Computing lower and upper bounds for a large-scale industrial job shop scheduling problem

In this paper we present a case study from the lighting industry concerned with the scheduling of a set of job families each representing the production of a particular end-item in a given quantity. It is a job shop type problem, where each job family has a number of routing alternatives, and the solution has to respect batching and machine availability constraints. All jobs of the same job family have a common release date and a common due date, and they differ only in size. The objective is to minimize the total tardiness of the job families, rather than that of individual jobs. We propose a two-phase method based on solving a mixed-integer linear program and then improving the initial solution by tabu search. We evaluate our method on real-world as well as generated instances.