Integrated capacity, demand, and production planning with subcontracting and overtime options

Models for integrated production and demand planning decisions can serve to improve a producer's ability to effectively match demand requirements with production capabilities. In contexts with price-sensitive demands, economies of scale in production, and multiple capacity options, such integrated planning problems can quickly become complex. To address these complexities, this paper provides profit-maximizing production planning models for determining optimal demand and internal production capacity levels under price-sensitive deterministic demands, with subcontracting and overtime options. The models determine a producer's optimal price, production, inventory, subcontracting, overtime, and internal capacity levels, while accounting for production economies of scale and capacity costs through concave cost functions. We use polyhedral properties and dynamic programming techniques to provide polynomial-time solution approaches for obtaining an optimal solution for this class of problems when the internal capacity level is time-invariant.