Marie-Louise Lackner

Marie-Louise Lackner, Christoph Mrkvicka, Nysret Musliu et al.

The Oven Scheduling Problem (OSP) is a new parallel batch scheduling problem that arises in the area of electronic component manufacturing. Jobs need to be scheduled to one of several ovens and may be processed simultaneously in one batch if they have compatible requirements. The scheduling of jobs must respect several constraints concerning eligibility and availability of ovens, release dates of jobs, setup times between batches as well as oven capacities. Running the ovens is highly energy-intensive and thus the main objective, besides finishing jobs on time, is to minimize the cumulative batch processing time across all ovens. This objective distinguishes the OSP from other batch processing problems which typically minimize objectives related to makespan, tardiness or lateness. We propose to solve this NP-hard scheduling problem via constraint programming (CP) and integer linear programming (ILP) and present corresponding models. For an experimental evaluation, we introduce a multi-parameter random instance generator to provide a diverse set of problem instances. Using state-of-the-art solvers, we evaluate the quality and compare the performance of our CP- and ILP-models. We show that our models can find feasible solutions for instances of realistic size, many of those being provably optimal or nearly optimal solutions. Finally, we derive theoretical lower bounds on the solution cost of feasible solutions to the OSP; these can be computed within a few seconds. We show that these lower bounds are competitive with those derived by state-of-the-art solvers.

Christoph Einspieler, Matthias Horn, Marie-Louise Lackner et al.

The task of finding efficient production schedules for parallel machines is a challenge that arises in most industrial manufacturing domains. There is a large potential to minimize production costs through automated scheduling techniques, due to the large-scale requirements of modern factories. In the past, solution approaches have been studied for many machine scheduling variations, where even basic variants have been shown to be NP-hard. However, in today's real-life production environments, additional complex precedence constraints and resource restrictions with calendars arise that must be fulfilled. These additional constraints cannot be tackled efficiently by existing solution techniques. Thus, there is a strong need to develop and analyze automated methods that can solve such real-life parallel machine scheduling scenarios. In this work, we introduce a novel variant of parallel machine scheduling with job precedences and calendar-based cumulative resource constraints that arises in real-life industrial use cases. A constraint modeling approach is proposed as an exact solution method for small scheduling scenarios together with state-of-the-art constraint-solving technology. Further, we propose a construction heuristic as well as a tailored metaheuristic using local search to efficiently tackle large-scale problem instances. This metaheuristic approach has been deployed and is currently being used in an industrial setting.

Johannes Vass, Marie-Louise Lackner, Nysret Musliu

In this paper we introduce a new problem in the field of production planning which we call the Production Leveling Problem. The task is to assign orders to production periods such that the load in each period and on each production resource 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. A formal model of the problem is proposed and NP-hardness is shown by reduction from Bin Backing. As an exact method for solving moderately sized instances we introduce a 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 Variable Neighborhood Descent and Simulated Annealing. Regarding exact techniques, the main question of research is, up to which size instances are solvable within a fixed amount of time. For the metaheuristic approaches the aim 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 is contributed to the literature, as well as random instance generators. The experimental evaluation conveys that the proposed MIP model works well for instances with up to 250 orders. Out of the investigated metaheuristic approaches, Simulated Annealing achieves the best results. It is shown to produce solutions with less than 3% average optimality gap on small instances and 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.