Linear Programming as a Method

Linear Programming as a Method for Solving Transportation Problems

Linear programming is described as a mathematical technique designed to determine the best use of scarce resources (Schermerhorn 1989, p. 685). Each problem is solved based on an objective function, which is what the organizations wants to achieve, and the constraints, which refers to the factors that limit the decision that can be made. One of the types of problems that linear programming can solve is transportation problems. Linear programming is a method that can be used to optimize transportation and reduce the costs of transportation.

Transportation problems are important to manufacturing firms that have to organize for the distribution and storage of their created products. For these organizations, the costs of distribution are part of the overall costs of producing the product and supplying it to the customer. This means that reducing the costs of transportation will increase the profits that can be made for the product. For these organizations, the transportation problem that exists is how to most cost effectively transport products to any number of locations.

Linear programming is a useful tool to optimize distribution because the number of options possible often makes it impossible for the best decision to be reached by human decision alone. For example, consider the case where an organization creates products and has to ensure that they are always available to meet demand at several locations. Is it better to ship large amounts infrequently and store them at the individual locations? Is it better to ship small amounts infrequently from a single storage area? Is it better to send shipments to individual locations or to send shipments to many locations via certain locations? Cheung, Cheung, and Powell (1996, p. 52) also show how the most cost-effective solution can even include having one location serviced by several storage locations. This shows just some of the possibilities that may need to be taken into account to find the best distribution option. This clearly shows that the possibilities that need to be taken into account are beyond what a single person is able to reasonably consider. Linear progression can take into account all of the possibilities and determine the most cost effective solution.

In the example given above, the objective is to minimize costs. The restraints might include that all locations must have enough product to meet demand at any given time. The restraints will also include the number of products the company has to distribute each day, since the organization cannot ship more than it is able to produce. The restraints will also include the storage limits at each location. Completing the linear progression will also require data on the cost of distributing each product to each location. With this information, computerized analysis of the data can determine the most cost-effective transportation option.