Modeling a periodic electric vehicle–routing problem considering delivery due date and mixed charging rates using metaheuristic method

The coupling of ever-increasing consumption of fossil fuels around the globe with the decrease in the availability of fossil fuel supplies has led to an increased cost of energy commodities, which together with ever-expanding requirements for reducing the level of environmental pollutions has resulted in an ever-increasing deal of attention to alternative transportation schemes such as electric vehicles (EVs). Since decades ago, national governments and environmental activists have initiated various efforts towards reducing atmospheric pollutions. A part of such effort has been focused on reducing the use of internal combustion vehicles and rather replacing them with EVs. In this research, we attempt to fill in this research gap by presenting a mathematical model for minimizing the sum of traveled distance and recharging cost of EVs per a given period and then solving it by simulated annealing (SA) algorithm. Results of the proposed algorithm were then compared to those of coding in GAMS for 30 different sample problems with different counts of customers, EVs, and charging stations. Numerical results indicated good efficiency of the metaheuristic algorithm in terms of processing time and solution quality. Indeed, with the SA algorithm, the processing time was seen to increase gradually with increasing the problem complexity, while the rate of increase in processing time was much steeper with the GAMS.