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 BLOG >> Decision Making

Fudge Factor [Decision Making
Posted on May 1, 2018 @ 07:12:00 PM by Paul Meagher

Wikipedia defines a fudge factor as an ad hoc quantity or element introduced into a calculation, formula or model in order to make it fit observations or expectations.

A common use of a fudge factor is in project management where you estimate how long a project might take and then multiply that time by some fudge factor to account for events or difficulties you can't anticipate. The size of the fudge factor might vary by task type or by how much estimating skill you have.

Another use of a fudge factor is in pricing your services. You might, for example, price your services differently depending on how busy you are. If you are busy already then you might multiply your going rate by some premium (e.g., x1.20 = 20% more) because you don't really need to add more work to your plate. If the customer bites at that price then it would be worth taking on the extra work but if they don't then you already have more than enough work at your going rate. Many different factors might influence your service pricing and the corresponding fudge factors you might want to use.

Fudge factors are also common in valuation where the value of a company is estimated to be some multiple of earnings (or some other quantity) common to companies in that industry. This reduces a very complex analysis to a simple rule of thumb that may or may not prove to be predictively accurate.

I recently did some year-end accounting for my farm and had to apply a fudge factor to my books to account for some uncertainty in my final numbers. A farm is like a small manufacturing plant that incurs lots of different types of expenses and receipts. The farm accounting fudge factor involved not claiming a certain amount of expenses that my bookkeeping told me I could claim. I left them unclaimed because I wanted to give myself a margin of error in case I was ever audited. The use of fudge factors in accounting is generally frowned upon and for good reason (see below), however, there is a cost to striving for extreme accuracy and there are judgement calls as to whether certain expense should be claimed. There is also procrastination and deadlines that force you to spend less time than you would like re-examining your receipts and numbers. To protect myself, and to terminate the accounting process faster, I used a fudge factor that involved not claiming a certain amount of expenses on the off chance that I might be audited. If audited, the government may end up owing me money. I can sleep soundly at night knowing that.

Fudge factors in accounting are often used to inflate earnings to make a company look more profitable than it is. Such practices are often called "creative accounting". Creativity in accounting is apparently a bad thing but you will often hear people say a good accountant will pay for themself - not because they are "creative" but are good at finding ways to decrease income and increase expenses. See The Ethics of Creative Accounting for more discussion of "creativity" as it applies to accounting.

Does the use of a fudge factor indicate that there is a problem with your approach to estimating, pricing, valuation, and accounting? It very well could be, but I also think that there is just alot of uncertainty out there that that involves diminishing returns to try to tame. You can keep on trying to estimate how long it will take to build a house but mother nature, suppliers, workers and financial institutions can all throw a wrench into your meticulously prepared estimates. People of action may be happy with throwing a fudge factor onto an estimate and getting on with the business at hand.

What causes these adjustments to be called fudge factors is that they seem ad hoc, not based in any solid theory but perhaps based on experience. The definition of a fudge factor does not indicate why we might be tempted to introduce an ad hoc quantity into our calculations. In this blog, I've provided a few reasons why we might be tempted which often comes down to a fudge factor being a strategy for dealing with uncertainty and time constraints. Because entrepreneurs and investors are often mired in uncertainty and have a limited amount of time to get things done, fudge factors may be the key to moving forward.

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Personal Values Worksheet [Decision Making
Posted on April 13, 2017 @ 07:09:00 AM by Paul Meagher

I started reading Richard Wiswall's book The Organic Farmer's Business Handbook: A Complete Guide to Managing Finances, Crops, and Staff - and Making a Profit (2009).

A particular strength of the book is an enterprise budgetting approach to tracking expenses, revenues and profitability accross multiples lines of business. Each crop is considered a separate line of business. I recommend the book as a useful reference for learning how enterprise budgetting works in an organic farming context that makes enterprise budgetting concepts easy to read about and understand. A real estate entrepreneur managing multiple flips, for example, might benefit from seeing a practical example of how enterprise budgetting works. Adapt as required to your context.

The motivation for today's blog, however, comes from Richard's discussion of goal setting and an interesting worksheet he presented as part of that process. The worksheet is called the Personal Values Worksheet (p. 9) and the idea is that you set your goals based upon your values. You can use the worksheet to clarify what values are important to you. According to Holistic Management, the process of personal (and business?) decision making and goal setting should derive from clarified personal values so spending some time studying and completing this worksheet might be a useful exercise.

Personal Values WorksheetABCD
Accomplishments (achieving, master)    
Affectation (close, intimate relationships)    
Collaboration (close working relationships)    
Creativity (imaginative self-expression)    
Economic Security (prosperous, comfortable life)    
Exciting Life (stimulating, challenging experiences)    
Family Happiness (contented with loved ones)    
Freedom (independence and free choice)    
Health (for self, others, and environment)    
Inner harmony (serenity and peace)    
Intellectual stimulation (thought provoking)    
Order (stability and predictability)    
Personal growth and development (use of potential)    
Trust (in self and others)    
Pleasure (enjoyable, fun-filled life)    
Power (authority, influence over others)    
Responsability (accountable for important results)    
Self-respect (self-esteem, pride)    
Social service (helping others, improving society)    
Social recognition (status, respect, admiration)    
Winning (in competition with others)    
Wisdom (mature understanding of life)    

The originator of the Personal Values Worksheet is Ed Martsolf and you can follow this link to download the instructions for completing the personal values worksheet (PDF).

