The method of sectioning with application to simulation

Abstract

The objective of this investigation is to adapt the standard search by sectioning to response surfaces confounded by random error and to develop cost related termination criteria for the application thereof. Replication is employed at each point of the search in an effort to reduce the random error. Of particular concern is the application of this procedure to simulation models where the cost of such a search could prove to be very expensive. When the response can be expressed in terms of cost or profit, the expense incurred by the optimization procedure is viewed as a direct charge against any gain revealed.

The statistical model selected assumes that the measure of effectiveness at each point in the search is normally distributed and that two adjacent points possess the same, but unknown, variance. The expected value at each point is unknown and is estimated by the sample means. A test of hypothesis employing the sample means is employed to assess the difference between successive points in the search. Two test statistics of known distribution--normal and t--are considered. The search is terminated when an economic point of diminishing returns is indicated.

Computerization of the search procedure is discussed and a wide range of computational studies are presented using four different test functions.