Heuristics for generalized shop scheduling problems based on decomposition

In this paper we consider generalized shop scheduling problems, where arbitrary precedence constraints among the operations are given (general shop), sequence-dependent changeover times between the processing of operations are taken into consideration, multiprocessor requirements of operations can occur and, in each technological stage of a job, several identical machines of the corresponding type may be available (hybrid or flexible shop). Also the number of machines of each type that are used is not fixed a priori. The objective is to minimize an arbitrarily given non-decreasing function in the completion times of the operations and in the numbers of machines of each type which have been used. By applying the mixed multigraph model, we propose two heuristic decomposition procedures and several algorithms for constructing and improving a schedule. The algorithms developed have been tested on a set of problems with up to 20 jobs and up to 10 machine types.