What I like about this worksheet is that it provides concrete examples of what we mean when we use the term values. It shows the diversity of values and offers a useful partitioning of the space of all values. The worksheet rating system (columns A to D) is also an interesting approach to clarifying value preferences.

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Stopping Rules [Decision Making
Posted on March 9, 2017 @ 11:37:00 AM by Paul Meagher

A stopping rule is used to determine when one should stop searching for things like a spouse, parking spaces, investment deals, a new home, a new secretary, etc.... The "look then leap" stopping rule suggest that we should just look for awhile so that we increase the likelihood of encountering the optimal spouse, the optimal parking spot, the optimal investment deal, the optimal house, the optimal secretary, etc... The question is how long we should keep looking before deciding to leap?

A considerable amount of research has been done to find an optimal strategy for determining when we should stop looking. It turns out that we should stop looking at secretary applicants after we have interviewed 37% percent of them. After that we should jump at the next secretary that is better than the previous secretaries we interviewed. If we are looking for a marriage partner, then we should figure out how long we are prepared to look for that partner and once we have used up 37% of that time, we should consider proposing to the next marriage partner that we regard as better than the ones we have been with to date. The 37% rule applies to either the number of items to be searched or the amount of time we have to search.

If you use this optimal strategy then 37% of the time you will pick the optimal item you are looking for. There is no optimal stopping rule that gives you certainty that you will pick the optimal item. The best investment deal may have been in the 37% of deals you reviewed to date and didn't make an offer on or perhaps if you waited until you reviewed 60% of the deals you would have found the optimal deal. If you set your optimal stopping rule at some number other than 37%, however, your chance of finding the optimal item will be less than 37%. That is all that optimal means in this context.

This form of the optimal stopping rule makes alot of assumptions so whether it is applicable or not depends on your particular situation. For example, if you are allowed to go back and pick the best secretary of the 37% you have interviewed, or if the secretary is allowed to refuse your offer, then the math behind the stopping rule changes and we would have a different optimal strategy for that situation.

The "look then leap" stopping rule also assumes that we are ranking items relative to each other (ordinal scale) rather than relative to some absolute scale (cardinal ranking). If we have some absolute criteria we can use to evaluate candidates then we can pick a candidate if they exceed some threshold we have set for selecting them. Using a "threshold rule" to determine when to stop is another stopping rule stategy we can use.

A "threshold rule" allows us to potentially finish our search faster than using the "look then leap" strategy. Instead of looking for who you might "love" the most by comparing each to the last, you instead set some criteria that your potential marriage partner must meet and as soon as the person meets those criteria you propose.

Stopping rules are important to determining when we should walk away from an investment. Those who lost everything during the 1929 Wall Street crash did not stop in time. Gerald Loeb pulled out before the crash and credited his stopping rule for his success in doing so: "If an investment loses 10 percent of its initial value, sell it".

There is also a rule when climbing Mount Everest that if you are not on the top by 2 o'clock then you should turn around. It does not end well for those who ignore this rule.

In my next blog on The Lean Startup book, I'll be dealing with the chapter titled Pivot and we'll see that this is very much concerned with knowing when to stop in your present course and when to persevere.

Stopping rules can be informed by mathematics and probability theory but can also involve general rules of thumb that have proved useful in the past. This discussion of stopping rules was inspired by Algorithms to Live By: The Computer Science of Human Decisions (2016) which focused on the more formal approaches to stopping rules, and Simple Rules: How to Thrive in a Complex World (2015) which focused on the rules of thumb that are used to guide our stopping decisions.

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Priorities and Constraints [Decision Making
Posted on May 24, 2016 @ 07:35:00 AM by Paul Meagher

Lately I've been thinking about how to prioritize what to do first. The problem of prioritization arises, for example, in trying to figure out what renovation would be most beneficial to an old house that we are gradually fixing up. There is a long list of things that could be done to improve the look and functioning of the house and often when I think one job should have the highest priority, some constraint or opportunity may present itself that reshuffles the list to make some job gain the higher priority. For example, if the highest priority job requires a certain skillset and that skillset is not available but another skillset is, then another task that utilizes the available skillset may become the highest priority.

Sometimes when we prioritize we don't assign a clear time frame for when the priority will be addressed. Sometimes this can be a weakness in our prioritization process as putting a time frame on the task might clarify whether the skillset required will be available then, and if not, cause us to reshuffle our priorities for a particular time frame. Prioritization is, afterall, something we must engage in every day and often on an hour-by-hour basis, so putting a time frame on our task list might help us be more realistic about whether the task can be accomplished within the time frame.

