Dispatching Buses in a Depot Using Block Patterns

In this article we consider the problem of assigning parking slots to buses of different types so that the required buses can be dispatched easily in the morning. More precisely, if a bus of a certain type is needed at a given time, the buses that precede it in the lane must have departed already. Thus care must be taken to ensure that the buses arriving in the evening are parked in an order compatible with the types required for the morning departures. Maneuvers (i.e., rearrangements of buses within lanes) might be necessary to achieve this goal. Because the transit authorities need robust solutions to this problem (known as the dispatching problem in the literature), we formulate a model in which the depot lanes are filled according to specific patterns, called one-block or two-block patterns. We present two versions of this model, study their properties, and show that some real-life instances can be solved within reasonable times by a commercial MIP solver. We also demonstrate that the solutions of the model are very robust, and can thus be used by transit authorities.