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I have heard that Linear Programming was first used by:

  • Dantzig to solve problems involving US military logistics in the Second World War
  • Kantorovich to solve problems involving transportation of goods and soldiers in the Second World War

I am trying to find more information about the exact circumstances of these problems. For instance, are there any references that show the exact objective functions and the exact constraints that were involved in these optimization problems?

I would be really interested to see something which showed the equations for the objective functions and the constraints with exact numbers involved in these original problems. I have searched for this online (e.g. http://www.math.toronto.edu/mccann/assignments/477/Kantorovich42.pdf, https://dl.acm.org/doi/10.1145/87252.88081), but I can't seem to find anything which provides these kinds of details.

Can someone please recommend a reference where these kinds of details are provided for the first Linear Programming problems?

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The Linear Programming and the Simplex Method were invented by Dantzig during October 1948 to June 1952 when he was the chief mathematician of Project SCOOP (Scientific Computation of Optimal Programs) of the U.S. Air Force [1].

After searching for works by Dantzig from 1948 to 1952, [2] and [3] are probably what you want (though we can not assume they are the first Linear Programing problems).

Additionally, I found a collection of Dantzig papers [4] where there are some titles that have the keywords "military", e.g. "Typical Military and Industrial Applications of Linear Programming". Copies may be obtained by contacting the Stanford University.

Then, [5] also provides some historical facts about the SCOOP and Dantzig.

Finally, after June 1952, Dantzig left the Pentagon for RAND Corporation, so technical report by Dantzig in RAND may also be useful, e.g. [6]. See this link for a full list.

References:

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Some more references on the history of Linear Programming, and Optimization more generally, can be found at

https://www.informs.org/Explore/History-of-O.R.-Excellence/O.R.-Methodologies/Optimization-Mathematical-Programming

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