Exact methods for the Oven Scheduling Problem

Abstract

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 using exact techniques and present two different modelling approaches, one based on batch positions and another on representative jobs for batches. These models are formulated as constraint programming (CP) and integer linear programming (ILP) models and implemented both in the solver-independent modeling language MiniZinc and using interval variables in CP Optimizer. An extensive experimental evaluation of our solution methods is performed on a diverse set of problem instances. We evaluate the performance of several state-of-the-art solvers on the different models and on three variants of the objective function that reflect different real-life scenarios. We show that our models can find feasible solutions for instances of realistic size, many of those being provably optimal or nearly optimal solutions.