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Some independent plants making up a chemical or petrochemical site are linked by process streams. Linking process streams are, in general, cooled in up-plants and reheated in down-plants to satisfy process requirements. These streams, even more, travel from up-plants to storage tanks and, then, to down-plants, which results in low energy-use efficiency. Up-plants with multiple hot discharges and down-plants with multiple hot feeds are proposed in this paper, and a T–Qgraphic method is presented to target the temperature of multiple hot discharges/feeds between plants. The T–Qdiagram is composed of a grand composite curve (GCC) and a composite curve that only involves process streams employed for hot discharge/feed. A mixed integer linear programming (MILP) model is formulated to minimize the total hot and cold utilities of up- and down-plants and to solve the temperature of hot discharge/feed and the heat transfer between plants. Some examples are utilized to demonstrate the performance of the presented method for multiple hot discharges/feeds between plants. Results show an obvious decrease in the total hot and cold utilities of up- and down-plants, along with less investment for equipment. [ABSTRACT FROM AUTHOR]