The off-line group seat reservation problem

In this paper we address the problem of assigning seats in a train for a group of people traveling together. We consider two variants of the problem. One is a variant of two-dimensional knapsack where we consider the train as having fixed size and the objective is to maximize the utilization of the seats in the train. The other is a variant of two-dimensional bin packing where all requests must be accommodated while trying to minimize the number of passenger cars needed. We present a number of bounds for these two variants and develop exact algorithms for solving the problems. Computational results are presented for various instances known from the packing literature adapted to the problems addressed.