History of Linear Programming
to formulate feeds a personal view
By Paul Poornan
The author started his career at Oldacre in 1981 as a nutritionist responsible for the formulations at seven feedmills, then in the following year joined Oldacre International becoming an agent for Format International. He joined Format full-time in 1984 as Market Development Manager and left in 1989 to become CEO of Lys Mill Ltd. His first formulation was in 1981, and his last in 2019 when he retired as CEO of Humphrey Feed Ltd. Possibly one of the longest-serving mill formulators in the industry?
Linear Programming (LP) is the mathematical heart which lies behind feed formulation. In 1939 Russian mathematician Leonid Kantorovich was tasked with optimizing production in the plywood industry and invented the technique now known as LP. Using this technique he later calculated the optimal distance that should be maintained between vehicles travelling on ice, depending on the weight of the vehicle, the thickness of the ice, and the air temperature. The purpose was to keep Leningrad provisioned by vehicles crossing a frozen lake whilst it
Leonid Kantorovitch, 1976
was besieged by the German Army in 1941. Eventually his work was recognised, and in 1976 he was awarded the Nobel Memorial Prize for his contribution ‘to the theory of optimum allocation of resources’. Similarly in World War II George Dantzig1 was working for the US
Air Force (USAF) and in 1947 invented the Simplex method for solving LP problems, which is universally recognised as one of the most important alogarithms of the 20th century. Prior to the Simplex method, many LP problems were infeasible. The following year, Danzig was Chief Mathematician in the USAF’s Project SCOOP (Scientific Computation of Optimum Programs), the remit of which was the application of computers to military planning and scheduling ie the acquisition, storage and movement of men, machinery and armaments from points A to B in the quickest time and least-cost, over multiple time periods. The Simplex algorithm was adapted for various early computers
George Dantzig.
Photo Credit: Ed Souza / Stanford News Service
(SEAC and UNIVAC) in the 1950s, and at its simplest is a series of simultaneous equations that are solved in an iterative process. Dantzig
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presented Simplex to the world at a mathematical conference in 1951, and in the same year FV Waugh published ‘The Minimum-Cost Dairy Feed’2. In 1953 WD Fisher & LW Schruben presented ‘Linear Programming applied to feed-mixing under different price conditions’3. In 1954, IBM launched its first mass-produced computer, the IBM 6504, which initially could be leased at $10,000 per month, and two years later fell to $3,200 per month. In 1959 FV Waugh presented ‘Low-cost feed formulation’ to the International Animal Feed Symposium in Washington DC; the principle of computer feed formulation had become mainstream. It was not until the 1960s when IBM produced a mainframe
The IBM 650. Cushing Memorial Library and Archives, Texas A&M - Flickr: IBM Processing Machine
computer with 8k of RAM and the RAND Corporation had released FORTRAN (in 1957) that it was possible to hold all the data for 500 rows of equations as well as the program. By 1952 Dantzig had moved to the RAND Corporation who offered LP services to businesses. In 1957, ‘Least-cost formulation’ (LP) became commercially available to animal feed companies. Many computer companies started to produce LP software and in the USA, Computrol became the market leader. In the UK, few firms could afford to purchase a mainframe, so some utilised remote formulation services via a telephone modem, where operators dialled an overseas telephone number and then inserted the handset into rubber ‘cuffs’ to link their own terminal to a LP mainframe. The majority of UK feed compounders still calculated formulations ‘by hand’. In 1965, a simple LP diet solution could take 24 hours running
time to formulate on an IBM. At this time, both the program and data was stored on punched cards (a medium that started in the 1890s and survived into the 1980s) before being transferred to magnetic tape (first used for the Univac in 1951). Between 1960 and 1980, the decision to implement LP for a feed company involved selecting
1. Dantzig was a genius. As a student, he arrived late for a lecture and saw two equations written on the blackboard, which he assumed was homework. It took a few days but he solved them. The equations were examples of ‘two of the most famous unsolved statistical problems that mathematicians since Einstein had been trying to solve without success.’
https://www.snopes.com/fact-check/the-unsolvable-math-problem/
2. American Journal of Farm Economics, Vol 33, No3, (August), pp299-310. 3. American Journal of Farm Economics, Vol 35, No4, (November), pp471-483. 4. The CPU of which measured 6 feet by 5 feet, and weighed 600kg.
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