These days prioritization feels more like a process of working within the constraints of labor, weather, skillsets, safety and what needs to be done. Dealing with the flush of spring growth around the farm is a dance with nature, how many helpers I have, what their skillsets are, whether they can do the work safely and what needs to be done. I have a list of tasks that I would like to see done in the next week, and some have a high priority, but if the weather is not cooperating then obviously I need to figure out what is the next best use of everyone's time. What is the next best use of everyone's time is often not simply a matter of what I want done, but also a negotiation with the helpers so as to ensure high levels of motivation to work on the jobs.

The idea that prioritization involves coming up with a rank-ordered task list represents only part of the prioritization process. The relationship between the task list order and when those tasks get done is quite dynamic and is sensitive to the constraints in effect. The selection of tasks is driven by constraints with the rank order of tasks being one of the constraints determining what gets done on a day-to-day basis.

Today we will be mowing grass to reduce competition between vines/trees and the grass. I wish I didn't have to prioritize this job but if I want to achieve my goal of growing grape vines and apple trees, this is part of the price of doing so. If I changed my goals to focus on growing vegetables instead, then grass would not be as much of a concern and would be something I might only do once a year to make hay. So we have priorities, constraints, and goals and from this brew we decide what to do on a day-to-day basis.

There are suggestions out there on how to prioritize what to do next and the book Simple Rules offers some useful suggestions in terms of tasks will "move the needle". Some companies devise a set of simple rules, perhaps 3 or 4 in number, that help guide the prioritization process towards "moving the needle" on a companies' growth. It seems to me, however, that the task list is like a business plan that can change substantially once we start to execute it and react to the constraints that we find ourselves in. How much weight should we give to the task list and how much weight should be given to the active set of constraints we are working within? Is there evidence one way or the other that companies acting according to a rigid and well defined set of priorities does better than one that is more reactive to opportunities and constraints?

I don't have any clear answers which is why I'm thinking and blogging about this issue. I do think that that prioritization involves working with constraints and that we might approach priorization decision making as more typically involving constaint-driven problem solving than task-list planning. The problem of what to do next often feels like it is completely determined by the current constraints (which includes the task list as one component). To say that I decided to do this work today because it was high on my task list is often just a nice story we tell ourselves when the reality is that the task list played a relatively minor role in comparison with the set of constaints that were active or acknowledged on that particular day. Prioritization decision making is more of a quasi-rational process than a fully analytical process of deciding what to do next.

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Multiple Fallible Indicators [Decision Making
Posted on April 14, 2016 @ 01:35:00 PM by Paul Meagher

In my last 3 blogs (1, 2, 3) I've been discussing the Lens Model which was proposed by the psychologist Egon Brunswick (1903-1955) as a way to simultaneously understand how a person relates to world and how we might go about researching and designing experiments to understand that relationship. Today I want to add a few more details.

If you do a google image search using the term "lens model" you will see lots of variations of Egon's original lens model. Here is a variation from Kenneth R. Hammond's book Human Judgment and Social Policy: Irreducible Uncertainty, Inevitable Error, Unavoidable Injustice (1996).

Kenneth Hammond was very influential in promoting Egon's ideas and also expanded upon his ideas in several books. For example, instead of using the term "cues", Kenneth prefers to use the term "indicators". In the lens model above the indicators could be economic indicators such as jobless rate, GDP growth, business sentiment, etc.... and we might be trying to figure out if the economy will grow in the next quarter or not.

One aspect of the lens model that I have not discussed so far is the arc at the top of the diagram labelled "Accuracy". Egon preferred the term "Achievement". The arc is sometimes referred to as the "functional arc". The idea is In my version of the diagram, I might use the term "Adaptation" because the utilization of indicators to make judgements is in the service of adapting to the environment. We do that if our judgements are "accurate" or if the result leads to an "achievement" of some sort. When we speak of judgements being accurate or not, Kenneth argues that Brunswick was putting forth a correspondence theory of truth in contrast to a coherence theory of truth. Most theories of decision making look at how well decisions cohere with some logical or normative ideal and in so doing portray reasoning as fallacious, biased, and error prone and we are left to wonder how we get along in the world. Egon didn't see coherence as being necessary to achieving success in the world and put forth the lens model as a way to explain how our cognitive system can adapts to the world. Note that most popular books on human reasoning dwell on errors in reasoning (using a coherence framework) and as such don't really tell us much about how we get along in the world. Egon offers a different worldview, which he called Probabilistic Functionalism, that is more focused on explaining how we achieve perceptual and cognitive competence in light of the multiple fallible indicators that we must rely upon to make judgements.

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Simple Rules Video [Decision Making
Posted on April 1, 2016 @ 11:15:00 AM by Paul Meagher

I just finished reading the book Simple Rules (2015) and will be blogging more about the contents next week. In previous blogs I introduced simple rules and discussed some intellectual context for simple rules.

In today's blog I want to offer up a nice Steve Jobs quote from the book, present a video of one of the authors discussing the book, and finish off with a possible simple rule for startups courtesy of Jessica Livingston, partner at Y-Combinator.

