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Kassel, Universität Kassel, Fachbereich Wirtschaftswissenschaften

Koopmans’ Transport Model 
Did Koopmans base his 1949 Econometrica Paper on 
Fictitious Data? Evidenz from Statistischen Reichsamt 
Berlin 
(Map of global shipping routes in Tjalling Koopmans: Optimum Utilization of the Transportation System, in: 
Econometrica, vol. 17, Supplement, July 1949, p. 140) 
Working Paper on Logistics No. 26/2023 
Richard Vahrenkamp 
Prof. em. for Logistics at University of Kassel   
Logistik Consulting Berlin 
Tel. 0177-628 3325 
Mail: vahrenkamp2016@gmx.de 
 
Source of this paper: Server of University of Kassel doi:10.17170/kobra- 2025022310925 
 
1 Introduction 
 
Alongside the travelling salesman model and the shortest path algorithm, the transport model is one of 
the most famous models in computer science and operations research and can be found in every 
textbook on operations research. The question here is, where does this model come from? Is this 
model derived from empirical data? And what is the purpose of this model? In which logistical contexts 
can it be used? Are there any applications at all in logistics or is this model merely academic?  
 
In recent years, the demands of academia and the public have grown significantly with regard to the 
transparency of the sources of publications and the traceability of the origin of data and methods. In 
2021, for example, the German Economic Association (Verein für Socialpolitik) adopted an ethics 
guideline. 1  
   
The aim of this paper is to critically assess the scientific basis of a famous publication by Tjalling 
Koopmans in the prestigious journal Econometrica in 1949 and to prove that the origin of his data is 
extremely dubious. For this article, among others, Koopmans was awarded the Nobel Prize in 
Economic Sciences in 1975 for his contribution to the optimal allocation of resources. The Nobel Prize 
Committee emphasised Koopman's achievements in researching the optimal allocation of resources. 2  
   
The Econometrica publication is particularly interesting for the German public in that Koopmans cites 
the Berlin Statistical Office of 1928 as the source of his data. This makes it possible to judge the 
quality of his data. 
 
 
1 https://www.socialpolitik.de/sites/default/files/2022-01/Ethikkodex_2021_12_08_DE_final_0.pdf,  Zugriff am 14. 
Juli 2023. 
2 Siehe press release Swedian Reichsbank unter: 
     https://www.nobelprize.org/prizes/economic-sciences/1975/press-release/. 
Seite 2
2 The career of Tjalling Koopmans 
 
Tjalling Koopmans initially trained as a mathematical physicist. During the Second World War, he 
worked as a statistician at the Combined Shipping Adjustment Board of the USA from 1942 to 1944 
and observed bottlenecks in the transport chain of worldwide ship rotations. In a memo, he asked 
which shipping routes could be reduced in capacity if additional shipping space was needed for 
another route.3  From 1944, he worked on economic issues at the Cowles Commission think tank at 
the University of Chicago. He was appointed professor at the University of Chicago in 1948. 4   
   
At the Cowles Commission, he came into contact with Martin Beckmann, who was also trained as a 
mathematical physicist. 5  Together with him, Koopmans published an article on the quadratic 
assignment problem in the field of operations research in 1957, which was to be cited almost 3,000 
times according to Google Scholar. Beckmann became extremely influential among European 
researchers in mathematical economics when he began publishing the series ‘Lecture Notes in 
Operations Research and Mathematical Economics’ with Springer Verlag in 1968. In 1970, Beckmann 
published Koopmans' scientific papers in a volume at Springer Verlag in Berlin, paving the way for 
Koopmans to win the Nobel Prize. 6  
 
 
3 Exchange Ratios between Cargoes on Various Routes (Non-Refrigerated Dry Cargoes). Memorandum for the 
Combined Shipping Adjustment Board, Washington, D.C., 1942, published in Scientific Papers of Tjalling C. 
Koopmans, Springer Verlag, edited by Martin Beckmann, Berlin 1970, pp. 77-86. This paper is not really 
“scientific” because it has no source of its data. 
4 The biografic data according to “Scientific Papers of Tjalling C. Koopmans”, edited by Martin Beckmann, 
Springer Verlag, Berlin 1970, preface by Martin Beckmann.  
5 Mirowski, Philip: Machine Dreams – Economics becomes a Cyborg Science, Cambridge (Mass.), Cambridge 
Univ. Press 2002, p. 252. 
6 Scientific Papers of Tjalling C. Koopmans, edited by Martin Beckmann, Springer Verlag, Berlin 1970. 
Seite 3
3 Koopmans' transport model 
 
In 1947, Koopmans gave a lecture at an international statistics conference in Washington D.C. on his 
model of global ship circulations entitled “Optimum Utilisation of the Transportation System”, which 
later served as a model for the optimal use of resources in economics and also became known as the 
transport model, which is one of the standard models in the field of operations research. 7 His paper 
was published in the Proceedings and reprinted in the journal Econometrica in 1949, which according 
to Google Scholar was to be cited over 500 times. 8 Figure 1 below outlines the transport model, 
showing flows of commodities from supplies to customers. On the relations prevail constant prices per 
ton. 
Figure 1: The transport model 
 
In his 1947 paper, Koopmans published a table of 15 seaports worldwide (‘representative ports’), 
where he shows the inbound and outbound of bulk goods in millions of tonnes for the year 1925, see 
the following table in Figure 2. 9  
 
7 Frederick Hillier: Introduction to Operations Research, 11th edition, 2020, New York. 
8 Koopmans, Tjalling: Optimum Utilization of the Transportation System, in: Proceedings in the International 
Statistical Conference, Vol. 5, Washington D.C. 1947. (Reprint in Econometrica, Band 17, Supplement, July 1949, 
pp. 136–146). 
9 Cited according to reprint 1949: Koopmans, Optimum Utilization, 1949, p. 136. 
Seite 4
Figure 2: Fictitious data on overseas trade in 1925, source: Statistisches Reichsamt Berlin, according 
to Koopmans 1947, reprint in Econometrica 1949, p. 136. 
 
