A Novel Integer Linear Programming Formulation for Job-Shop Scheduling Problems

Job-shop scheduling is an important but difficult problem arising in low-volume high-variety manufacturing. It usually solved at the beginning of each shift with strict computational time requirements. To obtain near-optimal solutions quantifiable quality within limits, a direction to formulate them Integer Linear Programming (ILP) form so as take advantages widely available ILP methods such Branch-and-Cut (B&C). Nevertheless, requirements for on existing formulations are high. In this letter, novel formulation minimizing total weighted tardiness presented. The new has much fewer decision variables and constraints, proven be tighter compared our previous formulation. For fast resolution large problems, recent decomposition-and-coordination method “Surrogate Absolute-Value Lagrangian Relaxation” (SAVLR) enhanced by using 3-segment piecewise linear penalty function, which more accurately approximates quadratic function absolute-value function. Testing results demonstrate that drastically reduces B&C problems where difficulties, efficiently obtained SAVLR under