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In this paper we introduce a new problem in the field of production planningwhich we call the Production Leveling Problem. The task is to assign orders toproduction periods such that the load in each period and on each productionresource is balanced, capacity limits are not exceeded and the orders'priorities are taken into account. Production Leveling is an importantintermediate step between long-term planning and the final scheduling of orderswithin a production period, as it is responsible for selecting good subsets oforders to be scheduled within each period.  A formal model of the problem is proposed and NP-hardness is shown byreduction from Bin Backing. As an exact method for solving moderately sizedinstances we introduce a MIP formulation. For solving large problem instances,metaheuristic local search is investigated. A greedy heuristic and twoneighborhood structures for local search are proposed, in order to apply themusing Variable Neighborhood Descent and Simulated Annealing. Regarding exacttechniques, the main question of research is, up to which size instances aresolvable within a fixed amount of time. For the metaheuristic approaches theaim is to show that they produce near-optimal solutions for smaller instances,but also scale well to very large instances.  A set of realistic problem instances from an industrial partner iscontributed to the literature, as well as random instance generators. Theexperimental evaluation conveys that the proposed MIP model works well forinstances with up to 250 orders. Out of the investigated metaheuristicapproaches, Simulated Annealing achieves the best results. It is shown toproduce solutions with less than 3% average optimality gap on small instancesand to scale well up to thousands of orders and dozens of periods and products.The presented metaheuristic methods are already being used in the industry.

Exact and Metaheuristic Approaches for the Production Leveling Problem