Fisheries Economics

5.1.2. Linear programming

Linear programming is one of the widely used techniques in managerial decision making. It is essentially a problem of either maximizing (say, income) or minimizing (say, cost) a function of several variables subject to certain constraints. As resources are scarce and have alternative uses we are often encountered with the problem of best “choice: to ensure that the resources were used in the most advantageous way. However, we may have several options and frequently it may not be all that simple to find out that best “option” by working on manual methods. Consider that 10 inputs are required to produce a commodity. The possible combinations of these inputs is given by 10; that is, there are 36,28,800 way in which these inputs could be combined to produce the output. It is not easy manually to identify that particular input combination that yields the maximum output or income. However, using the linear programming technique, this problem could be solved in a computer in few minutes.

George. B. Dantzig is said to have developed the linear programming technique in 1947 as a tool for planning the diversified activities of the U.S. Air Force. The development followed the concept of game theory propounded by John Von Newmann and Oskan Morgenstern in 1894. According to this concept, although it appears that it may not be possible to draw any conclusions in a game, however, something definite can be said about the outcome of the game. Linear programming, which forms the base for linear economics benefited much from this theory, apart from the input – output analysis developed by W.W. Leontif (1936, 1951) Dantzig needed a way or method to identify the best one among the several plans available for achieving a goal for the American combat aircraft. Subsequently, he developed the linear programming technique for this purpose.