### Original Post Date: Wednesday, December 17, 2008

This was a fun and gratifying week at PRICE Systems. In our Mt. Laurel, NJ headquarters we had our annual holiday gift wrapping of presents we donated for needy children and families in the area.  The PRICE team gathered in our classroom and the wrapping began with no pre-instruction or guidance - but much merriment.  What a study in production process and learning!  Wrapping that first present was awkward.  It had been a while since I wrapped last.  How to measure the paper?  Where to cut?  How to keep the cut straight?  Which way do I fold first? How to fold?  What to do if I have too much paper on the ends?  Where do I put the tape?  ...and so on.  Needless to say that first present took some time, I wasted a lot of paper and tape, and the final product had some wrapping defects.  After reflecting on the results, I looked around at others to see what they were doing, asked some questions, processed that information along with my own experiences, and set out on the second package.  I did much better.  I wrapped faster, I wasted less, and the final product was an improvement over the first.  With each new gift I got better and better.  I "learned" how to be more productive, reducing the effort and materials with each present.  By the eight present, I started to focus on how I could reduce materials.  How can I use less paper?  How can I use the least amount of tape and still keep the paper form coming off?  I was improving the overall process.

Productivity increases like mine occur with each and every production process and it is an essential part of cost and schedule estimating.  The method most commonly used to model this effect is called "learning curve", and we use it in all of our models. You can find hundreds of references and equations on the web, but generally the model uses a "learning curve parameter" (LC) to estimate the cost for a certain production quantity.  The LC is expressed as a percentage, and (1-LC) represents the amount the production cost is reduced every time the quantity doubles.  For instance, if I say an 80% learning curve applies to the process, then every time the quantity doubles the cost to produce is reduced by 20%.  So if the first unit cost \$100, then the second would be \$80, and the fourth would be \$64, and the eighth would be \$51.20.  For the same starting point, a 90% learning curve represents less learning and higher costs, while a 70% learning curve steeper learning and lower costs.

If I had timed my wrapping and measured the materials used, I could have used simple math to determine the learning curve that applied. I suspect it was close to 70%.  Determining the learning curve for everything from paper clips to space ships is more complicated, but that is one of the things we do at PRICE.  We perform operations research and analyze data to keep our models as accurate as possible, and embed that research in our cost management software.  Accurate learning curve estimates help our clients optimize their investments, prepare better budgets, plan more effectively.  And as part of this most recent study, we made  a lot of kids happier for the holidays.  Happy Holidays to you.