Moving Policies in Cyclic Assembly-Line Scheduling

Abstract

We consider an assembly line problem that occurs in various kinds of production automation, for example, in the automated manufacturing of PC boards. The assembly line has to process a (potentially infinite) number of identical workpieces in a cyclic fashion. In contrast to common variants of assembly–line scheduling, the forward steps may be smaller than the distance of two stations. Therefore, each station may process parts of several workpieces at the same time, and parts of a workpiece may be processed by several stations at the same time. The throughput rate is determined by the number of (cyclic) forward steps, the offsets of the individual forward steps, and the distribution of jobs over the stationary stages between the forward steps. Even for a given number of forward steps and for given offsets of the forward steps, the optimal assignment of the jobs to the stationary stages is at least weakly ${\cal NP}$–hard.

We will base our algorithmic considerations on some quite conservative assumptions, which are greatly fulfilled in various application scenarios, including the one in our application: the number of jobs may be huge, but the number of stations and the number of forward steps in an optimal solution are small, the granularity of forward steps is quite coarse, and the processing times of the individual items do not differ by several orders of magnitude from each other. We will present an algorithm that is polynomial and provably deviates from optimality to a negligible extent (under these assumptions). This result may be viewed as an application of fixed–parameter tractability to a variety of real–world settings.

This work has been partially supported by DFG grant MU 1482/2.