Taking the location of highways as an example, the author develops a Bayesian decision theory model for guiding any engineering, planning, or design process. This model recognizes that such processes are “hierarchically structured,” in that they progress from preliminary concepts through successively more detailed levels of analysis to the final design.
The process of solving a highway location problem involves the application in sequence of one or more operators. Given a number of operators, in general there is only one that produces actions sufficiently detailed to be considered solutions to the particular problem. An experiment is defined as the application of an operator to a previously produced action to yield a new action, more detailed than the first. Each time the engineer executes an experiment, he incurs a cost. The utility of an action resulting from the experiment is the best one to do next, considering the costs of each experiment and possible utilities of the resulting actions.
The model represents the location process as a sequential decision problem. Using the Bayesian point of view, the model requires the engineer to place a subjective “prior” probability distribution over each action previously generated. Each operator is characterized by a “conditional” distribution, as well as a cost. Based upon the results of the experiments, the priors are revised in a Bayesian fashion, modified to represent the hierarchical structure. The best experiment at any time is calculated using preposterior analysis.
An example computation is given for a hypothetical location process, and several other types of analyses using the model are illustrated. A program incorporating several heuristics enables the experimenter to perform the computations on a time-shared computer system. Finally, the implications and assumptions of this work are explored.
