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 BLOG >> June 2017

Multiple Factor Optimization [Lean Startup
Posted on June 29, 2017 @ 11:04:00 AM by Paul Meagher

Lean Startup Theory advocates the use of ongoing experimentation to find out if customers value your product or not. The use of A/B testing is often used determine if some feature is having a significant positive influence on customers or not. The popularity of A/B testing derives from the fact that it is easy to change some minor feature of a website to see if some success measure is improved or not relative to the control/existing version of the website. The technique is easy and the math is easy (but check this out).

A/B testing is only one experimental technique that might be used and it has some limitations. One limitation is that it is often used to test only one factor or version at a time to see if the factor/version improves success metrics or not. Optimal performance is often a function of the interaction of two or more factors that can not determined by testing one factor at a time. Chemical reactions can occur optimally at a combination of temperature and pressure that is not predicted by studying each factor separately.

Today I want to mention a methodology that is not that well known but which is used in industry to find the factors and the levels of each factor that produces optimal outcomes. That methodology is called Response Surface Methodology (RSM) and is commonly used in chemical industries to find the optimal operating conditions (temp, pressure, catalytic agents, reactants, pH, etc..) for producing a chemical reaction.

Response Surface Methodology begins by listing all the factors that might contribute to the response. It also examine the levels that each of these factors might take on. When you do this you quickly run into a combinatorial explosion of factor levels to test. Where Response Surface Methodology comes in is to help guide you towards a reduced set of factors/levels to interatively test to arrive at an estimate of the optimal factor level settings.

All I can hope to do in this blog is mention a couple of ideas from response surface methods that I found interesting and am still exploring.

If you have, say, 3 factors (temperature, pressure, pH) with 5 levels then to run a full factorial design requires that you measure responses under each of the possible 125 conditions. This is generally not economically feasible so the question becomes whether you can find the optimal condition by studying some subset of conditions, often called a fractional factorial design. One such design that is popular in RSM is called Central Composite Rotable Design. That is an intimidating phrase for a neat idea. Basically you reduce the number of levels by only testing the extreme levels of each factor along with the median level of each factor and interpolating all the values that would fall in between.

So if you wanted to test the growth of a plant as a function of nitrogen and moisture instead of studying all the levels of each factor you would only test the response for the median levels of each factor and the extreme levels of each factor and try to interpolate what the response would be between these levels. Other fractional designs are possible.

The second idea from RSM that is worth thinking about is to plot the levels of your factors on each axis to generate a response surface that depicts our how the variables interact. The combination of moisture and temperature levels will generate a growth response in the plant that can be plotted as a response surface that an educated eye can read to better grasp what the optimal factor levels might be, or what tradeoff might might be best to make. We are all familiar with drawing and interpreting graphs consisting of curves, but not so familiar with drawing and interpreting surfaces and contours so as to understand the interaction of 2 variables. Being able to visualize the interaction of 2 variables as response surfaces can allow our visual system to process the information more thoroughly than a set of numbers would.

I have found that a good starting point for understanding response surfaces is Khan Academy's tutorials on Multivariate Calculus. You don't have to know calculus to learn some useful multivariate skills from the first few tutorials.

I hope this blog has helped to convince you that there are experimental methodologies besides A/B testing that might be applied to discovering the right combination of factors for your product or service. One at a time testing does not provide any insight into the potential interactions of that factor with other factors. For that you need a factorial design and to administer it efficiently you may want to consider response surface methodologies.

The definitive text on RSM is by George Box and Norman Draper with the title Response Surfaces, Mixtures, and Ridge Analyses (2nd, 2007). Not an easy read but worth scanning for ideas and probably very useful if you want to use RSM to optimize your product or service.

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Increasing Yield: Part 5 [Agriculture
Posted on June 22, 2017 @ 09:47:00 AM by Paul Meagher

Jean Martin Fortier, in his excellent book The Market Gardener (2014), explained and illustrated how he and his wife make 100,000$ per acre. There farm is an example of a very high yielding enterprise measured by the quantity of produce grown or income generated.

