those contractors would be the best.

Â I'm not sure if that's coming apart.

Â Now the students can get into that.

Â >> Yeah.

Â >> They'll find.

Â This kind of information, maybe not in

Â elementary statistical courses, but always in econometrics courses.

Â The econometricians do a lot, a good deal of this.

Â >> So you've talked about the pipe

Â network, what about the other components if you.

Â Pumping stations, overhead storage tanks, you know, transmission lines.

Â >> Yeah, I think I probably mentioned when

Â I was talking about these two different kinds

Â of systems, integrated or separate components, that those

Â kinds of data are easier to get hold of.

Â And as.

Â Why are they easier?

Â Let's first of all talk about why they are easier,

Â because as a matter of fact, even in developing countries it's

Â not easy to find too many integrated systems that are being

Â constructed from scratch all at one, that include all the components.

Â What most cities are doing, or most communities

Â are doing, or even development, neighborhoods are doing.

Â Is that they are making changes or improvements in individual areas.

Â So it's pretty easy to find lots of information on the individual components.

Â Without question Dale,

Â 20:50

The most common mathematical form of the model that is fitted to the cost data.

Â Furnished and installed cost data for individual components.

Â Let's think about, let's think about treatment plants right now.

Â Water filtration plants.

Â Not hard to get those kinds of data the mathematical formula that fits is

Â a power function with a single explanatory variable on the right hand side.

Â And that would be the hydraulic capacity of the system.

Â The dependent variable on the left hand side would be the total

Â construction cost, unlike the pipe networks

Â where it was cost per unit length.

Â So, it would be the total construction cost on the left hand side.

Â And the explanatory variable on the right hand side would be

Â the hydraulic capacity, and it's not the hydraulic capacity of the

Â number of people that are going to be using that system,

Â when it gets, after it's constructed, in a year or two.

Â It's going to be the design capacity.

Â So if we're talking about treatment plants, they're typically designed for a

Â design period of maybe 15 or 20 years into, into the future.

Â Even in developing countries, long design periods, so one

Â would have to know what was the design population.

Â And the, of course the bonding design flow.

Â That raises then some questions about, what flow?

Â Is it the average flow?

Â Is it the peak hourly flow?

Â Is the the peak daily flow?

Â So I think for these kinds of components,

Â so pumping stations or treatment plants or water intakes.

Â The variable on the right hand side is a measure of flow capacity and had units

Â of something like cubic meters per day and

Â is probably the average, the average design flow.

Â For that, for that system.

Â That would be the best indicator explanatory for it on the right hand side.

Â >> Okay, so Don, you're talking about cost functions for one component, but how

Â do we get from that one component up to the total cost for a system?

Â So, our, our students are really not mostly engineers, right?

Â So I, I'm hoping that they can get a sense of.

Â You know, ball park cost for serving

Â households in different places in developing countries.

Â So they know when they're kind of in the, in, in the right range.

Â >> Yeah.

Â >> So how do they.

Â How do they get to that, you know, up to the

Â system level, and then also from there back to the household level.

Â >> Okay.

Â Great questions.

Â 23:50

Let's take that basic equation.

Â Let's bring L, the length of pipe that was on the left hand

Â side of the equation, over on to the right hand side of the equation.

Â So, what figure two shows, is that the total

Â construction cost first and salt of a network, C,

Â is equal to some parameter alpha, some explanatory variable

Â diameter, D, raised to a parameter beta, all times L.

Â We want to use this equation for

Â predicting the cost of an entire pipe network.

Â How are we going to do it?

Â For L.

Â Use the total length of pipe that's in the network, okay?

Â So, the length of all the pipe that goes into the network.

Â Huh?

Â If you do that, then what are you going to use for D?

Â D is going to be the average diameter.

Â Well, what does that mean.

Â The average diameter is a diameter, it's,

Â it's, it's the diameters of all the different

Â kinds of pipe that go into the

Â pipe network, weighted by their respective lengths, okay?

Â Now.

Â So, f I have some 2-inch diameter pipe, 4-inch diameter

Â pipe, 6-inch diameter pipe, 8-inch diameter pipe, 10-inch diameter pipe.

Â If I multiply each individual diameter, multiply

Â it by its respective length, sum it up

Â over all different diameters, and divide by the

Â total length of pipe, that's the average diameter.

Â And that shows up in figure three.

Â 25:20

Okay, so if we have an idea of what

Â is the average diameter of pipe that's in network.

Â Average being weighted by their individual lengths.

Â >> You mean for a whole city?

Â >> For a whole city, for a whole network and we

Â have a pretty good idea of what's the total length of pipe.

Â How do you get that?

Â Well, what's the length, length of streets?

Â If you're going to have house connections, you need a pipe in front of each of them.

Â In front, on, on each on each street.

Â So if we have an idea of what the total

Â length of the streets is, so that's the easy part.

Â What's the average diameter?

Â Depends on the size of the city.

Â In the United States, what drives the diameters of pipes is not so much

Â the hydraulic capacity, as much as the capacity that's needed for fighting fires.

Â That's not the case in developing countries.

Â In developing countries, even in pretty large cities,

Â the pipe network is designed to carry the flow.

Â That, that people are going to use

Â in their households and in their businesses, right?

