Multiple Types of Plug-In Charging Facilities’ Location-Routing Problem with Time Windows for Mobile Charging Vehicles

Abstract

Abstract:Increasing attention is being paid to the technology of battery electric vehicles (BEVs) because of their environmental friendliness. However, their short range, extended recharging times, and insufficient charging facilities hinder the improvement in the market share of BEVs. As a remedy, this paper presents a novel approach to providing a service for the battery charge replenishment of BEVs. Instead of using traditional alternative methods by only providing a charging service in a fixed location, such as battery-swapping and charging lanes, the novel charge replenishment is provided by mobile charging vehicles (MCVs), which could offer a charging service at any time and at location requested. To consider the limited running range and the opportunity to recharge from MCVs, as well as to determine the location strategy of multiple types of plug-in charging facility locations and the routing plan of the MCVs simultaneously, the location routing problem (LRP) that can integrate two decision levels, with a strategic level (location) and tactical level (routing), is applied. Then, we present the multiple types of plug-in charging facilities' location-routing problem with time windows for mobile charging vehicles (MTPCF-LRPwTW-MCVs), and formulate the MTPCF-LRPwTW-MCVs as a mixed integer linear program for the convenience of solving. To demonstrate the model, test instances are designed and computational results are presented. Furthermore, sensitivity analyses on battery capacity, recharging rate, and so on, are also examined. The results show that with the increase of the battery capacity or the improvement of the charging rate of the charging facilities, the service efficiency of the MCVs can reasonably be improved. Therefore, the proposed method could be used in real world problems.

An Optimization Model for the Temporary Locations of Mobile Charging Stations

“…A linear form of condition (11) can be obtained similarly to those obtained for (9) and (10). Assuming service times in each service center are exponentially assigned with a mean serving rate µ j > 0, to have a balance in the system, we have the condition µ j ≥ m j λ j where m j represents the number of mobile stations of center j, and λ j is the intensity of the Poisson process of charge requests arriving to center j. Marianov and Serra [45] showed that…”

“…The routing problem that arises with the current operational mode of a mobile charging station was also analyzed in the literature. Two decisions (location and routing) with time-windows were investigated in [11], with the results showing a need for a more efficient service in the sense of improving the charging rate or increasing battery capacity. Similar results were obtained by Cui et al in 2018 [12] by modeling the routing problem of a mobile charging station as a mixed-integer linear problem with time windows.…”

“…Assuming that each service center is represented by a M/M/m queuing process, we can calculate the probability from (11). Assuming that the two events are independent, this probability can be written as P[center j has at least a EVs and at most b EVs in queue] = P[center j has at least a EVs in queue]× P[center j has at most b EVs in queue]…”

“…This equation is equivalent to Equation (11). However, due to it being a nonlinear equation, we require an equivalent linear equation.…”

“…Therefore, once a value for γ is chosen, we determine the value for ω γ with any root-finding numerical method. The constraint (11) in optimization problem (P2) becomes (for mobile charging station):…”