Satisficing - Relationship With Optimization

Relationship With Optimization

One definition of satisficing is that it is optimization where all costs, including the cost of the optimization calculations themselves and the cost of getting information for use in those calculations, are considered.

As a result, the eventual choice is usually sub-optimal in regard to the main goal of the optimization, i.e., different from the optimum in the case that the costs of choosing are not taken into account.

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 denotes the set of all options and denotes the set of "satisficing" options, then selecting a satisficing solution (an element of ) is equivalent to the following optimization problem

where denotes the Indicator function of, that is

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

A solution to this optimization problem is optimal if, and only if, it is a satisficing option (an element of ).

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 what should be optimized and what should be satisficed.

The following quote from Jan Odhnoff's 1965 paper is appropriate:

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.

More on the "satisficing" vs "optimizing" debate can be found in Byron's 2004 edited collection of articles.

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