An algorithm for the general resource constrained scheduling problem by using of cutting planes

Abstract

We formulate the general resource constrained scheduling problem, including the fact that every job can be split at any time, as follows:

Every set F_j of jobs is called front, if these jobs can be processed simultaneously (from point of the precedence relations and the resource restrictions). x_j describes the period, in which F_j is active in the schedule. Then the problem is a disjunctive-linear program in which the disjunctive constraints

mean, that the corresponding fronts F_K1 ,..., F_Kr(k) cannot occur in the same schedule.

We intend to solve this program with a combined cutting plane and branch & bound technique. Two cut-constructions are used. The first is the intersection cut by Balas confined to a subspace. An additional cut-conception yields faces of the convex hull of the feasible solutions. A procedure is given, by which the dimension of these facecuts can be increased by one. To guarantee finiteness of the whole method, a branch & bound algorithm has to be incorporated. It is started, if by a determined number of cuts no optimal solution is found.