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Prudential Algebra 

  1. Benjamin Franklin's Prudential Algebra
    1. On  September 19, 1772, Benjamin Franklin wrote a letter to Joseph Priestly, a noted chemist best remembered for his discovery of oxygen.  The letter was in response to a request by Priestly for some advice.
    2. In the letter, Ben Franklin states that he can not advise Priestly because of insufficient knowledge.  However, he goes on to state that his Prudential Algebra may be of help.
    3. Steps of Prudential Algebra
      1. Form a two column list of Pros and Cons
      2. Estimate the respective weights of each Pro and Con
      3. Strike out equal weighted groups of Pros and Cons
      4. The column with remaining factors is the appropriate decision.
    4. See text of letter below.
  2. Letter to Joseph Priestly
    1. References
      1. Book - "Letter to Joseph Priestly", Benjamin Franklin Sampler, Fawcett, NY, 1956.
      2. Online - HistoryCarper - 
    2. London, September 19, 1772

      Dear Sir,

      In the affair of so much importance to you, wherein you ask my advice, I cannot, for want of sufficient premises, advise you what to determine, but if you please I will tell you how. When those difficult cases occur, they are difficult, chiefly because while we have them under consideration, all the reasons pro and con are not present to the mind at the same time: but sometimes one set present themselves, and at other times another, the first being out of sight. Hence the various purposes or inclinations that alternatively prevail, and the uncertainty that perplexes us.

      To get over this, my way is to divide half a sheet of paper by a line into two columns; writing over the one Pro, and over the other Con. Then, during the three or four days consideration, I put down under the different heads short hints of the different motives, that at different times occur to me, for or against the measure. When I have thus got them all together in one view, I endeavor to estimate their respective weights; and where I find two, one on each side, that seem equal, I strike them both out. If I find a reason pro equal to some two reasons con, I strike out the three. If I judge some two reasons con, equal to three reasons pro, I strike out the five; and thus proceeding I find at length where the balance lies; and if, after a day or two of further consideration, nothing new that is of importance occurs on either side, I come to a determination accordingly.

      And, though the weight of reasons cannot be taken with the precision of algebraic quantities, yet when each is thus considered, separately and comparatively, and the whole lies before me, I think I can judge better, and am less liable to make a rash step, and in fact I have found great advantage from this kind of equation, in what may be called moral or prudential algebra.

      Wishing sincerely that you may determine for the best, I am ever, my dear friend, yours affectionately,
      B. Franklin
  3. Factor Rating Method with Ben Franklin's Prudential Algebra
    1. Procedure
      1. Assign a weight, wi , to each factor to reflect its importance.
      2. Assign a score, si j , for each location and each factor.
      3. Sum wi si j for each location.
      4. Select the site with the highest sum as the best candidate.
      5. Form a comparison matrix by subtracting each site’s wi si j from the best candidate’s wi si j .
      6. Qualitatively compare each site with the best candidate using the least number of positive factors to outweigh all negative factors.
      7. Conclude that best candidate is best or revise weights and scores.
    2. Application of Factor Rating Method to the location of a manufacturing plant.  This is from Example S5.1, page 202 of Operations Management: Multimedia Version, fourth Edition, Roberta S. Russell and Bernard W. Taylor, Prentice Hall, 2002 (ISBN 0-13-034834-1).
      Factor Weight  Site1  Site2  Site3 
      Labor pool 0.30   80   65   90
      Prox. Suppliers 0.20 100   91   75
      Wage rates 0.15   60   95   72
      Community 0.15   75   80   80
      Prox. Customers   0.10   65   90   95
      Shipping modes 0.05   85   92   65
      Air service 0.05   50   65   90


        a. Weighted scores b. Comparison
      Factor Site1  Site2  Site3  Site3-Site1 Site3-Site2
      Labor pool 24.00 19.50 27.00    3.00    7.50
      Prox. suppliers 20.00 18.20 15.00   -5.00   -3.20
      Wage rates   9.00 14.25 10.80    1.80   -3.45
      Community 11.25 12.00 12.00    0.75    0.00
      Prox. customers      6.50   9.00   9.50    3.00    0.50
      Shipping modes   4.25   4.60   3.25   -1.00   -1.35
      Air service   2.50   3.25   4.50    2.00    1.25
        77.50 80.80 82.05    

      Site 3's (best candidate) favorable
              Labor pool,
              Proximity to customers, and
              Air service
          outweigh Site 1's favorable
              Proximity to suppliers, and
              Shipping modes.

      Site 3's favorable
              Labor pool, and
              Air service
          outweigh Site 2's favorable
              Proximity to suppliers,
              Wage rates, and
              Shipping modes.

      Therefore, Site 3 is the best.

    3. Please note that Steps 5, 6, and 7 in Section III.A above do not appear in Russell nor Heizer and Render, but represent my extension of the Factor Rating Method to include Ben Franklin's Prudential Algebra.  This pairwise qualitative comparison allows me to probably use both sides of my brain to come to a harmonious resolution of important decisions.
  4. Prostate Cancer Example
    1. For many prostate cancer patients, the selection of the best treatment is a difficult decision because of the many trade-offs.  Below is a link to an Excel worksheet showing a typical solution.
    2. Prostate Cancer Treatment Selection - TreatmtSelection.xls

                        (This page was last edited on May 31, 2009 .)