Fortran Codes for Mathematical Programming

Fortran Codes for Mathematical Programming - Linear, Quadratic & Discrete Authors: Ailsa. H. Land & Susan Powell ISBN-13: 9780471512707 ISBN-10: 0471512702 Publication Date: 1973 Publisher: John Wiley & Sons Ltd Hardcover 6.1 x 9.25 inches, 249 pages This book lists the source code for various Mathematical Programming algorithms: linear, quadratic, integer, branch & bound, and parametric linear, plus discusses enough of the mathematics involved to make it all rational. The codes were developed at the London School of Economics to support coursework, so they have been debugged by generations of students. This author has used the code for Quadratic Programming to do mean-variance optimization for selection of efficient investment portfolios. ----------------------------------- Ailsa Horton Land (née Dicken; 14 June 1927 – 16 May 2021) was a Professor of Operational Research in the Department of Management at the London School of Economics and was the first woman professor of Operational Research in Britain. She is most well-known for co-defining the branch and bound algorithm along with Alison Doig whilst carrying out research at the London School of Economics in 1960. She was married to Frank Land, who is an Emeritus Professor at the LSE. After securing a position as Research Assistantship in the Economics Research Division at LSE in 1950, Land progressed through the ranks of research assistant, lecturer, senior lecturer, reader, and then chaired professor. Her economics background informed her subsequent contributions to OR, beginning with her 1956 dissertation on the application of OR techniques to the transportation of coking coal. Ailsa is most known for her development, along with Alison Doig, of what later came to be called the branch-and-bound method for optimisation problems with integer variables. Their work was published in Econometrica in 1960. This work was initially carried out at the London School of Economics under the sponsorship of British Petroleum, with the aim of enhancing existing linear programming models for refinery operations. Ailsa and Alison did not have access to a computer at the time, but they developed an algorithm that could be converted to Fortran by British Petroleum Staff. The method is now the most prevalent solution method for NP-hard optimisation problems. Land also worked with Helen Makower and George Morton in the late 1950s on a number of integer programming problems. This included her early investigations of the travelling salesman problem, beginning with a 1955 paper with Morton, and continuing with a 1979 research report on 100 city traveling salesman problems. In addition, Land advanced OR methodology through publication of notable work on shortest path algorithms, quadratic programming, bicriteria decision problems, and statistical data fitting. Following her retirement from the LSE in 1987, she continued several research projects, resulting in contributions to data envelopment analysis, the quadratic assignment problem, and combinatorial auctions. In addition to her methodological work, Ailsa worked on the development of computational tools. In 1973, Ailsa published her book Fortran Codes for Mathematical Programming: Linear, Quadratic and Discrete, written jointly with Susan Powell. This provided detailed documentation for computer implementations of optimisation techniques as well as the underlying mathematical background and a suite of test problems. A subsequent 1979 publication, also with Susan Powell, offered guidance to consumers of mixed-integer programming and combinatorial programming. Her computer codes for data envelopment analysis and for the traveling salesman problem were all made freely available to the optimization community.