This work presents a new MILP mathematical formulation for the resource-constrained short-term scheduling of flowshop batch facilities with a known topology and limited supplies of discrete resources. The processing structure is composed of multiple stages arranged in series and several units working in parallel at each one. All production orders consist of a single batch and follow the same processing sequence throughout the plant. The proposed MILP approach is based on a continuous time domain representation that relies on the notion of order predecessor and accounts for sequence-dependent setup times. Assignment and sequencing decisions are independently handled through separate sets of binary variables. A proper formulation of the sequencing constraints provides a substantial saving in sequencing variables and constraints. By postulating a pair of conditions for the simultaneous execution of processing tasks, rather simple resource constraints requiring a few extra binary variables are derived. The proposed MILP scheduling approach shows a remarkable computational efficiency when applied to real-world problems.