A critical aspect of their argument as to why the farm was high yielding was because he did not use a standard tractor and its accompanying implements to cultivate the land. Instead he relied on smaller scale equipment that was appropriate to the permanent bed system he setup on his 1.5 acre gardening area. He argued that this helped also with the financial yield of the system because he did not have associated machinery debt and maintenance costs. He was not afraid to spend money on tools that improved his productivity, he just made the decision that he didn't see a role for a standard tractor in maximizing yield.

The metaphor of the market gardener is that there are alot of potentially good paying niches our there were our focus might turn to improving quality and getting better at production, rather than getting bigger. Investments into quality and efficiency can still increase yield without dedicating more physical area to production. By focusing on quality and efficiency, we might increase yield by getting more production using less work and inputs and higher prices for better quality. Fortier's argument is that getting bigger in physical scale is not the best route to increasing yield.

That being said, Jean Martin had a generous benefactor invest alot of money into scaling up the market gardening approach to more than 1.5 acres (to 8 acres). This latest video shows how he is scaling up in a way that remains true to many of his market gardening practices, but he now has the room to incorporate new animal and permaculture systems to potentially produce even greater per-acre yields. That is still to be determined. As far as his benefactor is concerned, the most important yield of the system might be the trained market gardeners that the larger scale operation can foster. There are multiple types of yield a business can try to optimize for and which defines what the enterprise considers success.

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Increasing Yield: Part 4 [Agriculture
Posted on June 13, 2017 @ 06:47:00 AM by Paul Meagher

In previous blogs (part 1, part 2, part 3), I have argued that the term yield is most useful as a measure of productivity per unit area. Some usages of the term yield are simply productivity measures without any accounting of the area involved (e.g., stock and bond yields). Here we will delve deeper into the spatial aspect of yield and talk about yield mapping. Yield maps are visual depictions of how yield varies as a function of GPS coordinates.

There is a convergence of technology in agriculture that enables on-the-fly calculation of yield as an operator is harvesting a field. Yield mapping technology is built into some combine harvesters now so the operator can gauge or verify that a certain part of a field is yielding more than others and to compare to historical yields from that area.

The 4 ft x 8 ft garden I planted in my cold frame exhibits a similar variability in productivity per unit area with yield being quite high in most areas, but with a noticeable gap in one area where I have planted basil (at the same time as the other crops).

The power of yield mapping comes from comparing it with other maps that contain information about the presence of other variables. A combine harvester might also contain sampling tools that record the level of nitrogen or moisture in the soil as it progresses through the field enabling the operator to see how the yield map might be explained by the levels of nitrogen and moisture in those areas. The yield maps might also be compared with maps produced by flyover drones doing multi-spectral imaging as a basis for measuring different field characteristics. The point is that to increase yield we can't just measure yield itself, we also have to measure other characteristics that might explain the yield patterns and, in the case of farming, would allow us to make precise interventions to improve yield.

So the concept of yield mapping includes not just mapping the levels of productivity over an area but can also be extended to mapping associated variables that might be used to explain and improve yield (e.g., where it might be lacking in, say, nitrogen in a certain part of the field).

In a store front, we could measure yield per square foot or cubic foot of space. We could do yield mapping of each shelf in the store and compute the relative yield derived from the different locations of the store. We might measure yield by computing the amount of income generated by a given area of shelf space. Perhaps we could optimize store front yield by co-relating the yield map to the presence of other variables that might co-vary with such yield. Yield in agriculture is also affected by ambient conditions like the weather. Similarly, yield in a store front would be affected by factors such as types and levels of traffic, socioeconomic status of the catchment area, and the competitive landscape. Something like yield mapping might be useful to do in bricks and mortar establishments.

The term yield mapping was briefly mentioned in the interesting book Push Button Agriculture: Robotics, Drones, Satellite-Guided Soil and Crop Management (2016) by K.R.Krishna. The author argues that the next level of productivity improvement in industrial agriculture is now happening but will become more pronounced as robotics, drones, and gps technology makes further inroads into farming. The level of productivity per unit area of land will increase because we have more precise control over what needs to be done to maintain or increase yields (via maps created using drones, gps, and onboard sensors) but also because robotic innovation will continue to reduce the need for repetitive work to be done by humans. A lesson from industrial agriculture is that precision and robotics are two major factors that are now being targeted to increase yields even further.

