Research Reports from the Department of Operations
Document Type
Report
Publication Date
7-1-1958
Abstract
We are frequently faced with having to make decisions in situations where there is uncertainty about the outcome, but where we can exercise some control. In order to do so in a rational manner we must first define a criterion of optimality. Many workers have used the expected outcome when the actual outcome could not be determined in advance; they have then minimized the expected outcome*. Other definitions of optimality are possible and will be discussed here. A typical situation may be represented by a mathematical model E = f(X_i, Y_j) i = 1, 2, ... n, j = 1, 2, ... k where E is our measure of the outcome when we choose the value X_i for the i^th control variable, and Y_j is the value of the j^th parameter. We can think of a decision as specifying (X_i) in advance of a trial in which nature specifies (Y_j). If we knew nature's choice in advance we would minimize E by choosing a set (X_i*) = {g_i(Y_j)}. If we do not know nature's choice, there are two possibilities: (1) Nature will choose (Y_j) from a population with a known density function p(Y_j). (2) We can take observations on the (Y_j) in advance of the trial and use them as a basis for estimating (Y_j), but there will be a cost, dependent on how observations are made. This cost then becomes part of the outcome of the trial and must be considered in choosing the course of action.
Keywords
Operations research, Decision making--Mathematical models, Mathematical optimization, Mathematical models, Distribution (Probability theory)
Publication Title
Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 5
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Gupta, Shiv K.; Yaspan, Arthur J.; Sasieni, Maurice W.; and Dean, Burton V., "Errors, Estimates, Optimality" (1958). Research Reports from the Department of Operations. 186.
https://commons.case.edu/wsom-ops-reports/186