توالی خط مونتاژ بر اساس ویژگیهای T شبکه پتری

Mass production of goods with customer specific features is mostly carried out on production lines. Job-dependent processing times in the lines’ individual work zones requires line sequencing in order to use the line to capacity. This paper presents a two-step method allowing fast sequencing even for large numbers of jobs and product types. The knowledge about the line characteristics and about the possible jobs is modelled using a Petri-net. The resulting model is independent of the set of jobs to be scheduled. Based on the Petri-net's T-invariants, a valid production sequence is efficiently determined for a particular job set.

Products with customer specific features, e.g. automobiles, are mostly manufactured on production lines as well as in plants combining production lines and team workstations (Buzacott, 1990). In this paper a paced production line with partially overlapping work zones and a fixed launching rate (cycle time) is considered. In accordance with the type of job, it takes the worker in the individual work zone a certain amount of time to perform the necessary tasks. To use the line to capacity, a cycle time, i.e. the time chosen between the launching of two successive jobs is equal to the average processing time. Assuming that the processing times of several succeeding jobs at a particular work zone are always greater than the cycle time, it occurs that a job cannot be processed completely within the zone boundaries. In that case, the job cannot be processed any further on the line, or at least it has to be re-worked later on. Therefore, line sequencing, i.e. determination of a valid job sequence, is necessary. An example of such a situation would be a car assembly line where at most every third car can be equipped with air-conditioning.

In this paper a paced production line with overlapping work zones and a fixed launching rate was considered. Manufacturing different products with customer specific features leads to line sequencing problems, which can be formulated as Mixed Integer Linear Program for a given job set. The complexity of the problem grows exponentially with the cardinality of the job set and has to be solved completely for each new job set. To handle the complexity, a two-step method introducing a discrete-event systems view of the process is proposed. First, the given information about the production line and about the possible jobs is processed within a branch-and-bound algorithm to generate a Petri-net model. Model reduction is carried out by aggregating states and events as well as grouping events. The extension of the Petri-net T-invariants to group invariants leads to an algebraic system description. This description has to be determined only once for a given production line and range of product types. Second, valid sequences for a new job set are calculated by solving the obtained equations. The algorithm was applied to an example from the automotive industry. Determination of a valid job sequence even for job sets of practical relevance was possible within a minute.