In Memoriam: C. Bartlett McGuire (19252006) and Christopher B. Winsten (19232005)

F years after the publication of the classic book Studies in the Economics of Transportation by Beckmann, McGuire, and Winsten (1956), we are mourning the deaths of two of its authors, C. Bartlett “Bart” McGuire, on January 23, 2006, in Richmond, California, and Christopher “Chris” Blake Winsten, May 28, 2005, in Chelmsford, England. That their seminal contributions to transportation science have continued to stimulate our field for over half a century, and now influence fields not even in existence at that time, speaks to the achievement of this incredible book as well as its scientific collaborators. The sad news of both deaths came to us via e-mail, a mode of scientific communication possibly unimaginable 50 years ago; yet their contributions remain fresh and pertinent. Bart McGuire and Martin Beckmann, together with their wives, were present on November 15, 2005, at special sessions organized by us at the INFORMS Annual Meeting in San Francisco, California, where many of us had the privilege of meeting Bart McGuire for the first time. This story really begins at the Cowles Commission for Research in Economics in 1951, which was then based at the University of Chicago. Under the directorship of Tjalling C. Koopmans, who later received the Nobel Memorial Prize in Economic Sciences in 1975, Martin Beckmann, Bartlett McGuire, and Christopher Winsten began the research that resulted in Part I of Studies in the Economics of Transportation (hereafter referred to as BMW). They succeeded in formulating and extensively analyzing a nonlinear optimization problem whose optimality conditions correspond to the statement, “Demand refers to trips and capacity refers to flows on roads. The connecting link is found in the distribution of trips over the network according to the principle that traffic follows shortest routes in terms of average cost. The idea of equilibrium in a network can then be described as follows: the existing traffic conditions are such to call forth the demand that will sustain the flows that create these conditions” (Beckmann, McGuire, and Winsten 1956, p. 59). This was an enormous advance in the rigorous modeling of road network traffic, a completely novel result for urban traffic, and most likely for any complex system involving interactions of human behavior with technology. Moreover, they provided a parallel model and analysis for the case of cost-minimizing (now called system optimum) flows in a congested traffic network. Prior to joining the Cowles Commission, Bart McGuire received his BA in economics and political science from the University of Minnesota in 1949, and his MA in economics from the University of Chicago in 1952. Chris Winsten was educated at the University of Cambridge in England. Winsten, a mathematician and economist, had an interest in applying probability concepts to industrial issues, whereas McGuire, an economist, provided a pragmatic and realistic check on the model development and saw the model’s description through to publication. TheCowlesCommissionReport for the period July 1, 1952–June 30, 1954, noted how Beckmann, Koopmans, McGuire, Winsten, and (during parts of the period) Nerlove and Goldman, formed the team working on two facets of resource allocation problems concerning transportation systems: highway traffic and railway operations. The report noted how highway transportation has many features in common with markets and also emphasized how, in the context of the railroad contributions, “Thus we enter an area of research, variously called ‘management science,’ ‘operations research,’ or ‘industrial engineering.’ ” BMW was the first to provide a rigorous mathematical formulation of the conditions described by the first criterion of Wardrop (1952, pp. 344–348) (also stated in concurrent research) that allowed for the ultimate solution of the traffic network equilibrium