First, a relevant Steve Jobs quote to consider:

You have to work hard to get your thinking clear to make it simple. But it is worth it in the end because once you get there you can move mountains. ~ Steve Jobs, Simple Rules, p. 225.

Here is first author, Donald Skull, discussing the contents of the book:

Co-author Kathleen Eisenhardt has also given talks on simple rules.

Finally, Jessica Livingston wrote an interesting essay that argues for a simple rule for startups:

Why Startups Need to Focus on Sales, Not Marketing.

The simple rule focus on sales, not marketing can be applied to starting a business and serves to improve the chance of a startup succeeding. The reason to focus on sales is not necessarily to make sales but to gather critical early feedback on your product or service that you can only get if you are engaging in sales.

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Introducing Simple Rules [Decision Making
Posted on March 29, 2016 @ 10:26:00 AM by Paul Meagher

In today's blog I want to set some groundwork for future blogs related to a Simple Rules (2015) book that I'm currently reading. You can can also read the article Simple Rules for a Complex World for a synopsis of some of the ideas contained in the book. The book advocates the use of domain-specific simple rules to manage decision making in those domains. For example, instead of trying to compute an optimal diet using food databases and combinatorial algorithms, you could also use Micheal Pollan's simple rule to Eat food. Not too much. Mostly plants. Following the latter rule would likely lead to as much or more success in deciding what to eat than using some diet optimization technique.

The impetus to use simple rules is that the world is complex and simple rules often capture the most significant features to pay attention to. Often they can be shown to be effective if not optimal according to some criterion. Often the optimal decision is not clear and/or we don't have the computational resources to figure it out. Defining and attending to simple domain specific rules can help us to make adaptive decisions in many aspects of our lives.

Herb Simon won a Nobel Prize in Economics in part because he criticized a foundational assumption of economics that humans are rational actors attempting to make optimal decisions, the so-called "Rational Man" assumption. One of his best critiques of this "Rational Man" viewpoint can be found in chapter 2 his book The Sciences of the Artificial (3rd Ed., 1996). That chapter is titled "Economic Rationality: Adaptive Artifice".

One of Simon's arguments against the rational man assumption involves a critique of Game Theory as a method to compute an optimal strategic move in business or other interactions. One problem you can run into if you set two big-brained computers against each other is the problem of mutual outguessing. If I think A is going to do X, but A knows that I know she might do X, then I should instead do Y, but A might also anticipate this, so perhaps I should do Z and so on. This chain of reasoning can go on indefinitely when two competitive big-brained computers are trying to find an optimal strategic move. Simon drew the following conclusion from this mutual outguessing problem in Game Theory:

Market institutions are workable (but not optimal) well beyond that range of situations [monopoly and perfect competition] because the limits of human abilities to compute possible scenarios of complex interaction prevent an infinite regress of mutual outguessing. Game theory's most valuable contribution has been to show that rationality is effectively undefinable when competitive actors have unlimited computational capabilities for outguessing each other, but that the problem does not arrive as acutely in a world, like the real world, of bounded rationality.

If we are not the optimizing machine that the Rational Man image from economics suggests, then how do we go about solving problems in the real world? Simon calls this the problem of "Adaptive Rationality" and he makes the following suggestions and observations:

If the adaptation of both the business firm and biological species to their respective environments are instances of heuristic search, hence of local optimization or satisficing, we still have to account for the mechanisms that bring the adaptation about. In biology the mechanism is located in the genes and their success in reproducing themselves. What is the gene's counterpart in the business firm?

Nelson and Winter suggest that business firms accomplish most of their work through standard operating procedures - algorithms for making daily decisions that become routinized and are handed down from one generation of executives and employees to the next. Evolution derives from all the processes that produce innovation and change in these algorithms. The fitness test is the profitability and growth rate of the firm. Profitable firms grow by the reinvestment of their profits and their attractiveness for new investment.

Nelson and Winter observe that in economic evolution, in contrast to biological evolution, successful algorithms may be borrowed by one firm from another. Thus the hypothesized system is Lamarkian, because any new idea can be incorporated in operating procedures as soon as its success is observed, and hence successful mutation can be transferred between firms. Transfer is of course not costless, but involves learning costs for the adopting firm. It may also be impeded by patent protection and commercial secrecy. Nevertheless, processes of the kinds just described play a large role in the gradual evolution of an economic system composed of business firms. (p. 48).

The purpose of this blog is provide some context for the idea of simple rules. Simple rules, bounded rationality, and satisficing can be contrasted with the vision of humans as fully informed and always optimizing - the rational man viewpoint. I do not want to completely dismiss the rational man viewpoint as we do in fact have broad range of useful analytic techniques for computing optimal outcomes (inventory management, route planning, scheduling, etc...); however, the rational man viewpoint can be taken too far if we view it as being able to account for or guide all our economic decision making. Given our bounded rationality and the complexity of the decisions we have to make daily, it makes sense to seek out and rely upon simple rules as a method to achieve "economic adaptation". Indeed, sometimes these simple rules perform as well or better than complex optimizing rules (see Naive Diversification vs Optimization). Finally, Herb Simon made some interesting observations about the importance of standard operating procedures and the Lamarkian nature of business evolution that offer some ideas on what Simple Rules in business might consist of (standard operating procedures, routines) and how they might spread and evolve over time (copying and mutation).

