What Optimization Can do for You

Optimization

Optimization helps you find the answer that yields the BEST result--the one that attains the highest profit, output, or happiness, or the one that achieves the lowest cost, waste, or discomfort. Often these problems involve making the most efficient use of your resources--including money, time, machinery, staff, inventory, and more.Optimization problems are often classified as linear or nonlinear, depending on whether the relationships in the problem are linear with respect to the variables. LINDO Systems has the LINDO API, LINGO and What'sBest! to solve non-linear and linear problems.

Mathematical Programming

Mathematical programming, or constrained optimization, or math programming for short, is a mathematical procedure for determining optimal allocation of scarce resources. Math programming, and its most popular special form, Linear Programming (LP), has found practical application in almost all facets of business, from advertising to production planning. Transportation and aggregate production planning problems are the most typical objects of LP analysis. The petroleum industry was an early intensive user of LP for solving fuel blending problems.

It is important for the reader to appreciate at the outset that the "programming" in Mathematical Programming is of a different flavor than the "programming" in Computer Programming. In the former case, it means to plan and organize, as in "Get with the program!". Whereas, in the latter case, it means to write instructions for performing calculations. Although aptitude in one suggests aptitude in the other, training in the one kind of programming has very little direct relevance to the other.

For most optimization problems, one can think of there being two important classes of objects. The first of these is limited resources, such as land, plant capacity, and sales force size. Second is activities, such as "produce lowcarbon steel," "produce stainless steel," and "produce high carbon steel". Each activity consumes or possibly contributes additional amounts of theresources. The problem is to determine the best combination of activity levels that does not use more resources than are actually available. Many managers are faced with this task everyday. Fortunately, LINDO Systems' software helps determine this for you when a well formulated model is input. For more information on optimization, the LINDO textbook, Optimization modeling with LINDO, or the LINGO textbook, Optimization modeling with LINGO, are available, both by Linus Schrage.