Climate change and environmental policies have compelled the transportation sector to reconsider its operational patterns. The adoption of Electric Vehicles (EVs) is rapidly expanding, but limitations such as restricted driving range, long charging times, and lack of charging infrastructure transform route planning into a non-linear and complex problem. This research introduces a novel Electric Vehicle Routing Problem with Competitive Time Windows (EVRPCTW), modeling supplier competition under energy constraints and a partial charging policy. Customer demand is divided into a time-independent base portion and a time-dependent opportunistic portion realized only if delivery occurs before competitors. The objective is to maximize net profit by balancing operational costs, charging times, and revenue from time-sensitive demand. Quantitatively, the proposed competitive model improves net profit by 18.7% on average and up to 87% in highly competitive scenarios compared to classical cost-minimization models. To solve this problem, a precise mathematical model along with a Variable Neighborhood Search (LNS) metaheuristic and an Adaptive Simulated Annealing (ASA) algorithm are developed. The ASA algorithm outperforms LNS by 3.2% in profit while reducing computation time by 65% on large instances. Numerical results demonstrate that considering competitive conditions and partial charging significantly impacts route patterns and fleet size. Notably, contrary to common expectations, full charging yields 1.2% higher profit than partial charging on average, revealing a strategic trade-off between short-term agility and long-term energy security. Neglecting the time-dependent portion of demand can lead to a substantial decrease in overall revenue.
Orazani et al. (Mon,) studied this question.