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Abstract. Many production planning problems call for the minimization of stocking/storage costs. This paper introduces a new global constraint StockingCost([X1, . . . , Xn], [d1, . . . , dn], H, c) that holds when each item Xi is produced on or before its due date di, the capacity c of the machine is respected, and H is an upper bound on the stocking cost. We propose a linear time algorithm to achieve bound consistency on the StockingCost constraint. On a version of the Discrete Lot Sizing Problem, we demonstrate experimentally the pruning and time efficiency of our algorithm compared to other state-of-the-art approaches.