Â So, and those pipes tend to be smaller than what we find in the industrialized.

Â >> So, we should be, should be cautious transferring it, cost estimates

Â from developing countries where fire's important

Â to, I mean, for industrialized countries.

Â >> [CROSSTALK] That would only apply to integrated systems.

Â If you think about these models we're developing.

Â We have a pipe cost function, cost per, per unit dip,

Â length is equal to alpha, the diameter of pipe raised to beta.

Â Okay.

Â The question I think you're raising is, let's be careful that we make sure that we

Â don't use average diameter pipe in industrialized countries

Â and assume that the average diameter of pipe.

Â >> Right.

Â >> In developing countries is going to be in the same ballpark.

Â It's not.

Â In developing countries there's going to be a predominance

Â of small diameter pipe, a lot of 2-inch diameter pipes.

Â In our town where you and I live,

Â the smallest diameter pipe is 6-inch diameter pipe.

Â In New York City, it used to be 8-inch diameter

Â pipe is the smallest diameter pipe, now it's about 10-inch.

Â So, on individual streets 10-inch pipe is the smallest diameter pipe.

Â In developing countries, even in large cities, in metro Manila, with millions and

Â millions of people, they've got tons of pipe that's two inches in diameter.

Â So if one were going to be replacing pipe in a, let's say, a neighborhood

Â of metro Manila, one would need to have an idea what's the smallest diameter pipe.

Â What's the largest diameter pipe?

Â So, and you get that from the engineers.

Â And then you make some guess, probably,

Â or an engineering preliminary design of the pipe

Â network to come away with some idea of what would be the average diameter pipe.

Â Then you go back to your individual cost function and use that to

Â predict what would be the cost of

Â the entire network in that particular neighborhood.

Â Given that you have an idea of what's the total length of streets and maybe

Â what the average diameter is depending on

Â where that net, where that neighborhood is located.

Â If it's located near the, the center of the city, you're going to have

Â large diameter pipe service way out in

Â the perforates, going to have small diameter pipes.

Â >> Can we, can we step back again and, and.

Â >> Sure.

Â >> And talk about the, this issue of economies of scale.

Â >> Yeah.

Â >> And your equation that means so, what can, can you tell us a little bit

Â more about and so, what you think of

Â as economies of scale and pipe water networks and.

Â >> Oh yeah.

Â Okay.

Â I've already alluded to this and maybe I'll try to sharpen it.

Â 29:15

The exponent of diameter being a number greater than one

Â implies if we make a graph of that cost function,

Â with cost per unit length on the vertical axis, the

Â ordinate, and diameter on the horizontal axis, that is the abscissa.

Â That's a convex function.

Â It bends up and it goes through the origin.

Â So it starts at the origin and it bends up.

Â It's a convex function.

Â Right.

Â Now you and I, since we work with economies of scale, normally

Â think of those kinds of convex functions, do not reflect economies of scale.

Â But we know, we know, that there are large economies

Â of scale, and water pipe networks, not only in the

Â trenches, not only in the install part of the equation,

Â but in the furnishing part of the equation as well.

Â For example, the carrying, the hydraulic capacity of 6-inch diameter

Â pipe, is twice as large as the hydraulic capacity of 4-inch diameter pipe.

Â All you have to do is increase the diameter of the pipe

Â from 4 inches to 6 inches and it carries twice as much flow.

Â That is an indicator that there are economies

Â of scale, that is, if we had the cost

Â of that pipe, the average cost of using

Â 6-inch pipe in terms of it's flow carrying capacity.

Â Is a lower number than the average cost of a 4-inch diameter pipe in terms of it's

Â flow carrying capacity, so this pipe cost function Dale, is a little bit tricky.

Â It doesn't, it, it, the D, the diameter does not reflect hydraulic

Â capacity, and I don't recall if I said at the outset when we were talking about.

Â In general, what are the explanatory variables on the right hand side of these

Â cost equations, but in every one of them, flow carrying capacity is key.

Â It, it is ubiquitous.

Â It turns up in all of mathematical models that

Â have been developed for decades and decades and decades.

Â There are some components of systems that you can't use

Â flow carrying capacity, like, for example, an elevated storage tank.

Â Okay?

Â But for wells you can.

Â What's the capacity of the well?

Â Well, that's going to dictate the size of the, the tube that's

Â punched down into the ground, and that dictates much of its cost.

Â So we're talking about economies of scale.

Â In fact, this pipe cost function that has D on the right hand side.

Â Would reflect economies of scale if the D

Â were replaced by some indicator of flow carrying capacity.

Â And, engineers know there are lots of empirical equations for doing that.

Â The most, the most popular being, the so called, Hasner

Â Williams equation, that has a relationship between flow carrying capacity,

Â Q is usually used for that, and the diameter pipe,

Â so if you make a change of variables in that equation.

Â You find that the exponent of Q, the flow carrying capacity is about 0.5, or 0.6.

Â It's a number much less than one.

Â This is big economies of scale.

Â Big economies of scale.

Â Right.

Â >> Okay.

Â >> Okay.

Â And on the trench side.

Â So the installation side, big economies of scale, because those costs

Â of installing are not related to the flow-carrying capacity of the pipe.

Â [BLANK_AUDIO]

Â