Joel,
I stand corrected! Well done, though I havent seen dimensions/units even
mentioned in the index of any OR text (though I havent reviewed all of
them). One re-order formula I know of, which is in regular use by a large
organisation, is dimensionally invalid! When I pointed that out, they just
looked blank.
I wonder which came first and whether your very proper emphasis on units
comes from your SD background.
Good for you to teach Simplex. At least it gives the student some idea of
how LP works - I deprecate the plug the numbers into the software and let
the magic box work it out approach.
Geoff
From: "geoff coyle" <geoff.coyle@btinternet.com>
Dimensional Consistency
Dimensional Consistency
geoff coyle wrote:
> Yes, its very true but, as far as I am aware, SD is the only operaional
> resarch technique that even mentions dimensions.
>
I am surprised by Geoffs remark. In our introductory course in OR (mostly linear
programming) in a business school, we always mention the importance of checking
that the units of measurement (dimensions) of the left-hand side of a constraint
must match those of the right-hand side -to the point of discussing the dimensions
of the coefficients that multiply the activity or decision variables on the rhs.
In some contexts the rhs is called a representation of the technology i.e. the
usage of a capacity by multiple activities and the lhs is the capacity that is
available. But even if the constraint is an accounting convention like an
inventory constraint, the individual terms all have to have the same units of
measure, as they must also in the objective function. Of course, we are one of the
last business schools in North America still teaching the Simplex algorithm in
the introductory course (as verified by a survey at an INFORMS summer school), so
I guess that makes us very old-fashioned, very old-fashioned indeed...
Joel Rahn
joel.rahn@fsa.ulaval.ca
> Yes, its very true but, as far as I am aware, SD is the only operaional
> resarch technique that even mentions dimensions.
>
I am surprised by Geoffs remark. In our introductory course in OR (mostly linear
programming) in a business school, we always mention the importance of checking
that the units of measurement (dimensions) of the left-hand side of a constraint
must match those of the right-hand side -to the point of discussing the dimensions
of the coefficients that multiply the activity or decision variables on the rhs.
In some contexts the rhs is called a representation of the technology i.e. the
usage of a capacity by multiple activities and the lhs is the capacity that is
available. But even if the constraint is an accounting convention like an
inventory constraint, the individual terms all have to have the same units of
measure, as they must also in the objective function. Of course, we are one of the
last business schools in North America still teaching the Simplex algorithm in
the introductory course (as verified by a survey at an INFORMS summer school), so
I guess that makes us very old-fashioned, very old-fashioned indeed...
Joel Rahn
joel.rahn@fsa.ulaval.ca