A historical perspective on location problems

Abstract

Location problems represent a popular class of optimization problems in the field of logistics, and their applications play a key role in strategic planning activities related to both manufacturing and service industries. This paper presents a historical perspective of their evolution, from the historic challenge posed by Pierre de Fermat, through the contributions by Torricelli, Viviani, Simpson, Heinen, and other researchers, to Weber’s intuition about a practical use of the results of that challenge, and its subsequent developments. Modern developments of the discipline are also reviewed. There is particular emphasis on the work of pioneering researchers who provided seminal contributions to the field.

Notes

¹ Pierre de Fermat (1601–65) was a French judge and mathematician. He provided seminal contributions to modern mathematics, especially in the area of differential calculus, probability and analytic geometry.

² Evangelista Torricelli (Faenza, 1607–47) was an Italian mathematician, best known as the inventor of the barometer. He was a student of Galileo Galilei, and collaborated with him on several studies.

³ Francesco (Bonaventura) Cavalieri (1598–1647) was an Italian mathematician known for his work on the problems of optics and motion.

⁴ Vincenzo Viviani (1622–1703) was a student of Evangelista Torricelli and Galileo Galilei. In 1639, when he was 17, he became Galileo’s assistant and served in this role for three years, until the death of his mentor.

⁵ Gilles Personne de Roberval (1602–75) was a professor at the Collège Gervais and at the Collège Royal in Paris.

⁶ Thomas Simpson (1710–61) was an English mathematician. He is known for the approximate procedure for the calculation of definite integrals generally known as the Cavalieri–Simpson rule. He is also credited with the formulation of the Simpson’s casual variable. He came from a very humble background (his father was a textile worker); despite this, he was admitted, in 1740, at the Royal Academy of Stockholm. After 1743, he taught mathematics at the Royal Military Academy, Woolwich.

⁷ Alfred Weber (1868–1958) was a German economist and social scientist. He was the brother of the famous philosopher and social scientist Max Weber. From 1907, he started working as a professor at Heidelberg University. He was forced to resign in 1933, as he refused to join the National-Socialist Party. Alfred Weber continued to live in Germany, where he was one of the leaders of the intellectual resistance movement to Adolf Hitler’s regime. After the end of World War II, he went back to teach at Heidelberg.

⁸ Georg Alexander Pick (1859–1942) was an Austrian mathematician. Born from a Jewish family, he died in the Nazi concentration camp of Theresienstadt. Pick studied at the University of Vienna and defended his PhD in 1880. After receiving his doctorate he was appointed as an assistant at the Charles-Ferdinand University in Prague, where he became a lecturer there in 1881. He headed the committee at the University of Prague which appointed Albert Einstein to a chair of mathematical physics in 1911. Pick introduced Einstein to the work of Italian mathematicians Gregorio Ricci-Curbastro and Tullio Levi-Civita in the field of absolute differential calculus, which later in 1915 helped Einstein to successfully formulate the theory of General relativity.

⁹ Harold Hotelling (1895–1973) obtained a Master’s degree in Mathematics in 1921 at the University of Washington. In 1924 he obtained a PhD in Mathematics at Princeton University and, after a short while, he started teaching at Stanford University. In 1929 he moved to England to study with R A Fisher and, during the same year, he completed the first studies in competitive location.

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