Linear and Non Linear Programming Essay Example | Topics and Well Written Essays - 1750 words

Linear and Non Linear Programming - Essay Example Regression, for example, may help the manager to forecast his sales based on past record, but he must make sure that the user of his product has not undergone any changes in taste and preference. Therefore, an econometric model may prove a better aid than pure mathematics and statistics. In linear programming, the statement of the optimisation (maximisation or minimisation, as the case may be) problem runs in a linear form where these variables are restricted to values satisfying a system of linear constraints, i.e., a system of linear equations, and linear inequalities. In any optimisation, problem involving a single inequality constraint, the LaGrange method can still be used and is quite simple. However, when more than one inequality constraint is involved, linear programming will be a better method. In fact, the linear programming technique differs from the classical optimisation technique based on calculus, and it deals with optimisation problem in which the optimiser faces inequality constraints, and where the constraints as well as the objective function are all linear rather than non-linear. For example, while making the purchase decision, the buyer is required to finance the expenditure out of his or her budgeted income, B. Thus: Linear Programming (LP) is a mathematical method to determine optimum allotment of scarce resources. LP can be applied practically in almost all aspects of business like Transportation & distribution, advertising & production planning and the like. A linear programming solves the objective functions which are to be optimized and is linear. As such, the relations between the variables which correspond to the resources will also become linear. This problem solving method was first formulated and solved in the late 1940's. Seldom there is a novel mathematical technique being used with such a wide application as LP. In the present days this theory is productively implemented to problems of capital budgeting, conservation of resources, economic growth prediction, and transportation systems. Of late LP has also helped to solve and unite many outstanding applications. The most vital facet of a linear programming problem is to set it up appropriately for manual or automated solution. This calls for properly understanding the natures of the objective function and constraints so that their equations and inequalities may be well planned and formatted. Problem solving: The Transportation Problem Transportation models play a key role in logistics and supply chain management for decreasing cost and enhancing service. Therefore, the goal is to find the most cost effective way to transport the goods. Let us consider a model with 2 origins and 2 destinations. The supply and demand at each origin (e.g.; warehouse) O1, O2 and destination (e.g.; market) D1 and D2, together with the unit transportation cost are summarized in the following