Pinto, José PintoPato, Margarida Vaz2025-01-232025-01-231989Paixão, José Pinto and Margarida Vaz Pato .(1989). “A structural Lagrangean relaxation for two-duty period bus driver scheduling problems”, European Journal of Operational Research, Volume 39: pp. 213-222. 19890377-2217http://hdl.handle.net/10400.5/97586The two-duty period bus driver scheduling problem is a particular case of the generalized set covering problem, min {cTx : Ax ⩾ b, 0 ⩽ x ⩽h and integer) where, each column of the boolean matrix A 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, we 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 lagrangean relation approach wich combined with greedy heuristics, yeld a reasonably good and fast procedure for tackling real life problemsengLagrangean RelaxationHeuristicsGeneralized Set CoveringNetwork FlowsBus Driver Schedulingjournal article