Minimization of Penalties for Tardiness in a Flow Shop Systems

The article is devoted to the problem of effective control of a sequential type system. A flow shop scheduling problem is examined as a model problem; the criterion is cumulative tardiness of jobs. In the systems under consideration such a service procedure is technologically permissible where all the jobs are performed by various machines in different sequence. A pipelined system model is presented for an optimal scheduling in the class of schedules with different sequence of job performance on various machines. The model allows to break up the job into pseudo-jobs - fragments consisting of chains of sequentially executed operations. The rules for constructing a set of pseudo-jobs are indicated. It is shown that as a schedule for a system that allows for a different order of execution of jobs on different machines, a permutation schedule designed for pseudo-jobs can be used. Admissibility conditions of such scheduling are introduced. A schedule length determination method for pseudo-jobs is specified. An operator of the transformation of the schedule is introduced. Examples of the transformation operator and definitions of a neighborhood of a schedule and a locally optimal solution of the problem are given. An approach is proposed for constructing approximately optimal schedules that are optimal in some neighborhood. The approach is based on schedule transformations. It implements the local search method. An iterative procedure for obtaining a locally optimal schedule is described, constructed in accordance with the principle of successive improvement. An example is given of constructing an approximate optimal schedule.