Large-scale assembly job shop scheduling problems with bill of materials: Models and algorithms

In this paper, we study an assembly job shop scheduling problem with tree-structured precedence constraints and jobs characterized by specific bills of materials. We propose a mathematical model to deal with a simplified version of the problem, as well as a fast and efficient constructive heuristic that is able to easily face real-world-sized instances. The production schedule takes into account the actual availability of materials in stock as well as the supply times and the capacity constraints, with the goal to minimize the average delay with respect to the due dates associated to the customers' orders. Computational results on data related to real-life instances show that the mathematical model is able to solve (not always to optimality) small-sized instances only. On the other hand, our heuristic approach is able to solve efficiently very large problems. Moreover, the proposed heuristic turns out to be scalable as the instance size grows.