The two-duty period bus driver scheduling problem is a particular case of the generalized set convering problem, min{cµTxµ:Axµ≥bµ, 0µ•xµ•hµ and integer} where, each column of the boolean matrix Aµ consists of at most two strings of consecutive ones. Such a denomination for the problem is due to several real life applications, in particular for bus crew scheduling. In this paper, the authors present a ‘structural’ lagrangean relaxation and penalties for improving the bounds on the optimum for the problem. Two other lagrangean relaxation approaches, previously reported in the literature, are considered too. A computational study relative to these relaxations was carried out with both randomly generated test problems and real life cases from Rodoviária Nacional, a large mass transport operator in Portugal. The results reported in the paper evidence a better performance for the new lagrangean relaxation approach which, combined with greedy heuristics, yield a reasonably good and fast procedure for tackling real life problems.
