Markup estimation using neural network methodology

The results show that the two NN models can be trained satisfactorily on the training examples presented, however the single-network model generalizes unseen examples better than the hierarchical model.

Abstract

This paper introduces a neural network-based model for solving the percent markup estimation problem. Neural networks (NNs) are utilized as systems able to generalize solutions by learning from a set of examples representing previous encounters of problems and their corresponding solutions or decisions. NNs utilize these holistic examples (without their underlying logic) as patterns, to simulate the decision process and its related knowledge for devising solutions to new encounters even with incomplete and/or noisy information. In this paper, existing markup estimation models are reviewed and their limitations identified. The characteristics that render the markup problem more suitable for NN modeling are outlined. The markup estimation process is analyzed and the decision-governing attributes identified. Two alternative designs for the NN model are examined and their results compared. The first model is based on a single neural network architecture and the second is based on a five-network hierarchical system. As opposed to the single large network, the hierarchical model consists of four sub-networks, pertaining to the assessment of: job uncertainty; job complexity; marked conditions; and company capabilities. The results of the four sub-networks form the input to a macro-level neural network designed to estimate the optimum markup, for a given project environment. A questionnaire survey is developed to elicit the required knowledge, from general contractors in Canada and the U.S.A., pertaining to bidding situations or encounters of some past projects. Analyses of the survey responses are utilized to structure, design, implement, train and test the two NN models. The results show that the two NN models can be trained satisfactorily on the training examples presented, however the single-network model generalizes unseen examples better than the hierarchical model. Issues regarding practical implementation of the NN model, improving its generalization capabilities and integration with other decision analysis tools are outlined.