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A new world of sequences and schedules

Conference ·
OSTI ID:35859
In this paper we consider classical shop problems: n jobs have to be processed on m machines. The processing times t{sub ij} of job i on machine j is given for all jobs and machines. The machine orders are fixed (job shop) or arbitrary (open shop). We have to determine a feasible combination of the machine and job orders (sequence) which minimizes the completion time of all jobs. The modelling of shop problems by means of special latin rectangles has led to some interesting ideas for solving certain open shop problems. A survey on these results will be presented. Now we define a partial order on the set of sequences. In dependent of the given processing times for an ordered pair (A, B) the makespan of A is not greater than the makespan of B. Therefore, the optimal solution for such problems must be a minimal (or irreducible) element in the partial order defined above. It is possible to describe the sets of irreducible sequences for two machine shop problems in detail. The cardinalities of these sets are calculated. For the open shop problem we construct classes of irreducible sequences. Furthermore, we describe an algorithm to decide whether a given sequence is irreducible. In the framework of processing times we develop the first pictures of a new world of sequences and schedules.
OSTI ID:
35859
Report Number(s):
CONF-9408161--
Country of Publication:
United States
Language:
English