Sustainability, Vol. 10, Pages 4714: A Bi-Level Programming Model of Liquefied Petroleum Gas Transportation Operation for Urban Road Network by Period-Security (Sustainability)

As a clean energy, Liquefied Petroleum Gas (LPG) is consistent with the coordinated and sustainable development of both the economy and environment. However, LPG is a hazardous material (hazmat) and is thus always transported in cylinders by vehicles on urban road networks to meet varying demand. This transport can threaten the surrounding citizens, vehicles, and even the whole urban area. Hence, LPG transportation should be focused on maintaining its security while simultaneously minimizing shipping costs. When LPG is moved through an urban area, its threat level fluctuates with the network congestion level, which continually varies by different time periods. So, variation in the magnitude of the threat posed by LPG transportation causes additional changes in the safe-related cost as well as the shipping cost. This study aims to solve the problem of an LPG transportation operation on an urban road network according to congested periods; the solution is based on cutting its two types of cost. In general, we should choose an LPG transport period that results in a lower safety cost, however optimization of an LPG transportation operation must minimize both the safety cost and shipping cost. This paper presents the problem of LPG flow distribution and vehicle dispatch scheme by “period-security” to rationalize the LPG transport risk level. Firstly, the impedance function of LPG flow distribution was constructed with a focus on the safety cost in different periods. Meanwhile, a bi-level programming model was built, in which the upper mixed binary integer programming model aims to minimize the shipping cost and the lower model is a user-equilibrium model that is aimed at calculating the distribution of the LPG demands on the given lines and in feasible periods. Then, we designed a heuristic algorithm based on the Genetic Algorithm to solve the upper model and embedded the Frank-Wolfe Algorithm to get the optimal LPG flow distribution solution. Numerical examples are presented which validate that the LPG optimal operation can realize a minimal safety cost and the minimum shipping cost for three LPG demand values by considering the congestion situation.