Following on the sharing economy concept, which exploits the advancement in information and manufacturing technologies, the shared manufacturing paradigm has tremendous potentials to improve the performance of the production-distribution system and is prevailing in the current manufacturing industry. While the production routing problem that joins the optimization of production, inventory and distribution routing decisions has been intensively studied in the past decade, it has not been investigated in a shared manufacturing context. To fill the gap, this paper introduces a general model for the production routing problem with shared manufacturing resources. The problem is formulated as a robust chance-constrained model to address the uncertainty arising in customer demand and shared manufacturing resource demand and supply. Then, computationally tractable formulation is derived, for which a matheuristic that incorporates three diversification techniques is proposed to solve. Through extensive numerical experiments, the value of manufacturing resource sharing and the efficiency of the matheuristic are demonstrated. Several managerial implications are derived from the sensitivity analyses of key parameters.