THE 3-MACHINE FLOWSHOP PROBLEM WITH ARBITRARY PRECEDENCE RELATIONS

The scheduling problem n/3/F/C(max) with arbitrary precedence constraints between the jobs is studied. A branch and bound algorithm is described. Bounds are obtained by solving 2-machine subproblems which are relaxed versions of the current 3-machine problem. These 2-machine problems which have precedence constraints can be quickly solved in an optimal fashion only if the constraints are of a series-parallel (S-P) form. Using methods described in [5], we find an S-P constraints subgraph which may be solved to obtain a lower bound for each 2-machine subproblem. This provides the basis for the calculation of an effective lower bound for the 3-machine case. Computational experience with the algorithm is reported.