Universal Planning Horizons for Generalized Convex Production Scheduling

We study an infinite-horizon analog of the well-known finite-horizon convex production scheduling model with positive or negative demands, production, and inventory, and with constraints on inventory and production. We develop a forward algorithm for this problem allowing successively tighter bounds on the optimal first-period production to be given as successive demand forecasts are added to the problem. We show under very general conditions that the algorithm will always lead to an exact or asymptotic planning horizon. Planning horizon results due to others form special cases. Applications of the generalized production scheduling model include capacity expansion problems.