The Electric Vehicle Routing Problem Considering Nonlinear Battery Depreciation

With the rapid and steady growth of the global economy,human society faces new problems: energy crisis and environment pollution.The excessive exploitation and utilization of fossil fuels,such as oil,coal,natural gas,has resulted in higher energy prices and serious environment problem.As we all know,transportation industry consumes a large quantity of fossil energy and releases vast amounts of pollution gas.To pursue energy conservation and emission reduction,a worldwide car revolution,automobile electrification,is carried out vigorously.For example,Electric vehicles are taking the place of traditional fuel-consumption vehicles and serving as the tools of urban distributio n.VRP(Vehicle Routing Problem)is the very problem on the basis of urban distribution to make vehicle dispatching and minimize certain objects.As one of the most important variants of VRP,EVRPTW(Electric VRP with Time Windows)has become a research ho tspot recently.Previous studies have considered mostly the consuming and charging policies,such as the consuming speed and its influence factors,the charging speed,the charging place,the charging quantity when electric vehicles depart from the charging stations.To the best of our knowledge,sparse researches have addressed the effect of depth of discharge on battery degradation.On the basis of previous work on EVRPTW,a set of models,named as EVRPTW-BD,are presented by considering different battery depreciation methods,including DOD(Depth of Discharge),Cycle(the total number of charge-discharge cycles)and Meter(the total traveling distances).Meanwhile,three recharging polices are considered,namely the nonlinear charging,the full charging a nd the partial charging.Models are constructed to minimize the total cost including the fixed cost for the use of electric vehicles,drivers' salary,electricity cost,fixed recharging fee,and finally,the battery depreciation cost.The nonlinear battery depreciation cost is a power function of DOD,which is linearized by a piecewise function of the golden section points.Numerical experiments are conducted on the instances designed in the related research by CPLEX solver.Computational results show that: 1)when the customer distribution is clustered,differences of models are more obvious;2)considering DOD in models results in higher remaining charge levels when EVs arrive at the charging stations,which is beneficial to extend the battery life;3)model with consideration of DOD has a minimum cost,while model with Meter has the maximum cost.