Queue-constrained packing: A vehicle ferry case study

•A practical method for loading a vehicle ferry to maximise the efficiency of the packing.•Development of a novel two-stage metaheuristic for solving an optimisation problem with stochastic inputs.•We describe two methods for rectangular packing where the choice of which object to pack next is constrained; in this case by what is at the front of the dockside queues.•Results show that the number of dockside queues is critical to obtaining an efficient load on the ferry – if too few queues are used, the packing algorithm is unable to find a good solution. We consider the problem of loading vehicles onto a ferry. The order in which vehicles arrive at the terminal can have a significant impact on the efficiency of the packing on the ferry as it may not be possible to place a vehicle in an optimal location if it is not at the front of one of the dockside queues at the right point in the loading process. As the arrival order of vehicles is stochastic, we model the loading process as a two-stage stochastic optimization problem where the objective is to reduce penalties incurred by failing to pack booked vehicles. The first stage consists of optimizing the yard policy for allocating vehicles to dockside queues while the second stage solves the packing problem for a realisation of the arrival process using the yard policy determined in stage one. A novel stage-wise iterative metaheuristic is introduced, which alternates between packing optimization for each of a training set of scenarios whilst fixing the yard policy and optimizing the yard policy whilst fixing the packing solutions. We introduce two novel packing encoders for the second stage packing problem. Termed Sequential Block Packing Encode (SOPE) and General Packing Encoder (GPE), the arrangements they produce are designed to be efficient and easy to implement for loading staff. Results show that the number of yard queues available is critical to the efficiency of the packing on board the ferry.