Editing Satisficing (section)

==== As a form of optimization ====
Alternatively, satisficing can be considered to be just [[constraint satisfaction]], the process of finding a solution satisfying a set of constraints, without concern for finding an optimum. Any such satisficing problem can be formulated as an (equivalent) optimization problem using the [[indicator function]] of the satisficing requirements as an [[objective function]]. More formally, if {{math|<var>X</var>}} denotes the set of all options and {{math| <var>S</var> &sube; <var>X</var>}} denotes the set of "satisficing" options, then selecting a satisficing solution (an element of {{math|<var>S</var>}}) is equivalent to the following optimization problem

: <math>\max_{s\in X} I_{S}(s)</math>

where {{math|I<sub>s</sub>}} denotes the [[Indicator function]] of {{math|<var>S</var>}}, that is

:<math>I_{S}(s):=\begin{cases} \begin{array}{ccc} 1 &,& s\in S\\
0 &,& s\notin S
\end{array}
\end{cases} \ , \ s\in X</math>

A solution {{math|<var>s</var> &isin; <var>X</var>}} to this optimization problem is optimal if, and only if, it is a satisficing option (an element of {{math|<var>S</var>}}). Thus, from a decision theory point of view, the distinction between "optimizing" and "satisficing" is essentially a stylistic issue (that can nevertheless be very important in certain applications) rather than a substantive issue. What is important to determine is {{em|what}} should be optimized and {{em|what}} should be satisficed. The following quote from Jan Odhnoff's 1965 paper is appropriate:<ref>{{cite journal |last=Odhnoff |first=Jan |year=1965 |title=On the Techniques of Optimizing and Satisficing |journal=The Swedish Journal of Economics |volume=67 |issue=1 |pages=24–39 |jstor=3439096 |doi=10.2307/3439096 }}</ref>

{{quote|In my opinion there is room for both 'optimizing' and 'satisficing' models in business economics. Unfortunately, the difference between 'optimizing' and 'satisficing' is often referred to as a difference in the quality of a certain choice. It is a triviality that an optimal result in an optimization can be an unsatisfactory result in a satisficing model. The best things would therefore be to avoid a general use of these two words.}}