Throughput optimization for micro-factories subject to task and machine failures

In this paper, we study the problem of optimizing the throughput for micro-factories subject to failures. The challenge consists in mapping several tasks of different types onto a set of machines. The originality of our approach is the failure model for such applications in which not only the machines are subject to failures but the reliability of a task may depend on its type. The failure rate is unrelated: a probability of failure is associated to each couple (task type, machine). We consider different kind of mappings: in one-to-one mappings, each machine can process only a single task, while several tasks of the same type can be processed by the same machine in specialized mappings. Finally, general mappings have no constraints. The optimal one-to-one mapping can be found in polynomial time for particular problem instances, but the problem is NP-hard in most of the cases. For the most realistic case of specialized mappings, which turns out to be NP-hard, we design several polynomial time heuristics and a linear program allows us to find the optimal solution (in exponential time) for small problem instances. Experimental results show that the best heuristics obtain a good throughput, much better than the throughput achieved with a random mapping. Moreover, we obtain a throughput close to the optimal solution in the particular cases where the optimal throughput can be computed.