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Good, Bad & Debatable Advice [Decision Making
Posted on December 19, 2015 @ 08:37:00 AM by Paul Meagher

One book I'm currently reading is a gardening book called Decoding Gardening Advice (2012) by Jeff Gilman & Meleah Maynard.

The book is broken up into various gardening topics such as soil, water, disease and pest control, mulch, etc... For each topic they discuss advice that they consider good, bad, and debatable about that gardening topic and provide reasons for their classification.

On the topic of soil an example of good advice is "Add organic material to all garden soil before planting". An example of bad advice is "Always us a balanced fertilizer". An example of debatable advice is "Use urine as fertilizer". You can read the book to find out exactly why they consider these imperative statements to be good, bad, and debatable advice.

I find the format of the book is quite useful, easy to read, and stimulating. Reading these short advice-and-evaluation pieces is a good way to organize knowledge in an actionable way.

I think a similarly formatted book would be good when it comes to investment advice or managing a startup. In both cases there are different topic areas we might focus on and within these topic areas we might formulate various pieces of advice about the topic and then evaluate how true that advice is.

It is important to recognize, however, that advice is seldom infallible and that even good advice can be wrong in certain circumstances. For example, the advice to add organic material to all garden soil before planting would be incorrect if that organic material is, say, pine needles whose acidity and tannins might prevent the growth of the plant you are trying to grow. Many people would have regarded the advice to use urine as a fertilizer as universally good advice but the authors consider it debatable because urine has 10 times the dose of nitrogen that liquid fertilizers usually have so if you repeatedly apply urine to the same area you could damage your plants with too much nitrogen. Also if you don't apply it right away, stale urine could accumulate diseases and become even more concentrated. All of these problems go away if you dilute urine with water, use it immediately, and throw it on your compost pile rather than directly on a plant. They would even argue that the urine-added compost pile should only be used for non-food plants. The need to add more qualifications to the advice is the reason they consider it "debatable" advice.

There is alot of advice out there on the best way to invest or manage a startup. Much of it falls into the debatable category, but some is less debatable (good advice) or more debatable (bad advice). It is always necessary to contextualize advice and ask yourself whether this is really true for my circumstance and in the way that I am proposing to implement that advice.

As an exercise you might want to google "good advice for startups" or "good advice for investing" and ask yourself whether the suggested advice is really good advice. I doubt there is any advice that is always "good" so the question becomes whether there are enough circumstances where this advice could be "bad" advice that you should really put it into a category of "debatable" advice. Perhaps all that is required for the advice to be good advice is to be more precise in the formulation of that advice so it does not apply as broadly. I think the exercise of assembling your own pieces of "good" startup advice or investment advice is worth the effort because, like gardening, it should, if reliable, lead to more success than following debatable advice when you shouldn't or bad advice that you thought was good advice.

All advice needs to be decoded by evaluating whether it is appropriate to your particular circumstance and in the way you intend to apply that advice in practice. All investment, startup or business management advice is debatable to some degree and it might be useful to raise at lease one objection to any piece of advice touted as "good" advice. Expertise is the ability to recognize subtle nuances that often make a big difference in practice.

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Intro to Linear Programming: Part 2 [Decision Making
Posted on September 26, 2013 @ 07:59:00 AM by Paul Meagher

In yesterday's blog, I gave a brief overview of what Linear Programming is and the main equations that are used to specify a Linear Programming decision problem.

Today I want to provide you with some resources you might use to learn how to use Linear Programming to optimize some aspect of your business.

The first resource that I would direct you to are a series of IBM developerWorks articles on using the GNU Linear Programming Kit (GLPK) to solve linear programming problems. This 3 part series walks you through 5 different problem scenarios that you can apply linear programming to and how to specify the equations in a format that the GLPK Solver can work with.

The second set of resources I would point you to are the links to free opensource software that can be used to solve linear programming problems (often referred to as "LP Solvers").

The two main high-qualtiy opensource LP Solver packages that I am aware of are the GLPK package mentioned in the article links above and the LPSolve package. Here are a couple of links to learn more about these packages.

  • Wikipedia Page for GLPK. The page has useful links to various implementations of GLPK, including a javascript-based one that looks interesting as it would be easy to embed in a web page.
  • LPSolve Reference Guide. In my opinion, LPSolve's main feature is that is has bindings for many popular programming languages which makes it easy to call from these languages. Also, the documentation is quite good.

The 3 tutorial links and the links to 2 high-quality LP Solvers should help you to get started in learning more about the nuts and bolts of Linear Programming and whether it might be useful in the context of optimizing some aspect of your business.

