An Innovative Formulation Tightening Approach for Job-Shop Scheduling

Job shops are an important production environment for low-volume high-variety manufacturing. Its scheduling has recently been formulated as integer linear programming (ILP) problem to take advantages of popular mixed-integer (MILP) methods, e.g., branch-and-cut. When considering a large number parts, MILP methods may experience difficulties. To address this, critical but much overlooked issue is formulation tightening. The idea that if constraints can be transformed directly delineate the convex hull in data preprocessing stage, then solution obtained by using (LP) without combinatorial tightening process, however, fundamentally challenging because existence variables. In this article, innovative and systematic approach established first time tighten formulations individual each with multiple operations, stage. It major advancement our previous work on problems binary continuous variables link innovatively combining so uniquely determined With only, it proved vertices based LP after relaxing requirements. These converted tightened general use. This significantly improves results operations. Numerical demonstrate significant benefits quality computational efficiency. also applies other complex ILP similar characteristics changes way how such solved. Note Practitioners —Scheduling difficult planning operation job shops. form advantage methods. Given problem, there must exist all its problem. If found corresponding tight solved method one or novel exploitation relationship between job-shop scheduling. resulting characterized part parameters length horizon easily adjusted sets. Results