Of the 15 ports, three ports had a surplus, meaning that they had more incoming tonnes than outgoing 
tonnes. These are the ports of Athens, Lisbon and Yokohama. The situation is reversed for the other 
12 ports. Miraculously, the sum of the inbound volumes across the 15 ports is equal to the outbound 
volumes, so that, as required by the transport model, supply equals demand. Koopmans somewhat 
casually quotes the Berlin Statistical Office as the source for his table with the publication “Der 
Güterverkehr in der Weltschiffahrt” from 1928. In fact, it is a „Ergänzungsheft zum Heft 1“ of the journal 
‘Vierteljahreshefte zur Statistik des Deutschen Reiches’ from 1928 in the 37th volume. This publication 
presents global trade in the six commodities wood, coal, oil, iron ore, wheat and rice in millions of 
tonnes. Trade is organised according to the geographical categories of the individual countries, but not 
according to ports.  
 
Ports do not appear at all in the supplementary booklet. How Koopmans arrived at the 15 harbours in 
his table therefore remains unclear. As he writes in his publication, he aggregates the catchment area 
of his 15 ports. The port of Rotterdam, for example, serves the whole of north-west Europe, while New 
York covers the whole of the north-west of the USA. It does not specify which countries the port of 
Lisbon should aggregate. Apparently, the port of Athens aggregates the entire Mediterranean region. 
This is surprising, as the hinterland connection from Athens to the Balkans via railway lines is very 
poor. This shows that the table, which Koopmans enhances with the source ‘Statistisches Reichsamt’, 
is more of a fiction than based on verifiable statistical data. It is surprising that Koopmans, as a 
researcher working in Chicago, uses the Imperial Statistical Office as a source, but no sources from 
the Anglo-Saxon world, such as statistics from the U.S. Department of Commerce or the British Board 
of Trade. 
 
Koopmans asks how in his model, using fictitious data from the surplus ports, ships on empty runs can 
be routed to the demand ports at low cost in order to minimise the total transport costs for all these 
empty runs. He therefore compares the three surplus ports with the 12 deficit ports in a transport 
model and calculates dual variables in this model in order to work out the steering effect of the 
marginal costs. When calculating the dual variables, he proceeds on the basis of the three surplus 
ports of Athens, Lisbon and Yokohama. He sets the dual variable known as potential for Athens equal 
to zero and calculates dual values for the ports in the Indian Ocean and Pacific that can be reached 
from Athens by using the journey times in days, which are intended to approximate the transport 
Seite 5
prices, as dual variables. The following map in Figure 3 shows the routes from the surplus ports to the 
deficit ports on the oceans. 
 
Figure 3: Map of global ship circulations from the three surplus ports by Tjalling Koopmans: Optimum 
Utilisation of the Transportation System, in: Econometrica, Volume 17, Supplement, July 1949, p. 140. 
 
Koopmans referred to a theorem by M. Allais without citing a source, which further diminishes the 
academic quality of his paper. According to this theorem, under competitive conditions, the ratios of 
prices for transport services correspond to the ratios of marginal costs at the optimum. 10  However, he 
postulated that marginal costs can exert a steering effect towards the optimum regardless of 
competitive conditions. The optimum is a transport plan in which the sum of transport costs is minimal. 
To explain his model, he actually assumes a “global organisation” that carries out the transports. 
Transports by independent shipping companies under competitive conditions do not appear in his 
model. 11  This approach is surprising, as Koopmans appears as a competition economist from the 
Cowles Commission at the University of Chicago and at the same time assumes a centralised 
economic power. 12  He published the model under the title “Optimum Utilisation of the Transportation 
System” in the prestigious journal Econometrica in 1949 as a reprint of his 1947 publication.  
 
 
10 Koopmans, Optimum Utilization, 1949, p. 136. 
11 Koopmans, Koopmans, Optimum Utilization, 1949, p. 138. 
12 Zur Arbeit von Koopmans an der Cowles Commission see Philip Mirowski: Machine Dreams – Economics 
becomes a Cyborg Science, Cambridge (Mass.), Cambridge Univ. Press 2002, S. 252.Also other mathematical 
economists, as George Dantzig und Robert Solow, refer to central planning, to derive the mathematical optimum. 
Seite 6
4 Conclusion 
 
Koopman's 1947 publication on the transportation model, which is considered one of the first 
publications on the transportation model, shows weaknesses that diminish the scientific quality of his 
paper. The empirical data are mysterious, and sources from the Statistical Office of the German Reich 
are inaccurately cited. The reader is falsely led to believe that he obtained his data from the Reich 
Statistical Office in Berlin. What would later become typical for the transport model in the operations 
research literature is already explicitly demanded in Koopman's publication: a static model without a 
time dimension and a single homogeneous bulk commodity and on the relations constant prices per 
ton. However, this radical simplification of the economic relationships in the transport sector, which 
Koopmans undertakes in accordance with his background as a mathematical physicist, makes the 
transport model unsuitable for use in the complex economic reality of the transport sector, as I have 
explained elsewhere. 13  For the existence and validity of the transport model, however, it is irrelevant 
whether Koopmans used fictitious data or real data. It is striking that all later publications on the 
transport model used only fictitious data. 
 
 
 
 
13 Richard Vahrenkamp: Mathematical Management – Operations Research in the United States and Western 
Europe, 1945 – 1990, in: Management Revue – Socio Economic Studies 2023, Band 34, Heft 1, S. 69–91. 
Seite 7


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