Manufacturers regularly face the challenge of determining the best allocation of production resources to customer orders in make-to-order systems. Past research on dynamic requirements planning problems has led to models and solution methods that help production planners to effectively address this challenge. These models typically assume that the orders the production facility must meet are exogenously determined and serve as input parameters to the model. In contrast, we approach the problem by allowing the production planning model to implicitly decide which among all outstanding orders a production facility should satisfy in order to maximize the contribution to profit from production. The order selection models we provide generalize classical capacitated lotsizing problems by integrating order-selection and production-planning decisions under limited production capacities. Building on prior analysis of an uncapacitated version of the problem, this chapter studies strong problem formulations and develops heuristic solution algorithms for several capacitated versions. Using a broad set of more than 3,000 randomly generated test problems, these heuristic solution methods provided solutions that were, on average, within 0.67% of the optimal solution value.