«BASIC HUMAN DECISION MAKING: An Analysis of Route Choice Decisions by Long-Haul Truckers John Holland Knorring Advisor: Professor Alain L. Kornhauser ...»
The other disadvantage to using the Box Algorithm is that for cities that had the major highways passing through the city at some direction other than North, South, East, or West such as Northwest to Southeast, it was quite difficult to find a rectangle that would encompass enough of the highway so that there would be a sufficient number of observations on the route while also minimizing the interference from trucks on totally different highways. Additionally, finding a way to make Box 3 and Box 4 similar in size to each other was quite difficult. This thesis attempted to include the same number of miles of highway in Box 3 as in Box 4, but differences in box size could contribute to a bias in the data towards either the bypass or downtown route.
After analyzing the results of the FSM program, it became apparent that there were still trucks that were included in the data set that should not have been included.
This study is only concerned with trucks passing through the city without stopping. The data does not tell why a trucker would stop, either for gas or to make a delivery, so it is impossible to eliminate only select trips. As a result, it is necessary to eliminate all the trips where there analysis leads one to believe that the probability of a stop was rather high. There are a few ways of accomplishing this, but the simplest method involves using minimum average speeds for the trips.
As previously stated, the average speed for the trips were determined using a great circle calculation to find the approximate distance traveled and then using the travel time as the time divisor to find the approximate average speed. There is no theory or rule in place to determine if a truck made a stop on a trip or not based on its average speed, however, another heuristic was developed. This study decided that if a truck went slower than 30 mph for its entire trip, the data should be eliminated from the analysis.
One significant drawback to this method however was that more case cities were eliminated from the analysis. There were a few cities, such as Memphis and Chicago, that either had no trucks on the downtown or on the bypass route where the average speeds for their respective trip was greater than 30 mph. One possible explanation why so much data was eliminated results from the algorithm used to pull out the good data.
Because the Box Algorithm only sensed position data and did not reduce data that did not make sense, too much data was selected. A number of the trips had travel times that were
anywhere from ten to thirteen days where the trip was only 30 to 70 miles in length. This can be explained by the possibility that a truck passed through Box 1 early in the week.
Later in the week, it happened to pass through Box 3, and the next week through Box 4.
The Box Algorithm would record this as a single trip even though it is an impossibility.
Therefore, trips with average speeds less than 30 mph were eliminated.
Lastly, there was the issue of trucks traveling to fast on some routes. While it might seem unlikely that the data would show that a truck was traveling too fast on a route, it happened in a few cases. For example, in the Oklahoma City case study, truck 39960 had an average speed of 263 mph. This is impossible and is attributable to “bad data”. Like the minimum average speed case, there is no rule or theory for a maximum speed on a route. As a result, another heuristic was developed such that any truck that had an average speed greater than 75 mph was eliminated from the analysis.
Output statistics for the final data run including truck counts on routes and average speed characteristics can be found in the appendix.
5 Building the Model The goal of this thesis is to examine the basic human decision making process that long-haul truckers use to formulate and carry out route choice decisions. By analyzing the basic decision making process, this study is attempting to better quantify and more clearly define some of the more important factors in the decision making process. The most important factors to be analyzed are how long-haul truckers trade off between distances and time when faced with multiple routes.
The more general analysis began in earlier chapters with commentary on Utility Functions. Truck drivers were assumed to be rational decision makers and by extension utility maximizers. Some factors that have been shown to contribute to the overall decision making process and thus the utility function include factors such as: length of alternate routes, expected traffic on routes, risk aversion, income and education, and time of day. While some, including Nobel Prize winner Prof. Daniel Kahneman, propose that humans are not necessarily rational decision makers in reality, this thesis will attempt to explain this purported irrationality by proposing that humans base decisions primarily on perceptions.
This study will examine tradeoffs made by truckers between distance and time.
The most obvious place to analyze tradeoffs between distance and time are in areas where there are multiple plausible routes to get from point A to point B. Theoretically there are infinite routes between two points, however, plausible routes include routes that are suitably similar to either the time or distance minimized optimal solution. The most common area to have multiple alternate routes is around major cities that have a major
highway passing through the downtown area and a bypass route that skirts the downtown region. These particular case cities are fertile areas for analysis of tradeoffs between distance and time for a few reasons. First, typically, the downtown route follows the most direct path from one side of a city to the other and as a result is shorter than the bypass route. Next, the bypass route typically is designed as a limited access route that is used by travelers who are not planning on stopping in the central business area of the city. Limiting access to a road generally speeds up the flow of traffic because drivers have less of a need to alter their speed. Conversely, downtown routes typically have far more exits and entrances thereby increasing the probability of interrupting the flow of traffic resulting in congestion. Additionally, highway designers implement bypass routes to minimize the potential for excessive congestion caused by through traffic in the downtown area. The results of the differences between the downtown and bypass routes are that, in general, the expected value of the travel time on the downtown route is lower than the travel time for the bypass route, however, the variance in travel time is at the same time greater on the downtown route then the bypass.
