Volume 1 No. 4 Murphy

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Frederic H. Murphy

Abstract

This bibliography consists of the early papers on linear programming model formulations. It
includes some papers that are not about linear programming models but are relevant to
understanding the early literature. Examples of these non-LP papers are the Markowitz portfolio
model, some integer programming models and papers on input-output analysis.
The summaries of the paper are mine and not abstracts, since many of the papers from this era
did not have abstracts. I have not read the papers that do not have summaries because I was not
able to get copies of them.
The value of this bibliography resides in bringing together a literature that is still relevant for
understanding LP modeling issues and modeling in general. By scanning the papers, one can see
the evolution of issues and trends in the thinking of those involved in developing the field.
Personal creativity in model formulation often follows the same pattern as historical creativity,
that is, the first formulation of a new model, and this bibliography allows one to trace the
historical roots of model formulation. See Murphy and Panchanadam (1995) for an example of
how this bibliography can be used for current research.
There has been little systematic examination of how one formulates models. We too often
dismiss the subject by calling it an art. However, there are basic principles. H.P Williams (1975)
articulates some of these principles. One can see in these papers the evolution in the
understanding of the natural structures one uses in models to represent certain situations that cut
across industries. To make model formulation more of a science, we need to understand the
thought processes that lead to successful modeling.
One can see how ideas on a model evolve. For example, the LP model for media planning has
been the source of many articles and the model is not applied now. Yet, it still appears as a
homework problem in all of the textbooks. The literature shows the attempts to fix the model to
be sufficiently realistic and the ultimate failure to develop an adequate model. See Bass and
Lonsdale (1966) and Engel and Warshaw. With models of production processes, the successes
were immediate and the models grew in size and scope in subsequent papers.
One can see how one gets economic insights from models and why certain formulations are
inappropriate and others are. Charnes and Cooper were especially concerned about articulating
these insights into their articles.
Another use is to see who contributed to the development of the field. Charnes and Cooper and
Dantzig stand out in the development of new models. However, the number of people involved is
large and goes well beyond those we commonly recognize in the field. Interestingly, there are
few non-U.S. modeling papers. This can reflect several of possibilities: I could have missed the
non-U.S. papers, Europe was recovering from the war and European companies did not have the
resources to experiment with new technologies, U.S. companies may have been quicker to adopt
ideas from universities in the 50's, the basic technology was developed in the U.S. and national
boundaries were more meaningful then. I would welcome more non-US examples.
This bibliography also illustrates the kinds of overlaps that existed and, to some extent, still
exists with other fields. It contains a remarkable number of papers in economics, agricultural
economics, and agriculture. The connection with economics in the early years was quite strong.
The fields have far less in common now. Operations research/management science suffers from
the reduced interactions. LP models become much more useful in a corporate and governmental
policy context when combined with economic concepts.
Another area that appears early on is engineering design in the form of models on the plastic
limits of structures. Optimization continues to play an important role in engineering design.
However, this literature does not make it into our journals.
Many of the models in common use now were new inventions at one time. The authors describe
these models and, to some extent, what they were thinking about when they developed them.
Many of the issues raised in these papers continue, just on a different scale. For example,
Swanson and Woodruff (1964) describe how to use advanced bases and a sequencing of models
to make it economic to solve the feedmix model.
There are many clever reformulations. For example, Bowman (1956) reformulated the
production planning problem as a transportation problem. Then S. Johnson (1957) showed that
this problem could be solved directly, without resort to an iterative algorithm.
The main period covered in this bibliography is the 1940's and 1950's, essentially the first decade
of the field. I have included some particularly interesting later articles. As time permits, I will be
extending this bibliography through the 1960's. Online databases contain the more recent years,
typically starting with material from the 1970's. If readers note that I am missing an article on
model formulation from the period through 1970, please contact me with the reference. If it is in
an obscure journal, please send me a copy. My intention is also to create a physical archive of
these papers.

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