Supply chains in the sense of a centralized (or multi-centralized) logistics no, supply chains in the sense of mobile pastoral groups supporting armies' further extension yes. These did not stretch all the way back to central Asia. Groups like the White and Blue hordes, which later combined into the Golden Horde, were basically autonomous within the territory allotted them by the Qaghan -- they mostly owed the central authority a share of spoils, support for the postal system (örtöö or yam), and their presence when convened on matters of state. Armies would bring limited supplies with them as they campaigned, replacement horses and some small livestock, while the main group continued to focus on caring for the bulk of their herds. While not actively expanding their borders, steppe nomads usually moved between relatively well-established seasonal camps rather than continuously roaming.
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Supply chains in the sense of a centralized (or multi-centralized) logistics no, supply chains in the sense of mobile pastoral groups supporting armies' further extension yes. These did not stretch all the way back to central Asia. Groups like the White and Blue hordes, which later combined into the Golden Horde, were basically autonomous within the territory allotted them by the Qaghan -- they mostly owed the central authority a share of spoils, support for the postal system (örtöö or yam), and their presence when convened on matters of state. Armies would bring limited supplies with them as they campaigned, replacement horses and some small livestock, while the main group continued to focus on caring for the bulk of their herds. While not actively expanding their borders, steppe nomads usually moved between relatively well-established seasonal camps rather than continuously roaming.