May 142014

Have you ever walked into a dining room with several pictures and seen that one picture that is not hanging parallel to the floor? If you’re a recovering engineer like me, you feel an overwhelming urge to correct the problem. You just can’t be comfortable until the frame is in alignment… unless you find your molding or floor/ceiling are not parallel.   Then you have bigger problems!

Why does a slight misalignment (maybe just a couple degrees off bubble) set off instant and loud alarm bells in your brain? It’s because the human brain is very sensitive to two things:

  1. Linearity/symmetry
  2. Discontinuity (especially non-monotonic functions)

I was having a lively discussion the other day with a director of pricing at a Fortune 500 distributor.  We were talking about how this affects product pricing. For example, when you have a catalogue with millions of products, it can be very challenging to keep pricing consistent. Consider the figure to the right. The orange dots could be product offerings for electric motors, graphed by the price vs. a performance attribute, such as horsepower. We expect price to increase with performance. But what happens when you find the blue or green dots?   The brain says “that’s not right!”Hiller_Associates_Costing_Linearity

Now, there may be legitimate reasons for the negative or positive arbitrage.   Maybe there is a sale? Maybe there is an economy of scale on selling that particular model?  However, that brings us to the next challenge, pricing functions that are not monotonically increasing (i.e. they have a negative slope for at least one product model). This is a problem, because this is difficult for even economies of scale to overcome. And, the customer does not like it, because it makes the vendor look as if their pricing is capricious, which causes distrust.

Discontinuity in Product Costing

This happens in costing too. For example, although “sunk cost” is an important concept in capital investment, it can wreak havoc on product costing. If a certain machine is fully depreciated and now has a greatly reduced overhead rate assigned by the accounting department, this will likely confuse the purchasing or engineering folks using a Product Cost Management software. It will either cause them to distrust the costing software or your manual analysis or it will drive them to cost all the parts they can using that

This is yet another curse of the difference between the data relevance needs in order to perform good cost or pricing analysis versus the data reliability needs, over which accountants typically obsess. From an accounting point of view the depreciated resource is “free” (or highly discounted). However, from a costing viewpoint, the abilities of that machine will have to be replaced sooner or later. Worse, the distortion in the overhead rate will lead to underestimations of cost, and often, unpleasant surprises late in product development and sourcing.

What to do about non-linearity, discontinuity, and non-monotonic pricing/costing functions:

Hiller_Associates_Fix_it_or_feature_itYou have a couple of choices on how to resolve the geometric costing/pricing problems in the minds of your customers or colleagues:

  1. Remove them – the first solution is to correct the false arbitrage by fixing the pricing or costing data. For example, in the case of the machine that is fully depreciated, change the overhead rate back to reflect the cost at which a new machine with the same capability would depreciate.
  2. Highlight them – if the pricing or costing curve has an unexpected kink in it for a legitimate reason, then you should make everyone aware of this and use it to your advantage. For example, in the catalogue motor example, advertise the sale and let people know this is not natural or permanent!

A lot of mistakes in pricing or costing are difficult to notice without close inspection, but remember anything that violates the brains desire for smooth regularity will stick out like a sore thumb… or a good deal.




  19 Responses to “That can’t be right!? (Linearity and Discontinuity in Pricing and Costing)”

  1. Moderator reposting comment from linked in:

    Michael Shipley

    I work with pharmaceuticals and I see this occurring every single day. One day one product can cost $150.00 and the next day it can cost $550.00. There’s not much I can do about manufacturers raising their pricing due to other manufacturers dropping out of the market and the sole manufacturer wants to capitalize on this opportunity to make money. The hard part is trying to maintain competitive within the market while maintaining a positive margin on each product. This turns out to be a full time job seeing pricing on pharmaceutical drugs changes each and every day.

    • Michael,

      Thanks for the comment. I am working on an article which may give you some ideas of what one can do when you are in the situation of supplier oligopoly or monopoly power.


  2. Moderator reposting comment from linked in:

    Scott Harder
    Cost Estimator at Eberspaecher – North America, Inc

    This also happens to products with long term contracts that suddenly perform better than forecasted at an extreme level. If you quoted one system (an assembly line for example) to produce the product at say 85% capacity (room for temproary peak volumes), and you suddenly receive forecasting from your customer that would exceed the system to 110% for at least a couple of years during lifecycle. You’re in a delimma to procure another assembly system to produce the overflow. Which you now just split the capacity 55%/55% for each system. So the pricing would actually need to increase to recover for two systems running at half efficiency. Yet, most customers are linear thinkers and would expect a price “reduction” for being good sports and supplying your organization more business.

    Some may debate that this simplistic example I created didn’t address overtime, engineering change to improve system efficiency or changes to indirect costs (example: current indirect levels could be utilized simultaniously for both systems versus increasing indirects to support both), etc. That’s fine, I’m just making a point that systems have breaking points that blow the standard curve for estimation.

    • @Scott Harder

      Good example. My question here would be, shouldn’t the terms of the contract specify max capacity and reserve the right to change pricing if the customer changes the order?

      This is something that should be openly discussed with the customer. In my article, I was talking about people not understand non-linearity when they see prices of many products together without explanation, forethought, or explanation. In case that you describe, I think that any rational person would understand the price increase if you sat down and personally explained it to them. Certainly, the customer would expect the price to stay the same or decrease, EXCEPT in the case of the big caveat: exceeded capacity.


