Deterministic Production Planning with Concave Costs and Capacity Constraints

A multi-period single commodity production planning problem is studied in which known requirements have to be satisfied. The model differs from earlier well-known studies involving concave cost functions in the introduction of production capacity constraints. The structure of an optimal solution is characterized and then used in a simple dynamic programming algorithm for problems in which the capacities are the same in every period. Both the nonbacklog and backlog allowed cases are considered.