The acquisition of production flexibility is a well‐documented strategy pursued by many firms to counteract certain operational constraints. However, these flexibilities can increase the complexity of a production system and the difficulties in managing increased complexity may hinder exploiting the full benefit of flexibility. In this paper, we consider one such flexibility paradox at an agribusiness firm for an annual $800 million production decision: The firm produces a number of products (hybrid seeds) using limited inventories of several raw materials (parent seeds) and a production process that is subject to random variations. To handle the raw material availability constraint and to partially mitigate the supply risk, the firm invests in a costly second production in South America that can be used if the yield in the first production in North America is low. We solve this joint problem of raw material allocation and sequential production by reformulating it as a tractable simultaneous optimization problem. This tractable reformulation provides an exact solution in practical time durations for large assortments of products. We also establish that when profit margins are sufficiently high, sequential production has less cost, on average, than single production. The solution developed is in use at the firm and has led to an estimated increase in profit by 2%–3% annually.