Expanding the scope of linear programming solutions for vehicle scheduling problems

It is often suggested that zero-one linear programming can be used to tackle vehicle scheduling problems. In practice, optimal solutions can only be guaranteed for very small problems. Here an estimate is made of the size of problem which could be tackled by an ‘ordinary user’, particularly when using a formulation with reduced numbers of zero-one variables. Strategies for extending the scope of ILP are outlined. Changing the mode of data presentation to road networks can be useful but may introduce other difficulties. Overall, it is clear that considerable progress is still needed before ILP can be used for tackling real problems.