Recent crises have shown that the knowledge of the structure of input-output networks at the firm level is crucial when studying economic resilience from the microscopic point of view of firms that rewire their connections under supply and demand shocks. Unfortunately, empirical inter-firm network data are rarely accessible and protected by confidentiality. The available methods of network reconstruction from partial information, which have been devised for financial exposures, are inadequate for inter-firm relationships because they treat all pairs of nodes as potentially interacting, thereby overestimating the rewiring capabilities of the system. Here we use two big data sets of transactions in the Netherlands to represent a large portion of the Dutch inter-firm network and document the properties of one of the few analysed networks of this kind. We, then, introduce a generalized maximum-entropy reconstruction method that preserves the production function of each firm in the data, i.e. the input and output ... : main text: 26 pages, 9 figures; supplementary material 21 pages, 9 figures ...