Research on comprehensive recovery of liner schedule and container flow with hard time windows constraints

COVID-19 has had a huge impact on the global container market. Many liner companies have adopted a blank sailing for some voyages to adjust capacity, and vessel schedule reliability continues to be sluggish. From the perspective of the container liner company, this paper studies the integrated recovery of liner schedule and container flow under the background of suspension of shipping service. With the goal of minimizing the total cost of the liner company, the hard time window constraints of the container flow on the suspended routes are set to construct the integrated recovery problem.The increased carbon emission cost during the restoration of the container flow is taken into account.A mixed integer nonlinear programming model is established, and the adaptive mutation particle swarm optimization (AMPSO) is used to solve the model. The results show that the total cost of the model is reduced by 10.66% compared with the total cost of the shipping schedule recovery model that did not consider the recovery of container flow.