O ne's aim in solving logical puzzles is to find the solution by making use of several clues and restrictions. In this paper, we solve a logical puzzle, the Battleship puzzle, by integer programming. Moreover, two integer programming models (i.e., a cell-based model and a ship-based model) for the Battleship puzzle are compared based on their complexity and solution times. The ship-based model requires more preprocessing work before running the integer program than the cell-based model, but strongly outperforms the latter one. Finally, the models are used to check if a puzzle contains redundant information and to create a puzzle with a unique solution.

Express service carriers provide time-guaranteed deliveries of parcels via a network consisting of nodes and hubs. In this, nodes take care of the collection and delivery of parcels, and hubs have the function to consolidate parcels in between the nodes. The tactical network design problem assigns nodes to hubs, determines arcs between hubs, and routes parcels through the network. Afterwards, fleet scheduling creates a schedule for vehicles operated in the network. The strong relation between flow routing and fleet scheduling makes it difficult to optimise the Flex Serv Manuf J (2010) 22:3-35 DOI 10.1007 network cost. Due to this complexity, fleet scheduling and network design are usually decoupled. We propose a new tactical network design model that is able to include fleet scheduling characteristics (like vehicle capacities, vehicle balancing, and drivers' legislations) in the network design. The model is tested on benchmark data based on instances from an express provider, resulting in significant cost reductions. 123