This work studies a multi-item lot-sizing problem inspired by Califrais's supply chain, incorporating minimum order quantities, perishability, inventory bounds, and lead times. Califrais is the logistics operator at the Rungis market. Each item can be ordered in either standard or urgent mode, with different associated costs, and must be stored in a warehouse with limited capacity. The problem, which is NP-hard in its multi-item version, is addressed through a Lagrangian relaxation: relaxing the inventory bounds allows the decomposition into polynomial subproblems solved via dynamic programming, followed by the construction of a feasible solution. The multi-item-per-supplier case additionally requires a minimum-cost flow procedure.