Describe two applications of linear programming to management problems. What are the main disadvantages of the technique?

(a) Describe two applications of linear programming to management problems.

What are the main disadvantages of the technique?

When managers relate to the decision-making processes they face a problem of allocating several scarce resources. The opportunity cost of these scarce resources can be determined by the use of linear programming techniques. Linear programming was developed by George B. Dantzig in 1947 as a technique for planning the diversified activities of the U.S Air Force. Linear programming is a powerful mathematical technique that can be applied to the problem of rationing limited facilities and resources among many alternative uses in such a way that the optimum benefits can be derived from their utilization. The main objective of the linear programming problem is maximizing profit or minimizing cost. Applications of the linear programming are numerous in a variety of problem situations such as the blending problem and the product-mix problem.

One of the most important applications of linear programming is the formulation of blends which meet certain requirements at minimum cost. Blending problems occur whenever managers decide how to produce a blend out of specified commodities or constituents whose characteristics and costs are given. Therefore the manager’s problem is to design a blend that minimizes cost per pound and also satisfies the product specification and product demands. Blending problems take place most regularly in the food industry, gasoline industry and chemical industry where their final products are concerned with blends.

A product-mix problem exists whenever the manager is to determine an optimal production schedule or product-mix (which specify which product to produce and in what quantities). A product-mix problem can be solved by linear programming if the objective of the manager is determined by the production levels that will allow the company to meet the product demand requirements, given limitations on labor capacity, machine capacity and storage space, while minimizing production cost. The application of linear programming for production scheduling problems is beneficial because those problems reappear during a production year. Therefore managers have to resolve the problem knowing the limitations of the company and applying in the new linear programming demand capabilities.

Despite the fact that the linear programming technique can be applied in a variety of different problems there are unfortunately some disadvantages that we should take into consideration before using this method.

The Linear programming method assumes constant return to scale, which implies that outputs are thus exactly proportional to inputs. Doubling all inputs doubles outputs and doubles cost, and so on.

A second disadvantage is that linear programming may also

yield a non-integer solution and therefore may give unrealistic results or outcomes to the problem.

However, it is sometimes possible for two special cases to arise when ...