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Processing Decisions [Decision Making
Posted on September 12, 2013 @ 09:14:00 AM by Paul Meagher

In the last few blogs I've discussed using Graphviz to generate nice looking decision trees. Sometimes, however, it is difficult to get exactly what you want out of Graphviz because it is designed to generate graphs dynamically (easy to change values/labels and generate a new graph) rather than uniquely crafted one-offs. I decided to explore other alternatives to creating decision tree graphs and, to make a long story short, I have decided that a programming language called "Processing" (see http://www.processing.org website) offers the flexibility I need along with many other benefits. Processing opens up the possibilities for visualizing decisions exponentially because it can be used to create multimedia output, including graphs, on a huge range of devices (e.g., desktop browers, mobile devices, embedded devices). It is also a very elegant language and has a javascript+html5 implementation that makes executing "sketches" (e.g., the processing term for a program) in a webpage a breeze (the output of which can be static, animated, sonically enhanced, etc...). It also has an excellent development environment bundled with it and a large opensouce developer community. Finally, there are some extremely well written books on learning and using the language. The one to start with is by the language's authors:

Processing: A Programming Handbook for Visual Designers and Artists
Casey Reas and Ben Fry (Foreword by John Maeda).
Published August 2007, MIT Press. 736 pages. Hardcover.

To give you a flavor of the language I'll offer up a couple of processing sketches from the book above. I was looking for some code that would get me started on drawing a tree and found this code (p. 202) for drawing a T.

int x = 50;
int y = 100;
int a = 35;

void setup() {
  size(100, 100);
  noLoop();
}

void draw() {
  drawT(x, y, a); 


void drawT(int xpos, int ypos,int apex) {
  line(xpos, ypos, xpos, ypos-apex);
  line(xpos-(apex/2),ypos-apex, xpos+(apex/2), ypos-apex);
}

The code above generates a simple tree structure that could be the starting point for a decision tree:

Cool! By making a few modifications to this program (e.g., adding recursive calls to the drawT function) a fractal tree can be generated with the following code:

int x = 50;
int y = 100;
int a = 35;
int n = 3;

void setup() {
  size(200, 200);
  noLoop();
}

void draw() {
  drawT(x, y, a, n); 


void drawT(int x, int y,int apex, int num) {
  line(x, y, x, y-apex);
  line(x-apex, y-apex, x+apex, y-apex);
  if (num > 0) {
    drawT(x-apex, y-apex, apex/2, num-1);
    drawT(x+apex, y-apex, apex/2, num-1);
  }
}

Here is the output that the sketch above generates:

This, of course, is not a full-bodied decision tree but it gives us some insight into how the skeleton of a simple binary decision tree might be created - by calling a drawT function multiple times with the appropriate positional parameters. I'd prefer a left-to-right layout rather than a bottom-to-top layout so that connections can be labelled easier.

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A Framework for Managing Risk [Decision Making
Posted on July 24, 2013 @ 08:03:00 AM by Paul Meagher

What is risk and how do you manage it?

One aspect of the definition of risk is that it involves quantifying the probability of the relevant decision variables so that you can formally understand the probabilities associated with various possible outcomes. When I say "quantifying the probability" I generally mean specifying the probability distribution for that variable and using distribution statistics, such as the mean and standard deviation, to characterize the shape of the probability distribution.

When you decide to formally manage risk in your line of business you might consider using a decision making framework consisting of Actions, Events, and Outcomes.

A decision problem starts when you have the choice between multiple possible actions {a1, a2, etc...} and must make a decision as to which one to choose.

The effect of each action is not deterministic. If you decide to hire a new sales person, for example, you can't predict exactly what the effect of that decision will be other than that it will likely increase sales revenue by a certain amount, or better, by a range of sales revenue amounts with differing levels of probability. Various events affect the probability that you will achieve a certain level of sales - the economy, competitors, production capacity, etc... So, in addition to specifying the possible actions we can take, we must also identify the main events {e1, e2, etc....} that affect the outcomes we can expect.

The final component of a risk management framework involves specifying the outcomes {o1, o2, etc....} that are relevant to our decision making (e.g., o1 = increase sales by 25% to 50%, o2 = increase sales by 50% to 75%, o3 = increase sales by 75% to 100%).

We can now be very specific about what risk is: Risk = Actions {A} + Events {E} + Outcomes {O} where Events and Outcomes are quantified as probability distributions. In a later blog, I'll discuss how to use this framework to make calculations, but I'll devulge the goal of these calculations now - to compute p(O| A & E), in other words, the full conditional probability distribution.

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Picking your preferred social media platform [Decision Making
Posted on December 24, 2012 @ 05:52:00 AM by Paul Meagher

If you read about using social media to promote your business, you get the sense that you need to create a presence in all of them in order to be successful. So work on your facebook, twitter, youtube, linkedin, pinterest, etc.. profiles so that people can find you in all these forms of social media. This advice might make sense if you are a bigger business and have resources to dedicate to using these different social media effectively. Even then I'm not sure it is advisible. My suggestion is to pick one on them and make that one your main social media outlet. I've been reluctant to engage the social media surge for fear of wasting time online - I already spend enough time online. Nevertheless, I think the time has come for me to pick my poison - for me I think that poison will be YouTube.

