Linear programming 1: introduction
Linear programming 1: introduction
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In the early 1950's, a communication gap developed between those doing research in mathematical programming and those practicing its application. In the 60's and early 70's. the gap widened. Many, if not most, students who obtained even an advanced degree majoring in operations research or math programming were unaware of the process by which "real-world" applications were undertaken and solved. They were "spared" the trouble. Several groups, including the Computer Science Technical Section of the Operations Research Society of America (ORSA), the Committee on Algorithms (COAL) of the Mathematical Programming Society and the Special Interest Group for Mathematical Programming (SIGMAP) of the Association for Computing Machinery, have recognized this problem. The result was to organize sessions at the ORSA/TIMS meetings and the recent Mathematical Programming Symposium and to produce several Special Issues of the SIGMAP Bulletin to close the gap. This first special issue is the written account of the session on April 30, 1970, at the ORSA/TIMS meeting in New Orleans entitled "Recent and Future Developments in Mathematical Programming Systems," co-chaired by Richard Jackson and Richard O'Neill. Invitations to speak at the session and to submit a paper for the special issue were extended to each major commercial vendor of a math programming system in the free world. All accepted and presented papers. Only one, SCICONIC, by their choosing, is not represented in this issue. Additionally, a panel of long-time and knowledgeable users were also invited to comment on the presentations. The panel consisted of Harvey Greenberg, Milt Gutterman, Tom White and the co-chairmen. Throughout this issue, the theme is to summarize the develonment of math programming systems in the 70's and project their development in the 80'S. As an introduction we include a short historical summary. Computer codes for solving linear programs were initially developed between 1948 and 1952. In the early 50's, the solution of a linear program of 100 equations was considered a very difficult task for a computer. In the mid 50's, accuracy and speed of both the computers and the algorithms increased, and parameteric procedures were developed. In the late 50's, new inversion techniques, implicit upper bounding and the dual algorithm were introduced. In the early 60's, matrix generation and renort writing were automated and math programming systems became a part of a new generation of large computers. Problems with 1,000 rows and 5,000 columns were solved routinely. (For more detail on the historical development the reader is referred to the two references.