Citation for Beale Medal 2019
Emeritus Professor Ailsa Land
Emeritus Professor Ailsa Land has pioneered work on branch-and-bound which has reshaped the landscape of mathematical programming and its influence continues to this day. She was also one of the early pioneers of computational operational research, in which effective data structures and clever implementation strategies are developed to produce efficient computer code. Moreover, over the past several decades she has made outstanding contributions to the methodology and practice of Operational Research in a variety of applied problem domains. In addition she helped to establish an innovative two-year diploma in Operational Research at the London School of Economics (LSE) for the graduate apprenticeship scheme set up by the British Iron and Steel Association. Later, as Professor of Operational Research at the LSE she mentored both master’s level and PhD students, several of whom have achieved international distinction.
Ailsa Land began her education as an Economics student at the LSE in 1946, obtaining a BSc in Economics in 1950 and a PhD in 1956  for her thesis entitled “An application of the techniques of linear programming to the transportation of coal”. Her economics training has illuminated the study and solution of a wide variety of applied problems: in transportation (1957, 1958) [8, 3], international trade (1959) , manufacturing layout (1963) , machine scheduling (1978) , sports analytics (1985) , and combinatorial auctions (2006) . The range of these application areas is truly impressive.
Significantly, Ailsa Land and Alison Doig were part of a team that carried out research at the LSE under the sponsorship of British Petroleum. They were tasked with studying how to enhance linear programming models for refinery operations in which some variables are necessarily integral. The successes of linear programming then seemed to have encountered the unrelenting roadblock of combinatorial explosion. In a thoroughly original breakthrough, Ailsa Land and Alison Doig proposed and developed the so-called branch and- bound method for optimization problems with integer variables. This innovative approach provided a systematic (and efficient) enumeration of candidate solutions for discrete optimization problems. They published their ground-breaking work in Econometrica (1960) . This approach and its extensions have become widely used in the mathematical programming community. Indeed most serious implementations of OR optimization software include branch-and bound routines. Furthermore, according to Google Scholar, there have been over 3000 citations to their Econometrica paper, which has as well been reprinted in 50 Years of Integer Programming, 1958-2008 . The influence of the branch-and-bound method continues to the present time, and it appears as a key construct in machine learning contexts, such as MAP (Maximum A Posteriori) inference (2014) .
Influential early work on the travelling salesman problem began with the publication by Ailsa Land and George Morton (1955) . In subsequent work (1979) , Ailsa Land applied cutting planes and a heuristic for sub-tour constraints to this challenging problem.
To quote from a prestigious 2007 work on the topic , her research provided “a considerable improvement on previous algorithms … A major contribution is a mechanism for automatically dealing with the large number of variables that can appear in the LP relaxations … Variants of Land’s technique are adopted in all recent studies of the cutting plane method for large-scale problems”.
In addition, Ailsa Land has advanced the methodology of Operational Research through publication of significant work on shortest path algorithms (1967) [5, 20], quadratic programming (1973) , bicriteria decision problems (1981) , and statistical data fitting (1993) . Such work has appeared in the top academic journals of Europe and the USA. In 1994 she received the Harold Larnder Prize from the Canadian Operational Research Society for her contributions to mathematical programming. Since retirement from the LSE in 1987, she has continued research projects, resulting in contributions to Data Envelopment Analysis, Combinatorial Auctions, and the Quadratic Assignment Problem.
It is significant that Ailsa Land has not been content with methodological contributions alone. She has devoted much effort to the parallel development of computational tools for efficient solution of such problems. Indeed, she was at the forefront of computational OR, in which well-tested computer code is implemented, taking into account both theoretical considerations and efficient data structures. A significant work of this nature is the book
Fortran Codes for Mathematical Programming: Linear, Quadratic and Discrete (1973) , written jointly with her PhD student and colleague Susan Powell, which provides detailed documentation for computer implementations of optimization techniques as well as the underlying mathematical background and a suite of test problems. This valuable resource has garnered several hundred citations according to Google Scholar. Further considerations that guide consumers of mixed integer programming and combinatorial programming products are provided in a subsequent book chapter (1979) . In addition, Ailsa Land has developed computer code for Data Envelopment Analysis problems and for the Travelling Salesman Problem, all made freely available to the optimization community. Ailsa Land was notably the first woman professor of Operational Research in Britain and she was an inspiring role-model and supporter for women at earlier stages of their career. She mentored a number of highly successful students, both male and female. Many of these have gone on to distinguished careers and leadership roles in academia. Her students have become Editors-in-Chief of international journals (Computers & Operations Research, INFOR, Networks, and Transportation Science), academic administrators (Department Chair, 3 Associate Dean, Vice Rector), and have received prestigious honours (Order of Canada, INFORMS Fellow, Lifetime Achievement Award in Location Analysis).
In view of these significant contributions, extending over the past several decades, to methodology, practice, and education of OR, we can confidently recommend Ailsa Land for the 2019 Beale Medal. She is truly one of the pioneers of post war operational research in the UK.