Why YouTube? Well, for one, I already have 4 videos on YouTube. I can't claim any real expertise at this point in using it; but I have started using it to host some videos for a rental vacation property I own. I'm also starting to look into video editing so I can develop more professional looking videos. I have some ideas for content; maybe I can record Skype interviews and post these to YouTube as a form in interesting/useful content. I want to learn and experiment more with video and am not that concerned about making mistakes and posting some amateur footage as I learn more. Conversely, I worry about wasting time on Facebook. I created a facebook account under a false name and get spammed on a regular basis with friend requests. I don't use twitter myself much and don't have a cell phone (by choice) so I haven't looked into that option. Linkedin might be worth using as it is not a big committment of time; or at least appears not to be.

So maybe this will be one of my resolutions in 2013 - to become more proficient in social media, by which I mean, picking one of them, YouTube, and using it more to promote my business.

I still like to write in the essay format so blogging might be considered the social media that I already use. I will continue to work on my blog as a primary communications tool; but this year don't be suprised if my blog contains embedded YouTube videos that I have created. In case you are not aware, a few months ago, we made it easy for entrepreneurs to include YouTube presentations in their investment proposals. Entrepreneurs need to opt for the Express Plus or Global Express Plus package in order to access this feature.

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How to price your product or service [Decision Making
Posted on December 6, 2012 @ 10:03:00 PM by Paul Meagher

Entrepreneurs don't always have the luxury of setting a price for their product or service. If we are in a competitive market, the price of a product or service might already be determined by existing competitor prices. For example, it is difficult to price an oil change much higher than what local competitors charge (and expect to get a significant share of that business).

If you are in the fortunate situation where there is some elasticity in price setting, then the question arises as to what price you should charge for your product or service. Wikipedia offers a buffet of pricing strategies you might want to consider in such situations.

One pricing strategy that the Wikipedia article does not explicitly discuss is optimal pricing where we trade off volume for price in such a way as to maximize profit, which should not be confused with gross revenue. If we simply seek to sell as many units as possible so as to maximize gross revenue, then it is possible that our costs will start to go up once we hit a certain volume because we have to add more labor, equipment, buildings, traincars, etc... to the mix and these factors serve to reduce the overall profit such that our overall profit is less than if we sold fewer units.

You can't do optimal pricing if you don't know your fixed and variable costs and how they are affected when you increase production.

The next time you walk into Canadian Tire, you might ponder why they try to achieve the lowest pricing possible this time of year. If they are using an optimal pricing strategy, it could be because in the ramp up to xmas they can find economies of scale associated with significantly increased volumes of production that allow them to set prices lower and achieve the optimal level of profits possible over the forth quarter of 2012. Canadian Tire adverstises for pricing analysts whose job it is to find optimal pricing strategies for the products they carry. It might be a useful thought experiment to imagine yourself as a pricing analyst for Canadian Tire and then apply the same framework to figuring out how to price your own products or services.

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How to analyze an investment opportunity [Decision Making
Posted on July 10, 2012 @ 08:00:00 AM by Paul Meagher

Lately I've been researching formal methods that might be used to decide whether to invest in a project or not. Three commonly used metrics are:

  • Payback Period
  • Net Present Value (NPV)
  • Internal Rate of Return (IRR)

To compute these values, you need to specify a cashflow sequence where the first element in the cashflow sequence is a negative number denoting the investment amount. The next elements in the cashflow sequence are the net income amounts for year 1, year 2, up to year N. An example of a cashflow sequence would be:

year      0        1      2      3     
cashflow  -10,000  6,000  6,000  6,000 

A cashflow sequence like this would be sufficient to compute the payback period for an investment, which is simply the number of years it would take to earn back your initial investment. In this case, the payback period would be 1.67 years which is one useful investment metric to know when evaluating an investment opportunity.

The nice thing about payback period metric is that it is simple number to understand. One problem, however, with this metric is that it does not take into account the time value of money, or the idea that money in your pocket today is worth more than the same amount in your pocket a year from now (because money in your pocket today could be earning interest and be worth more a year from now). The Net Present Value calculation includes a discount rate factor that takes the time value of money into account.

The Net Present Value calculation involves computing the present values of a cashflow sequence given a discount rate. If you have a discount rate of, say, 5%, then the $6000 you estimate that you might earn a year from now, would be equivalent to a present value of $5714.4 (plus a year earning interest at 5%). You compute the present value of each projected cashflow, sum them up, and subtract it from your initial investment. If this "net present value" is greater than 0 than you should consider proceeding with the investment. If the net is less than 0, don't invest. NPV gives you simple rule for making a an investment decision, and the size of the NPV allows you to more accurately gauge how good the investment is because it takes into account the time value of money via a discount rate that you specify.

While technically the rate you enter into the NPV formula is a "discount rate", you can also construe the rate as the percent profit you would want to make in order for the project to be worth your while. As you increase the percent profit you would like to make, the NPV value returned will be smaller and smaller. You can keep increasing the profit percentage until you get an NPV of 0. The profit percentage that gets you an NPV of 0 is called the Internal Rate of Return (IRR) and is another useful number for deciding whether you should invest in a project or not. Obviously, the higher the IRR the better the investment. It is also a useful metric for comparing investment opportunities in an apples-to-apples manner.

