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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.
In the article "Optimizing Delta and Pine Land Company's Bag Seed Distribution" a real example is given describing how the manufacturer Delta and Pine...
The article reports that the improvement process "resulted in significant financial savings and a 14% reduction in their finished goods move ratio" (Smith, Cassady, Bowden & Ainsworth 2005). This shows the gains that can be achieved by utilizing linear programming to solve transportation problems.
References
Cheung, R.K., Cheung, M., & Powell, W.B. (1996). Models and algorithms for distribution problems with uncertain demands. Transportation Science, 30(1), 43-59.
Schermerhorn, J.R. (1989). Management for Productivity. New York: John Wiley & Sons.
Smith, J.D., Cassady, C.R., Bowden, R.O., & Ainsworth, L.M. (2005). Optimizing Delta and Pine Land Company's Bag Seed Distribution. Retrieved July 22, 2005, from Department of Industrial Engineering, Mississippi State University. Web site: http://www.ie.msstate.edu/ncit/NCIT_WEB_UPDATE/DPL%20Web%20Paper%20V2.htm
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