Abstract: Because market competition is being internationalized and information technology is making rapid progress, the prompt ability of an enterprise to meet markets variation can be enhanced by taking part in a virtual enterprise in which agile supply chain management is realized. The minimum supply planning of agile supply chain, with which purchase costs, earliness costs, tardiness penalties and appointment lost penalties are considered, is formulated next by lean production philosophy. Three simplified programming models with various constraints are present. The efficiency of various models and constraints adopted by firms, located at different position in a supply chain, are being evaluated too.