Developing a chaotic pattern of dynamic risk definition for solving hazardous material routing-locating problem

In the case of determining routes and locations for constructing distribution centers on hazardous materials (Hazmat) transportation, risk and cost are considered as the main attributes for developing mathematical models. Since, Hazmat transport risk may be defined as a chaotic factor, using dynamic risk changes the selected routes and optimized locations for constructing distribution centers.In the present paper, an iterative procedure has been proposed to determine the best routes and optimized locations of distribution centers for transporting hazardous materials based on the concept of chaos theory in which hazmat transport risk is defined as a dynamic variable. A mathematical model has been developed for solving Hazmat routing and locating problems, simultaneously. Daily transport risk, defined as a chaotic variable, is iteratively updated using one-dimensional logistic map equation over the time period (year). An experimental road network, consists of eighty nine nodes and one hundred and three two-way edges, has been selected for analytical process and model validation. Results revealed that although different amounts of risk and cost priorities change optimized locations of distribution centers and their associated supplies, but the most frequent set of optimized centers remains independent. Therefore, the proposed procedure is capable to determine the best routes and optimized locations for distributing hazardous materials. While risk is iteratively updated over a specific time period, results show that the main property of chaos theory known as dependency upon initial condition would not be a serious concern for decision makers who are dealing with Hazmat management.