Faster exact algorithms for hard problems: a parameterized point of view
Discrete Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Production planning problems in printed circuit board assembly
Discrete Applied Mathematics
Parameterized complexity: the main ideas and connections to practical computing
Experimental algorithmics
Parameterized Complexity
Workload balancing in multi-stage production processes
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
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We consider an assembly line problem that occurs in various kinds of production automation. Our original motivation lies 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 are variable and 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. The number of forward steps as well as the offsets are part of the output. However, no matter whether they are part of the input or the output, the optimal assignment of the jobs to the stationary stages is 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.