Quantitative Planning and Decision-Making Techniques (With Particular Reference to Agricultural Applications)

Since the birth of civilisation mankind has been experimenting with numbers The study of primes, radicals, and other number forms fascinated the early mathematicians and from their researches there emerged a body of knowledge which is known today as the Theory of Numbers In similar fashion the representation of physical units (length, mass etc) by the symbols (x, y, z, etc) led the early mathematicians to theories describing the relationships which can exist between these abstractions Their study of equations, complex numbers, series, and other like topics has resulted in the algebras with which we are familiar today The representation of time as an abstract quantity contributed to the development of the calculus which heralded the development of what has been called "the modern mathematics" However, up to the end of the nineteenth century mathematics was usually studied for its own sake, or m conjunction with the attempt to understand the physical sciences It seldom occurred to the people of that era to try to apply their mathematics to their economic, agricultural or industrial systems The Taylor brothers and the Gilbreaths in America, and Bedaux in France started a revolution in the traditional concepts of the relationships between men, money and materials At the lowest level m the industrial hierarchy, the shop-floor, the man and his job were examined m the cold light of scientific measurement A startling discovery was made-a man was quantifiable Once the full implications of this discovery had been grasped a transformation occurred in industrial planning ideas The catalyst for this revolution was a method of examination and analysis which is now known as Work Study Work Study can rightly be described as a forerunner of modern planning techniques Work Study ,m spite of its undoubted usefulness, however, had serious limitations m its range of application During the period 1920-1950, mathematical ideas were being examined and developed, notably in the field of linear and matrix algebra Von Neumann proved the celebrated mmi-max theorem and in conjunction with Morgenstern published their important work The Theory of Games and Economic Behaviour Wassily Leontief was researching m inter-industry problems which culminated in the publication of The Structure oj the American Economy, 1919-1929 G B Dantzing, the Rand mathematician published his general method for finding the optimum of a linear function subject to linear constraints-the Simplex Method Erlang, the Swedish engineer, first formulated the mathematical theories of congestion which today …