A tree search algorithm for the crew scheduling problem

In this paper we consider the crew scheduling problem, that is the problem of assigning K crews to N tasks with fixed start and finish times such that each crew does not exceed a limit on the total time it can spend working. A zero–one integer linear programming formulation of the problem is given, which is then relaxed in a lagrangean way to provide a lower bound which is improved by subgradient optimisation. Finally a tree search procedure incorporating this lower bound is presented to solve the problem to optimality. Computational results are given for a number of randomly generated test problems involving between 50 and 500 tasks.