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3- Cost Modeling
After the identification and determination of criteria and sub criteria effective on the cost model of the routes, in order to devote values to each part of the routes network after determination of effecting criterion factors on the value devoting process, these determined factors should be weighed and combined in a systematic manner [Sadeghi-2003]. These factors are put to gather in a model called cost model in this research. Since some of these factors are quantitative and some others are qualitative, a method should be used to enable the simultaneous evaluation and combination of both groups of factors. The Analytical Hierarchical Process is one of the most developed methods of multi attribute decision making models because this method enables the hierarchical formulation of matters and has this capability to contain both qualitative and quantitative factors in one single model [Ghodsi Pour, 1999]. This method was developed by a researcher called Thomas L. Saaty based on the method of analyzing complicated fuzzy matters by human brain in 1975 to the extent that many applications for this methods have been suggested by different researchers since that time. This process includes series of judgments, decision makings and personal evaluations via a logical method.

A scientist called Tomas L. Saaty in 1975 developed this method on the basis of brain pattern of analysis on complicated fuzzy cases. this is process of judgment, decision-making and personal evaluation through a logical procedure[Satty,1988]. This could be said that this method is dependent on personal imaginations and experiences to hierarchically formulating a matter and on the other hand relates to the logic and conceptions for making the final decisions. Another advantage of the AHP method is that it makes a structure for participation and group cooperation for resolving the problems and making decisions. It also provides a unique, simple and flexible model for resolving a broad range of unstructured problems which is understandable for everyone. So it uses both systematic approach and detailed analysis to solve sophisticated problems and also realize the relative importance of factors in a model and tries to make a equity between these factors and enables the user to select best alternative suits its special objectives.

Conception of sophisticated events and matters can be come a major problem for human mentality so breaking the major structure of a case into its separate elements through a hierarchical structure can contribute to better perception of human mentality. In these kinds of structures every component is placed in a specific level and is assumed as a sub branch of one or all other elements which are placed in higher levels so the first step in AHP is dedicated to the identification of criteria and the relative position of these criteria (Figure 1). After structuring the tree chart and AHP chart, the same level and relevant criteria are compared with one another. Now in order to combine the criteria cording to above mentioned method of AHP the criteria should be granted suitable weights and compared with each other by specialist experts of AHP.

Since the comparison of the criteria required to specify the type and season of the travels so the modeling was performed through four different divisions (summer – tourism traveling, summer - none tourism traveling, winter – tourism traveling and winter – none tourism traveling)

The modeling is addresses in two levels, the first level’s elements are the main criteria and the second level is composed of the sub criteria of each main criterion.


Figure 1 – the AHP diagram of main criteria and sub criteria of interurban cost modeling

• First level Modeling: after preparing a comparative table of criteria and sub criteria of the model and collecting the cost model experts points of view about the first level, two formulas were achieved:

After the paired comparison of criteria in four different statuses in first level this general formula for cost model is achieved:


In this formula f is the primary cost model of the roads excluding the length criterion, n is the quantity of effective criteria in cost model of the roads and Xi shows the effective criteria to cost model and K is a constant coefficient determined by experts of cost modeling.

The relative preference of one part to another part cost model is resulted from the quantitative result of F in above mentioned formula. In other word that part is selected after cost model analysis which has the highest value in all studied parts of routes network. Also the part with the shortest length is selected so the lengths of the route and F function have reverse relationship with each other. At last this general formula is offered as the general cost model:


The important point in these kinds of modeling is that the coefficients in the formula are normalized it means that the aggregate of these coefficients is equal to 1. The four different phenomena of the general cost model (formula 3) are mentioned bellow:

Summer – tourism traveling: in summer – tourism traveling status considering the high importance of sightseeing attractions criterion (F2), this criterion is granted the highest value in the model (formula 4), also another important case in tourism traveling is the extent of traffic in the roads so considering this case the next highest value is granted to traffic criterion (F3). In order to investigate the accuracy of granted values to different criteria and testing this issue that what would happen if one or more of criteria will be excluded from the model we will work it out in sensitivity analysis section.


in this offered formula FST ، FSNT ، FWT FWNT are cost model of summer – tourism, summer none tourism, winter tourism and winter none tourism traveling respectively. Also note that F1 is the criterion of weather condition, F2 shows the sightseeing attraction, F3 is the criterion of traffic, F4 stands for safety and F5 is the criterion of facilities, Li is the length of every part of the route. The F1 to F5 parameters are not constant but they are functions of their specific sub criteria which will be reviewed in next sections

Summer – none tourism traveling: in this kind of traveling since the sightseeing attractions have the least importance for the travelers the granted value two this criterion is 0. And since the traffic rate is very important for the traveler in this kind of traveling and he wants to get to the destination as soon as possible this criterion (F3) is the most important criteria in this specific model.


Winter – tourism traveling: in this cost model (formula 6) since this is a tourism traveling the sightseeing attraction (F2) and traffic criteria (F3) are the most important criteria and the weather condition criterion (F1) has relatively high importance.


Winter – none tourism traveling: the traffic criterion is the most important factor (F3) while the granted value to the sightseeing attraction factor is “0” since it has no importance for the user.

• Second level Modeling: After the paired comparison of criteria in four different statuses in Second level this general formula and tables for cost model is achieved (Table 3).

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