Enough theory. How to do we actually compute these investment metrics?

Rather than trot out a bunch of formulas, I will instead trot out a bunch of PHP code that computes these investment metrics:

<?php

/**
* A set of functions for quick financial analysis of an investment
* opportunity and a series of projected cashflows.

* For further details and pros/cons of each function please refer
* to the respective wikipedia page:

*     payback_period 
*         http://en.wikipedia.org/wiki/Payback_period
*     
*     net present value 
*         http://en.wikipedia.org/wiki/Net_present_value
*         
*     internal rate of return
*         http://en.wikipedia.org/wiki/Internal_rate_of_return
*/

/**
* The total present value of a time series of cash flows.
*/
function npv($rate$cashflows) {
  
$total 0.0;
  foreach (
$cashflows AS $i=>$cashflow)
    
$total += $cashflow pow($rate$i);
  return 
sprintf("%01.2f"$total);
}

/**
* The IRR or Internal Rate of Return is the annualized effective 
* compounded return rate which can be earned on the invested 
* capital, i.e., the yield on the investment.
*/
function irr($cashflows$iterations=100) {
  
$rate 1.0;
  
$investment $cashflows[0];
  for (
$i=1$i <= ($iterations+1); $i++)
    
$rate *= (npv($rate$cashflows) / $investment);
  return 
sprintf("%01.2f"$rate 100);
}

/**
* The payback period refers to the length of time required
* for an investment to have its initial cost recovered.
*/
function payback($cashflows) {
  
$investment array_shift($cashflows);
  if (
$investment 0
    
$investment = -$investment;
  return 
sprintf("%01.2f"payback_of_investment($investment$cashflows));
}

function 
payback_of_investment($investment$cashflows) {
  
$total 0.0;
  
$years 0.0;
  
$cumulative = array();
  if ( (
count($cashflows)==0) OR (array_sum($cashflows) < $investment) ) 
    die(
"insufficient cashflows");
  foreach(
$cashflows AS $cashflow) {
    
$total += $cashflow;
    if (
$total $investment
      
$years += 1;
    
$cumulative[] = $total;
  }
  
$A $years;
  
$B $investment $cumulative[$years-1];
  
$C $cumulative[$years] - $cumulative[$years-1];
  return 
$A + ($B/$C);
}

?>

This code is a port of some python code found here.

To test drive these functions we can create a test script:

<?php

// Include our investment analysis functions
include "investment_analysis.php";

// Rate used to discount future cashflows to their present values (also 
// can think of this as the desired profit percentage).
$rate  0.05

// The cashflow value at index 0 is the investment amount (always a negative value)
// The cashflow value at index 1 to N can be positive (net inflows) or 
// negative (net outflows).
$cashflows = array(-10000600060006000);

// Now feed these parameters into the three investment functions we discussed
$payback payback($cashflows);
$npv     npv($rate$cashflows);
$irr     irr($cashflows);

// Output the results
echo "Payback is $payback years<br />";
echo 
"NPV is $ $npv<br />";
echo 
"IRR is $irr%<br />";

?>

The output of this script looks like this:

Payback is 1.67 years
NPV is $ 6339.49
IRR is 36.31%

Each of these numbers gives us a different perspective on a potential investment and together provides a useful set of formal metrics for analyzing the worthiness of an investment opportunity.

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Optimize your life [Decision Making
Posted on June 28, 2012 @ 12:26:00 PM by Paul Meagher

What objectives are you trying to maximize in becoming an entrepreneur?

Do you want to maximize your wealth, your leisure time, your freedom to do as you please, time with family, or some other aspect of your life?

In mathematics, if you want to optimize a system, you need to define what the objectives of that system are and rank those objectives in order of importance. Only then can you start to optimize the system.

So how do you determine what are the most important objectives in your life? One way to figure this out might be to do a thought experiment in which you ask yourself how much satisfaction or "utility" you might gain if you were to double the current level of some factor related to one of your possible objectives. For example, if you doubled your monthly income would you derive more satisfaction/utility from that relative to if you doubled the amount of leisure time you had per month, or the number of hours with family, or the number of hours you could dedicate to self-directed projects? Under this doubling regime, ask yourself what objective would produce the biggest gain in net satisfaction and then weight that objective accordingly in optimizing your life.

Once you have a main objective that you want to maximize, the next step is to determine what variables influence that outcome the most. You should also distinguish between the variables that are under your control (e.g., number of cattle, number of planted acres, etc...) from the variables that are not under your control (e.g., weather, government policy, etc..). Decision making is mostly about optimizing the level of the variables that you can control.

Usually when we are taught optimization techniques such a linear programming we are given examples that involve figuring out the price and quantity of widgets to produce in order to maximize revenue. I would argue that you might want to consider using these techniques to optimize at a higher level, the level of your overall life satisfaction.

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