Exact and meta-heuristic approaches for the production leveling problem

Abstract

In this paper, we introduce a new problem in the field of production planning, called the production leveling problem. The task is to assign orders to production periods such that the load in each period and for each product type is balanced, capacity limits are not exceeded, and the orders' priorities are taken into account. Production leveling is an important intermediate step between long-term planning and the final scheduling of orders within a production period, as it is responsible for selecting good subsets of orders to be scheduled within each period. We provide a formal model of the problem and study its computational complexity. As an exact method for solving moderately sized instances, we introduce a mixed integer programming (MIP) formulation. For solving large problem instances, metaheuristic local search is investigated. A greedy heuristic and two neighborhood structures for local search are proposed in order to apply them using simulated annealing. Furthermore, three possible extensions that arise from the application in practice are described and implemented, both within the MIP model and within simulated annealing. We make publicly available a set of realistic problem instances from the industry as well as from random instance generators. The experimental evaluation on our test sets shows that the proposed MIP model is well suited for solving instances with up to 250 orders. Simulated annealing produces solutions with less than 3% average optimality gap on small instances, and scales well up to thousands of orders and dozens of periods and product types. The metaheuristic method presented herein is already being successfully used in the industry.