Application of the Fuzzy Optimization Method to the Adjustment of Trip Rates of the Multiple Cross-Classification Tables

The estimation of urban trips generated by each traffic zone in future is a crucial stage of urban transportation planning. In trip generation models, the relationship among the socio-economic characteristics of the region under study, the land-use features, and the transportation demand is analyzed. In order to predict the rate of trip generation (number of per capita or household trips generated), regression models are widely used. These models have been introduced based on theoretical framework of econometrics. However, cross-classification table is an alternative simple approach for predicting these rates. In this method families are categorized based on their common characteristics. The tables that are used for future prediction can be classified based on different trip purposes. Cross-classification tables can be used in two or more dimensional layout. In a two dimensional cross-classification table, the rate of daily trips produced per household is estimated for the categories created by only two variables (generally household size and car ownership). In multiple cross-classification tables, more than two (generally three) variables are used to categorize the people in different groups (table cells herein) and then estimate the produced household trip rates. In this paper the three variables are household size, car ownership and density. Like any other model, matching the reality (having reasonable rates herein,) is a main problem during the model development. The traditional method of trip rate adjustment in a cross-classification table is the ANOVA method. In this method, the rate in each table cell is modified by the average deviation of the relevant row and column of that cell. Although this modification to some extent improves the calculated rates, it does not necessarily lead to reasonable values comparing with neighboring cell rates.The trip rates for each category are achieved from the observed data. Sometimes these calculated rates do not show the expected trip pattern. For example a single man (as a one person family) without a car, that seems to have less trip rate than a five person family with two cars, has a more rate. Therefore, this irregularity should be modified. This paper uses fuzzy linear programming method for adjusting the values of the multiple cross-classification tables. In this method the understanding and judgment of experts is applied to make the adjusted rates as close as possible to the reasonable values. In this method, trip rates of table cells are modified using the relations and the constraints that are obtained from the exceptions of transportation analysts regarding trip rates. The resulting fuzzy models are solved using “LINDO” package software. Comparing the results shows that there is no significant difference between the rates before and after adjustment for each density category. The total number of observed trips differs from that of adjusted trips only about %5 on the average for the three density categories, which is acceptable. As seen, this method modifies the rates for each category simply and reasonably. In order to compare, and to show the reliability of the proposed method comparing to the ANOVA method, the coefficient of determination (R2) is used too. The achieved coefficients reflect the same results as above. The paper is organized as follows: First, the multiple cross-classification model is introduced. Then the problem is defined and the principles based on which the rates are adjusted, are explained. Then the study uses real data from Mash had Transportation Comprehensive Study in order to reflect the influence of the proposed method comparing to traditional ANOVA method. Finally, the results, conclusions and references are presented. The acquired results show that fuzzy optimization method works better than analysis of variance method for multiple cross-classification tables.