The pollution-routing problem with one general period of congestion

Purpose This paper aims to address a pollution-routing problem with one general period of congestion (PRP-1GPC), where the start and finish times of this period can be set freely. Design/methodology/approach In this paper, three sets of decision variables are optimized, namely, travel speeds before and after congestion and departure times on given routes, aiming to minimize total cost including green-house gas emissions, fuel consumption and driver wages. A two-phase algorithm is introduced to solve this problem. First, an adaptive large neighborhood search heuristic is used where new removal and insertion operators are developed. Second, an analysis of optimal speed before congestion is presented, and a tailored speed-and-departure-time optimization algorithm considering congestion is proposed by obtaining the best node to be served first over the congested period. Findings The results show that the newly developed operator of congested service-time insertion with noise is generally used more than other insertion operators. Besides, compared to the baseline methods, the proposed algorithm equipped with the new operators provides better solutions in a short time both in PRP-1GPC instances and time-dependent pollution-routing problem instances. Originality/value This paper considers a more general situation of the pollution-routing problem that allows drivers to depart before the congestion. The PRP-1GPC is better solved by the proposed algorithm, which adds operators specifically designed from the new perspective of the traveling distance, traveling time and service time during the congestion period.