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Increasing Yield: Part 3 [Agriculture
Posted on June 6, 2017 @ 07:23:00 AM by Paul Meagher

I had some additional thoughts on increasing yield this weekend that will be the focus of today's blog (earlier thoughts at part 1 and part 2).

Just to refresh, I use the term yield to refer to a measure of productivity per unit area. Productivity might be measured in dollars or in bushels of corn. Often dollars are used as a surrogate measure of yield but it is not perfectly correlated with physical yield because the yield in dollars is also affected by supply and demand. That being said, we are often interested in yield measured both in dollars and bushels as they both provide useful information.

The calculation of yield is also affected by two major complicating factors.

One complicating factor is that yield is a multidimensional concept. You can increase yield across several dimensions at the same time and a good designer often is.

In 2011 Ethan Roland & Gregory Landua wrote an influential essay called The 8 forms of capital. This diagram gives you a quick overview of the categories they posited.

Where Ethan and Gregory use the term "Capital" I might use the phrase "Types of Yield" and regard each of these as types of yeild a project might address.

Another complicating factor is that yield can be hard to assign. For example, I sell square bales of hay from my barn to clients consisting mostly of horse owners. One horse owner confided to me today that she keeps her horses in the barn during the hot part of the day when the flies are bad. She likes to have some hay available for them to eat. The hay that we sell to such horse owners is stored in the barn and sold from there.

What is the yield of the barn measured in dollars? Besides the tricky, but interesting math involved, we also have the problem of deciding what percentage of the final price obtained should be attributed to the storage aspect. There were also the costs of mowing, teddering, raking, baling, moving it into the barn, and beer to quench the workers. You can assign a percentage but to find solid grounds for doing so may also be tricky.

Ultimately, we always have to come back to the fact that yield is meant to be a practical concept that we might use to assess performance on a per unit area basis. These complications make the calculation of yield more difficult but possibly also more meaningful and relevant.

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Bottom Up Design [Design
Posted on June 1, 2017 @ 01:08:00 PM by Paul Meagher

This morning I spent some time googling designs for transporting bicycles as I will be confronted with that issue tomorrow. There were some good ideas for do-it-yourself bike carriers.

Before deciding on any design I decided to place my bikes in the back of my truck to see how they fit. Yesterday, I finally installed a metal carrier on the back of my truck that I intend to use for transporting lumber and kayaks. By chance, the position of the top metal railing is slightly above the top of the handle bars of the two bikes. Also, the handle bars of both bikes are roughly the same height of the ground.

This opens up the potential for a much simpler design than I've seen to date that takes advantage of these fortuitous circumstances. That design involves simply running 2x4 lumber from one railing to the other, using a couple of U-bolts to mount the 2x4 lumber to the railings, and then using some type of clip to mount the handles to the 2x4 lumber. After around an hour of working on it, this is what I finally came up with.

This little design episode reminds me that design should not be a top down exercise. It is definitely useful to get top down guidance by seeing how other people solved a similar problem but we should also do mock ups so that we can also get bottom up feedback on what might work. Sometimes the bottom up feedback is sufficiently good to suggest an opportunistic design that can solve the problem.

FYI: I used two 13cm rubber bungee cords to secure each bike handle to the pressure-treated 2x4. I removed an S clip from one side of the bungee cord so that I would have a hole to insert the remaining S clip into (forming a loop with one clip). So far the bike carrier appears to work ok. The bikes are very solidly in position and stayed in position when I took some sharp turns to test it out. It is easy to strap the bikes in and remove them. Hopefully there will only be minor wear on the handles from the rubber bungee cord and lumber holding them in place. I could install another beam and reverse the direction of a third bike to have it comfortably fit in the back of my truck. Bikes could be secured to the metal rail with a bike lock if that was a concern.

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