5.1 Foundation for Discrete Choice Models Previous chapters have already covered how the subset of trucks to be analyzed was selected. After implementing the Box Algorithm and performing significant data reduction, this study counted the number of trucks on the bypass route and the downtown route. With this information, this study then calculated the percentage of trucks on the bypass route. Information regarding specific counts and selected data can be found in the appendices. By incorporating the percentage of trucks on the bypass route in conjunction
with the specific characteristics of the downtown route and bypass such as distance of trip, time of trip according to calculations made by CoPilot®, and time of trip on each path assuming 55 mph on the downtown route and 65 mph on the bypass route, one can build a model that predicts the percentage of users that use the bypass route as a function of the perceived speed on the downtown route. This thesis chose to examine the usage of the bypass route because there is a greater chance of variability of travel times on the downtown route, thus perceptions for speeds on the downtown route have a greater variability.
5.2 Utility Maximization This thesis has proposed that truck drivers are rational decision makers, thus they are utility maximizers. When making a decision on which route to take, the truck driver will either consciously or unconsciously calculate his expectation of utilities for the potential routes based on his perceptions of the routes. Once this calculation is performed, the driver will then pick the route that offers the maximum utility. This study is focused solely on a choice between two options, so the difference in utility can be
quantified using the following equation:
Using this equation, the driver will only select the downtown route with certainty if ∆Utility is greater than 0. Otherwise, the driver is either indifferent between routes, or prefers the bypass route.
The problem now is how to determine either ∆Utility or the utilities for the downtown and bypass routes respectively using the travel times and distances for each route in addition to the derived quantity of the percentage of trucks on the bypass.
Because this is a discrete choice problem, a Logit model is the likely candidate.
5.3 The Logit Model The case studies in this study were picked because the truck drivers were essentially only able to choose between two plausible routes. As a result, the decision is a binary choice between two alternatives: take the downtown route or take the bypass route. Logit models are designed so that they predict the probability of choosing one of the routes based on the inputs to the model. The inputs to the Logit model are simply the distance and time characteristics of the respective routes. The output of the model is the probability of trucks that take the bypass route. The model is calibrated using the percentage of trucks on the bypass route, which was derived by sifting through the truck position data.55
The outcome of the route choice decision (R) will be defined as:
As was previously stated, the decision to chose a particular route is quite complex. There are theoretically an infinite number of factors that contribute to the decision process. However, when considering only distance and time, the decision
process can be modeled as a function defined as:
55 Burner. Pg. 70.
functions: ∆Utility. One complication results from this definition. It is now necessary to define one utility function for each route. However, one trick to get around this problem is to define ∆Utility to be a function of the Distance Factor and Time factor for both the downtown and bypass routes.56 One method to model the difference in ∆Utility is to use a combination of the difference in the distance and time factors while assuming speeds on the respective routes. However, this simplistic approach is not very helpful in modeling the decision making factors, because it does not capture enough of each factor. Essentially, the results of this method would be the differences in distances and speeds for the two routes.
However, when making route decisions, one must consider more than just the distance savings in absolute terms.57 The 90-94 case study in relation to the Wilmington, DE case study is a perfect example of this significance. Each of the routes in the 90-94 case are approximately 1000 miles in length. The Wilmington routes are approximately 10 miles in length. A change in distance of one mile on the Wilmington route should have more significance to the decision process than the 90-94 case because of the percentage change in the Wilmington case is significantly greater than the 90-94 case.
Todd Burner ’99 proposed using factors that show the percentage difference in routes as opposed to the absolute difference in routes. This has two important benefits.
First, units of time and distance drop out of the calculation. Secondly, when estimating parameters of the Logit function, multiple case studies can be used to calibrate the model
because the cases are relatively similar. The equation for the ratio that the individual uses
to evaluate the distances for the two routes is as follows:
The equation for the ratio of times for the two routes is similarly defined using the time considerations for the downtown and the bypass routes instead of the distance Plugging these distance and time factors into the ∆Utility function considerations.
When considering the ∆Utility function, it is important to keep in mind that the utility has no meaning across different cases. This concept was covered in Chapter 2.
The ∆Utility is merely used as a comparison to make a decision. In other words, the ∆Utility is not transferable between cases. A new ∆Utility must be calculated for each case because each case has a unique ratio of distances and times.
With ∆Utility defined, it is now necessary to define the odds of choosing the bypass route for the Logit model.
Now that these equations have been defined, it is necessary to estimate the parameters of the ∆Utility. Estimating the parameters used in the Logit function (L) for this study is an exercise in maximum likelihood estimation.
In this equation, n represents the number of case studies used to calibrate the model. The Di represents the respective probabilities for case study(i). The pi symbol is used to represent the sum of products.
It is now necessary to take the logarithm of equation (5-8) in order to derive the log-likelihood factors. Additionally, using properties of logarithms, equation (5-8) can be
Because this is an attempt to maximize the likelihood of the parameters the Excel solver is used. The following inputs were used in the optimization program to solve for the
parameters in the utility function: