Production Planning with Convex Costs: A Parametric Study

We consider the problem of choosing the amounts of a single product to produce in each of a finite number of time periods so as to minimize the (convex) production and (convex) inventory carrying costs over the periods while satisfying known requirements. The effect of changes in the various parameters, viz., the requirements and the production and inventory capacity limits, upon the optimal production levels is studied. The results obtained are exploited to provide simple and intuitive computational procedures for finding optimal production schedules for a range of parameter values.