With the economy still struggling to regain momentum, the use of resources (i.e., human and capital) continues to be heavily scrutinized to ensure they are put to their best use. Of course, the "best use" of resources can be defined in many ways, but generally what people refer to in this context would mean getting the most return for their investment. In economic terms, this is referred to as obtaining an optimum outcome. The process by which we determine an optimum outcome is simply referred to "optimization". There are two basic forms of optimization: 1) minimization and (i.e., cost) 2) maximization (i.e., profit).
In general, there are two components, or sets of information required to conduct an optimization routine. They are: 1) determination of an objective function and 2) identification/quantification of a set of constraints that must be satisfied. The objective function is a mathematical representation of the question at hand. Using an agriculture example, consider the process a dairy nutritionist must go through in order to properly feed a dairy herd in the most economical manner (cost minimization). First of all, a dairy cow must have a certain level of feed to simply maintain life. Getting more specific, a dairy cow must have certain levels of energy, protein, and other nutrients to allow her to optimally produce milk on a consistent basis. The nutrients themselves are what constitute the objective function.
The set of constraints that must be satisfied are the actual quantities of nutrients which are required in the dairy ration. When considering ration ingredients, a dairy nutritionist has multiple options for achieving a balanced ration. Inherently, each of the feedstuff options has a set of characteristics which can be used in an optimization problem. Once these characteristics are understood, we can adequately describe the problem and start down the path to solving for the optimum solution. In this dairy example, we are primarily concerned with the cost of the ration; as such we must have the prices of all potential ration ingredients as well as their associated nutrient characteristics.
In some cases, the process for determining an optimum solution to a business question can be done by hand in a relatively short period of time. Again using the dairy example, if we were after an optimum solution which simply required a certain amount (weight) of forage and certain amount of grain, we could look at the available forage options (i.e., alfalfa or grass hay) and available grain (i.e., corn or barley). Using prices for the available forage and grains, we would then include the ration ingredients which were the least cost per weight or volume measure. What this approach fails to account for, though, is the fact that just because a ration ingredient is cheaper in terms of weight of volume does not necessarily mean that it is the best ingredient to include in the ration. This is because a higher-priced ingredient may be able to supply energy or protein at a more competitive price by virtue of its composition (i.e., one ingredient may have a higher ratio of energy than another). By virtue of minimizing this particular ration cost function, we can obtain the maximum profit solution.
While we have used an agriculture example in this column, optimization has broad application across all industries and businesses. Logistics companies, equipment manufacturers, tire producers, restaurants, and even the healthcare industry are prime examples of industries that make regular use of optimization. Does your business have a need to define and find a solution to an optimization problem? We look forward to helping you find your optimum solution.