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The vacationing chief executive officer (CEO) problem combines the salient features of the so-called CEO problem and the multiple-description (MD) problem. In this setting, noisy versions of a source are observed by two encoders, as in the CEO problem. In addition, we require that each encoder generate MDs of the source, as in the MD problem. The vacationing-CEO problem arises in asynchronous multicast networks, and solving it is an essential step in developing a general theory for multiencoder and multidecoder lossy compression. In this paper, an achievable sum rate and two sum rate lower bounds are presented for the quadratic Gaussian vacationing-CEO problem. These bounds exactly determine the optimal sum rate over a wide range of parameters.