General Planning Horizons for Production Smoothing with Deterministic Demands

In Part I of this paper, we developed an algorithm for finding planning horizons for the deterministic production smoothing problem when all demand was required to be met from regular production, under rather general assumptions for the production, production smoothing, and holding cost functions. Here, in Part II, we develop analogous planning horizons when the model is extended to include such factors as overtime, lost sales, simple subcontracting, undertime, and backlogging. Part II depends heavily on Part I.

To avoid unnecessary tedium, all cost functions will be assumed to be stationary in Part II. Overtime, undertime, holding, and backlogging will be assumed to be convex increasing, all other costs linear and proportional. However, it is not difficult to see that the techniques of Part I can be utilized directly to cover more general cost functions. Part II concludes with a discussion of the application of our general approach to actual data.