Analysis of Uncertain Parameter Values included in Engineering Optimization Models: A Case Study of a Project Scheduling Model

• Main Authors: Sin-Siang Wang, 王信翔
• Other Authors: Shangyao Yan
• Format: Others
• Language: en_US
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/6jsf93

博士 === 國立中央大學 === 土木工程學系 === 103 === Decision makers have widely applied engineering optimization models in the field of engineering in order to effectively solve various types of engineering optimization problems and secure optimal decisions. However, confronted with practical engineering problems, some parameters of the optimization model may be uncertain. Uncertain parameter values are hard to accurately estimate, causing that they include errors. In case there are uncertain parameters involved in the engineering optimization model (i.e., the model input includes errors), the obtained solution may also include errors (i.e., the model output includes errors). In this case, the decision makers cannot make the optimal decisions. In the past, the studies regarding estimating uncertain parameter values have chiefly utilized the estimation or prediction approach to find the proper uncertain parameter values that can be used as model input data. However, there could still be unknown errors in model solutions obtained using estimated uncertain parameter values. Since it is hard to obtain a real optimal solution for a model that contains uncertain parameters, the evaluation of these solutions is carried out mainly by comparing them with the best solution secured previously. The gap between the obtained model solution and real optimal solution is unknown, that is to say, the performance of the solutions secured from previous studies cannot be confirmed objectively. Additionally, although there have been many studies that have employed approximate solution algorithms with a solution tolerance error to enhance the solution efficiency, there have not been any studies that further explore the effect of various solution tolerance errors on model solutions with input errors. Thus, the purpose of this study is to explore the output errors for an engineering optimization model that includes uncertain parameter values under different controllable and random error scenarios, coupled with different solution tolerance error settings (i.e., this study focuses on evaluating the optimality of model solutions with input errors). There are usually two sorts of uncertain parameters included in an optimal mathematical programming model. One is the uncertain parameters included in the objective function; the other is the uncertain parameters included in the constraint set. The results of the error analysis of the two types of uncertain parameters may be different. In order to reflect this, this dissertation is divided into three essays. In the first essay, an experimental evaluation approach is developed to evaluate the output errors of an engineering optimization model in which uncertain parameter values are included in the objective function, under various controllable and random error scenarios, coupled with various solution tolerance error settings. The second essay also develops an experimental evaluation approach to evaluate the output errors of an engineering optimization model in which uncertain parameter values are included in the constraint set, under various controllable and random error scenarios, coupled with various solution tolerance error settings. In the third essay, the methods discussed in the first two essays are combined to develop an experimental evaluation approach to evaluate the output errors of an engineering optimization model in which uncertain parameter values are included in the objective function and the constraint set, under various controllable and random error scenarios, coupled with various solution tolerance error settings. To facilitate comparison of the test results, the same engineering project optimization scheduling model is used in the testing in all three essays. In addition, regression analysis of the test results of each error scenario associated with the three essays is also implemented to further comprehend how model input errors (i.e., controllable and random errors) and solution tolerance errors affect model output errors. Finally, some useful information and managerial meanings for designing optimization models and solution algorithms in practice are extrapolated from the test results.