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Decomposing large problems into several smaller subproblems is well-known in any problem solving endeavor and forms the basis for our flowsheet decomposition heuristic (FDH) described in this short note. It can be used as an effective strategy to decrease the time necessary to find good integer-feasible solutions when solving closed-shop scheduling problems found in the process industries. The technique is to appropriately assign each piece of equipment (i.e., process-units and storage-vessels) into groups and then to sequence these groups according to the material-flow-path of the production network following the engineering structure of the problem. As many mixed-integer linear programming (MILP) problems are solved as there are groups, solved in a pre-specified order, fixing the binary variables after each MILP and proceeding to the next. In each MILP, only the binary variables associated with the current group are explicit search variables. The others associated with the un-searched on binary variables (or the next in-line equipment) are relaxed. Three examples are detailed which establishes the effectiveness of this relax-and-fix type heuristic.