In economics the term is expressed as opportunity cost, referring the most preferred alternative given up. A trade-off, then, involves a sacrifice that must be made to obtain a certain product, rather than other products that can be made using the same required resources. For a person going to a basketball game, its opportunity cost is the money and time expended, say that would have been spent watching a particular television program.
Trade-offs are important in engineering. For example, in electrical engineering, negative feedback is used in amplifiers to trade gain for other desirable properties, such as improved bandwidth, stability of the gain and/or bias point, noise immunity, and reduction of nonlinear distortion. The Golden Gate Bridge is a prime rare example where few engineering and aesthetic trade-offs had to be made.
In demography, trade-off examples may include Maturity, Fecundity, Parental Care, Parity, Senescence, and Mate Choice. For Example, the higher the fecundity (# of offspring), the lower the parental care. Parental care as a function of fecundity would show a negative sloped linear graph.
In computer science trade-offs are viewed as a tool of the trade. A program can often run faster if it uses more memory (a space-time tradeoff). It can be developed faster if it doesn't run as fast. It can be optimized for space or speed, but at the cost of longer and more complex development cycles. Consider the following examples:
The Software Engineering Institute have a specific method for analysing tradeoffs, called the Architectural Tradeoff Analysis Method or ATAM.
In medicine patients and physicians are often faced with difficult decisions involving trade-off. One example is localized prostate cancer where patients need to weigh the possibility of a prolonged life expectancy against possible stressful treatment side-effects (patient trade-off).
Governmental trade-offs are among the most controversial political and social difficulties of any time. All of politics can be viewed as a series of trade-offs based upon which core values are most core to the most people or politicians.
In music, the term "trade-off" can also refer to solo instruments that swap solo duties, such as musical groups with two lead guitarists, who both share guitar solos. The term is used frequently in heavy metal, where bands often feature "twin guitars", such as Iron Maiden, Judas Priest, Megadeth, and Slayer, all of which feature lead guitar song sections often involving 4 or more "trade-off" solos.
Trade studies are essentially decision-making exercises. In the FAA Systems Handbook (FAA 2004) the decision analysis matrix (aka Pugh's method) is suggested to support the activities, but this method can not support uncertainty, a mix of quantitative and qualitative information, or teams. To manage uncertainty, the authors suggest supplementing point estimates of the outcome variables for each alternative with computed or estimated uncertainty ranges. The Standard Approach to Trade Studies (Felix 2004), an INCOSE paper from 2004 suggests a similar approach. The NASA Systems Engineering Handbook (NASA 1995) suggests using multi-attribute utility theoretic (MAUT) or the Analytic Hierarchy Process (AHP). But, these too are not good with uncertainty, mixed information and teams. The authors suggest using probability based methods to maximize utility when uncertainty predominates, but give little detail on how to approach this.
In many situations linear programming methods like Simplex can be used but these too do not support uncertainty. Another approach to supporting trade study information is to use the Bayesian Team Support (BTS) methods. These methods were designed to manage uncertain and evolving information. A paper describing this method isTrade Studies with Uncertain Information (Ullman 2006).