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Some Fuzzy Logic --Dickeson

November 2003
Lotfi Zadeh, an electrical engineer in Southern California, calls this a "fuzzy" world we live in—a world where all the rules are "fuzzy logic." It's a gray, nebulous, world of shades and degrees.

We buy sophisticated computer systems to help us price our product. But when it comes to pricing a job, there's no single "right" computer price. Our computers produce a nice, "crisp" number that we mark up and say, "This IS the price." Then we say, "Yeah, right," and proceed to bargain for some fuzzy value based on hunch and guess. We know that budgeted "costs" are just arbitrary fictions. We're groping. As a result, we just give up on the computer for pricing.

Hang on a moment. Maybe all isn't lost for computer pricing. Suppose we use Zadeh's fuzzy logic to come up with a TSP—Target Selling Price. It would be an improvement over what we're doing. Can we try it out without having to spend a bundle? Sure.

Let's use that fuzzy logic to set a target price. It could look something like this table I've whomped up in Excel.

AI Job Target Pricing

Account ID: 22475
Date: 7/29/04

Job #: 47589
Job Name: Fictus
Quantity: 32,000

Matrl: $1,246
Avg. Mtrls: 36.00%
Avg. Price: $3,461

Pays as agreedMostly0.8000.0100.008
Keeps scheduleNot always0.5000.0150.008
Accepts oversOnly 1%0.3300.0020.001
Supplies paperYes 0.9990.0200.020
New accountNo0.0000.0000.000
Budget bidNo 0.0000.0000.000
Press approvalYes 0.9000.0020.003
Price bargainingAt times0.4000.0030.002
Second lookProbably0.6500.0010.003
Significance to customerVery high0.9000.0250.023
Re-runs expectedMost Likely0.7500.0030.002
Customer relationshipVery close0.9000.0400.036
Core competenceNot quite0.3500.0200.007
Very tight scheduleAverage0.5000.0500.025
Totals 7.9790.1910.137
Weighted/Weight Ratio0.717
Target Sell Price$4,829

At the top we have the header information about a job. Below that we have the fuzzy stuff. The Fuzzy Logic Target Sell Price is at the very bottom, all neat and crispy.

Two items are keys in the header: a.) the Direct Order Additives (paper, ink and outside job purchases) called DOAs and b.) the average ratio of DOAs to manufactured sales. Where did we get that average?

Add up your manufactured sales for a period such as a year. Then add up your total DOAs for that same period. Divide the total DOAs by the total sales and there's YOUR ratio. (I used 36 percent for the example since that's about what it's been for 10 years in the PIA ratio studies for the reporting firms.)

Personalized Ratios

Whatever YOUR ratio turns out to be, it's the one to use. It represents what you've been getting for all the jobs you've manufactured during the period you selected. Use that ratio as a divisor. Divide the DOAs for any job by the ratio. There's the average price you'd charge for such a job. But you want to "adjust" it to fit the circumstances, don't you? Aha! It's in the adjusting process that we leave crisp values and suddenly get fuzzy.

That average ratio means that there were a lot of jobs with higher value-added yield and a bunch with a lower yield. If we bid at a price below the average value we'll dilute our average downward—lower our price level. If we bid at a higher value and get the job, and do that often enough, we'll raise our average price level. Which do you want to do? We've got to noodle around a bit to come up with a valid TSP. This is where fuzzy fun starts.

In the left-most column are the "properties" called "sets" for the job we should think about in determining an opening bid price. You can have as many or as few as you want. I listed 70 in an earlier article! Or you can set up separate spreadsheet templates for groups of types of products.

A few sets have a Yes or No answer. Many sets require a gut feel about the job—a fuzzy notion of what may transpire. That's our nebulous/fuzzy world. Those gut feelings about sets are expressed in words in the second column headed "Gut Feel." But no computer can understand "probably" or "very high."

We've got to help the computer program. So we write "rules" assigning numeric values to the various "feeling" words that we use. For example, take the set called "Keeps Schedule." My feel is "Not Always." Our rule says that "Not Always" has a value of 0.500 on a scale from 0.001 to 0.999. So the computer program puts 0.500 in the "Assigned Value" column for the "Keeps Schedule" set.

What's the impact of not always keeping to schedule? That's where the column "Pricing Weight" enters the scene. In that "default" column we're saying that whether or not a customer sticks to an agreed schedule has a weighting impact of 0.015. (On a scale of 0.001 to 0.0999). In a spreadsheet, set this up as a series of "If this, then X, else Y" statements for all of the "feeling" statements for each set.

It's that fourth column, the one called "Pricing Weight," where the going gets tough. The first three columns were "local" to the particular job. The "weight" column is "global" to the printing company. Just how much should "keeping to schedule" affect the price of a job? It's well above average. On that scale I'd say it's at least an 0.015. What would you say?

We could debate these points for days. You must assign a weight for each set. What's important is what you think for your business, not what I, or someone else, may believe. Assign a weight for each set of properties. The value here should be a default. You'll have to fiddle with it until you're satisfied.

Multiply the Assigned Weight by the Pricing Weight for the "Weight Extension" column. Divide the sum of the "Weight Extension" column by the sum of the "Pricing Weight" column to get the ratio. Divide the "Average Price" in the table header by the ratio just determined and you have your "Target Selling Price."

Worth the Time

That's my take on Fuzzy Logic—Artificial Intelligence—for pricing a print job. Is it worth the effort? Yes, it is. In the model, the TSP will be greater than the Average Price yield of the company. That's as it should be. The result is still just a "Target" price to be negotiated as necessary. Save the spreadsheet for each job to build experience and to continuously improve your pricing. Add or delete "sets" as you gain experience.

What's impressive is the written record of thought that goes into a TSP. You develop an articulated, consistent, policy. The scheme starts with your own past experience and forces you to think logically about pricing the new jobs. When you do this you spend time "up front" thinking and developing an "informed intuition."

Try it and tell me what you think. It's an attractive idea. Kick it around and let's polish it up. It beats the hell out of what we've been doing.

—Roger V. Dickeson

About the Author

Roger Dickeson is a printing productivity consultant based in Tucson, AZ. He can be reached via e-mail:


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