Context. Several new multi-object spectrographs are currently planned or under construction that are capable of observing thousands of Galactic and extragalactic objects simultaneously. Aims. In this paper we present a probabilistic fibre-to-target assignment algorithm that takes spectrograph targeting constraints into account and is capable of dealing with multiple concurrent surveys. We present this algorithm using the 4-metre Multi-Object Spectroscopic Telescope (4MOST) as an example. Methods. The key idea of the proposed algorithm is to assign probabilities to fibre-target pairs. The assignment of probabilities takes the fibre positioners capabilities and constraints into account. Additionally, these probabilities include requirements from surveys and take the required exposure time, number density variation, and angular clustering of targets across each survey into account. The main advantage of a probabilistic approach is that it allows for accurate and easy computation of the target selection function for the different surveys, which involves determining the probability of observing a target, given an input catalogue. Results. The probabilistic fibre-to-target assignment allows us to achieve maximally uniform completeness within a single field of view. The proposed algorithm maximises the fraction of successfully observed targets whilst minimising the selection bias as a function of exposure time. In the case of several concurrent surveys, the algorithm maximally satisfies the scientific requirements of each survey and no specific survey is penalised or prioritised. Conclusions. The algorithm presented is a proposed solution for the 4MOST project that allows for an unbiased targeting of many simultaneous surveys. With some modifications, the algorithm may also be applied to other multi-object spectroscopic surveys.
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