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A trade-off (or tradeoff) is a situation that involves losing one quality or aspect of something in return for gaining another quality or aspect. It often implies a decision to be made with full comprehension of both the upside and downside of a particular choice; the term is also used in an evolutionary context, in which case the selection process acts as the "decision-maker".
Examples from common life 
In economics the term is expressed as opportunity cost, referring to 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 in specific fields 
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.
- By compressing an image, you can reduce transmission time/costs at the expense of CPU time to perform the compression and decompression.
- By using a lookup table, you may be able to reduce CPU time at the expense of space to hold the table, e.g. to determine the parity of a byte you can either look at each bit individually (using shifts and masks), or use a 256-entry table giving the parity for each possible bit-pattern, or combine the upper and lower nibbles and use a 16-entry table.
- For some situations (e.g. string manipulation), a compiler may be able to use inline code for greater speed, or call run-time routines for reduced memory; the user of the compiler should be able to indicate whether speed or space is more important.
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. A more limited number of bands, such as Dream Theater, also implement the trade-off with keyboards and lead guitar.
Analytical methods to support a trade study 
Trade studies are essentially decision-making exercises. In the FAA Systems Handbook. 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, an INCOSE paper from 2004, suggests a similar approach.
The NASA Systems Engineering Handbook NASA, 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 the simplex algorithm can be used but these too do not support uncertainty. Another approach to supporting trade studies with uncertain information is to use the Bayesian methods.
- "National Airspace System: Engineering Manual Version 3.1, Section 4.6, Trade Studies". Federal Aviation Administration. 2006.
- Felix A. (2004). "Standard Approach to Trade Studies: A Process Improvement Model that Enables Systems Engineers to Provide Information to the Project Manager by Going Beyond the Summary Matrix". INCOSE.
- "NASA Systems Engineering Handbook, Section 22.214.171.124 Trade Studies"". NASA. 2007.
- Ullman D. G., B. P. Spiegel (2006). "Trade Studies with Uncertain Information". Sixteenth Annual International Symposium of the International Council On Systems Engineering (INCOSE).