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This paper deals with the problem of preemptive scheduling in a two-stage flowshop with parallel unrelated machines and renewable resources at each stage. The resource requirements are of 0-1 type. The objective is the minimization of makespan. The problem is NP-hard. Heuristic algorithms using linear programming are proposed for solving this problem. Performance of the heuristic algorithms is analyzed by comparing heuristic solutions with the lower bound on the optimal makespan. The results of a computational experiment show that the proposed algorithms are able to produce good solutions in short computation time.