  3. Moderator reposting comment from linked in:

    Mohd Aizal Shah Mohd Rozaini
    Project Cost Controller

    Hi Eric, costing and pricing is always a challenge in a project. Sorry, I used to describe the 1 painting that not suppose to be there is actually ‘shit happen’. Sorry about the language used to describe the situation. We actually can do something about it by using certain mitigation plan toward it. I believe the best practice in my own opinion is to study and understand any lesson learn though out past project. Prevent is better than curing it. If this took place, the 1 painting should not be so that obvious. Bidding process play a major role in order it to be more price competitive in landing the project in hand. Exploring other area for saving and efficiency that will make the situation more curable. Identified the bid mis and opportunity will have an impact and put us back on track.

  4. Moderator reposting comment from linked in:

    Freddy Menacherry
    Senior Cost Engineer

    Dear Eric,
    This is a nice topic which we come across and face in our day today life, I agree to your opinion of becoming not comfortable when we see any thing in not in place or in alignment. When we try to link this human behavior to Pricing and Costing , Iam sure we have to face many challenges as most of the pricing & costing are done by factors outside the subject with out proper ethics and not true and to a good level exaggerated which leads to exorbitant pricing. So definitely we find non aligned & feel discomfort like the non aligned picture frames you mentioned as an example in the dining room. My view is that ,the outcome of any thing which is not proper,natural or exaggerated will be unnatural or non aligned, which is against the rule of fair costing & pricing.

  5. Moderator reposting comment from linked in:

    Mike Keating, PE, MBA
    Engineer / Contractor / Consultant / Adjunct Instructor

    An interesting discussion in microeconomics, but is there a question here? I’d be curious as to how many customers would really question the price discrepancy…particularly on an item that has elastic demand.

    • Mike,

      Thanks for the comment. I am working on getting an article published which shows a case in which a customer (in this case ME!) noticed strange pricing anomalies and used it to great effect.


  6. Moderator reposting comment from linked in:

    Julio Contreras
    Lead Estimator at Fluor

    I total agree with Eric, I consider that the time to save money is during Design, if the designer doesnot about cost estimation, it is the oportunit to incorporate a cost estmator to the Project.

    • jewel cameron, Construction & Q S , PM at CBRE SAYS:

      I think that the designer should involved a cost estimator or quantity surveyor in the preliminary stage of any project design.
      Jewel C Cameron MQSi MWOBO

      • Orlando Alston III, Chief Program Conceptual Cost Estimator-Engineer, SAYS:

        I’m not sure what’s the purpose of the comment. In June 2014 I’ll have completed 49 years of a cost estimating career wherein I began as an insurance policy rater and culminated in Lead Senior Conceptual Cost Estimator on the fast track project The New Stuyvesant High School, Battery Park City. NY, NY. Twenty-five years later We’re now trying to integrate the Affordable Care Act [Obama Care] into Affordable multi-family Public Housing.

        Costs are functions of human labor; in fact absent human labor you have nothing!! The unit measures you employ to create the human action-reaction is irrelevant; except to those who claim rights to other people’s money [pardon me: labor].

        Simply put profit takers are the problem because in order for one to profit another one must lose. The law governing economics on this planet is Sigma ‘f'(X)=0’. The Municipal Programs Group Inc

        • Freddy Menacherry, Senior Cost Engineer, SAYS:

          We cant blame selectively the designer only for the cost , as my belief is that total cost is a collective effort of the core team which finalize the design ,technology & strategy. A final design is made after consultation with experts of various departments with in and outside the Organisation .Then how the Designer himself only will be accountable ?

          • @Freddy,

            I don’t disagree. I am not trying to say that the designer is soley responsible. I would guess from experience that the designer, purchasing guy, and manufacturing engineer control 90+% of the ability to effect cost. They each have a role and each function has some inherent blind spots on how it deals with cost.

            But, the design engineering teams (speaking as an ex-design engineer) seem to be the most oblivious.

            Eric (HA)

  7. Moderator reposting from linked in comment:

    Giancarlo Vimercati
    Director of Spavale Pty Ltd

    Pricing and costing only comes if you hours database is correct, your hours database will be develop from subcontractors assemblies.
    The rest is common knowledge in the EPCM world.

  8. @ Giancarlo,

    My articles, unless otherwise specified are referring to the manufacturing world, not EPCM. The EPCM world is a very different beast with respect to costing.


  9. Moderator reposting from linked-in group:

    Freddy Menacherry, Senior Cost Engineer, ASKS:

    Dear Eric, Let me ask you one thing (from my observation ), suppose the design engineering teams submitted various designs as options before the core team , knowingly or by mistake if the core team not able to select the least cost effective product design, who will be responsible? I think it mostly depends on the structure of the organisation. In many organisations it is rarely seen the design engineers with top hierarchical position with deciding power.

    • @Freddy,

      Well, I suppose that depends on the situation.
      1. Who’s responsibility is it to provide the cost assessment for each of the design
      2. Who’s responsibility is it to make the decision based on the information

      If the person responsible for cost assessment gave incorrect info to the decision make who selected the “right” design based on the info, the cost estimator (design or whoever it was) is at fault. On the other hand, let’s assume that the cost assessments were perfect, they whoever picked the “wrong” choice is at fault.

      What is the motive of meaning behind the question you ask?

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