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This article proposes a two-level fuzzy supply chain inventory model, in which a single consignor delivers multiple items to the multiple consignees with the consignment stock agreement. The lead time is incorporated into the model and is considered a variable for obtaining optimal replenishment decisions. In addition, crashing cost is employed to reduce the lead time duration. This article investigates four different cases under controllable lead time to analyze the best strategy, focusing on two delays such as delay-in-payments and delay-in-shipment. In all four cases, all associated inventory costs are treated as a trapezoidal fuzzy number, and a signed distance method is employed to defuzzify the fuzzy inventory cost. An efficient optimization technique is adopted to find the optimal solution for the supply chain. Four numerical experiments are conducted to illustrate the four cases. Any one of these experimental results will provide the best solution for the ideal performance of the business under controllable lead time in the consignment stock policy. Finally, the managerial insights, conclusion and future direction of this model are provided.