Abstract
In the case of determining routes for hazardous material transportation, risk is considered as a main attribute. Transport risk, which is usually combined with other attributes such as cost or travel time, plays a significant role in determining paths for hazardous materials transportation. Since, risk is chaotically affected by road incidents, decision makers are dealing with selecting a method for defining chaotic risk factors in hazmat transportation. In this paper, transport risk has been defined as a chaotic variable using two different methods of generating chaotic patterns. In an experimental road network, which consists of eighty-nine nodes and one hundred and one two-way links, two different methods of generating chaotic variables have been used for applying the proposed procedure. In addition, results for different amounts of risk and cost have also been analyzed in case study. Results revealed that different cost and risk priorities change the frequencies of selected paths determined for hazmat transportation, but the route convergence of the route to chaos method is better than that of the logistic map equation.
Highlights
One of the most important issues in hazardous material management is to find the best path for transportation which is known as hazmat routing problem (HRP)
Transport cost and risk have been considered as main attributes in HRP, so mathematical model has been developed to be capable of considering both risk and cost attributes
Risk is defined as a chaotic variable using two methods of generating chaotic variables including logistic map and route to chaos equations
Summary
HRP is usually a double-sided consideration problem in which local authorities are interested in minimizing public risk and carriers are dealing with minimizing transport cost [5] In this case, a combination of risk and cost is usually used for developing mathematical models in order to find the best path for hazmat transportation. Logistic map equation is formulated by the following equation, where R(t) is the chaotic variable at time t and Kl is chaos parameter mainly set to 4 [9]:. Route to chaos equation is formulated by the following equation, where R(t) is chaotic variable at time t and Kr is defined as chaos parameter mainly set to approximate interval 1.0624–1.0807 [15]:. The aim of this research work is to apply both logistic map and route to chaos equations for defining chaotic risk variables in HRP. Path convergence according to the most frequent path is considered in order to check chaotic generation performances of the above equations
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