Planning and Scheduling by Logic-Based Benders Decomposition

We combine mixed integer linear programming (MILP) and constraint programming (CP) to solve an important class of planning and scheduling problems. Tasks are allocated to facilities using MILP and scheduled using CP, and the two are linked via logic-based Benders decomposition. Tasks assigned to a facility may run in parallel subject to resource constraints (cumulative scheduling). We solve problems in which the objective is to minimize cost, makespan, or total tardiness. We obtain significant computational speedups, of several orders of magnitude for the first two objectives, relative to the state of the art in both MILP and CP. We also obtain better solutions and bounds for problems than cannot be solved to optimality. We address a fundamental planning and scheduling problem that occurs frequently in manufacturing and supply chain contexts. Tasks must be assigned to facilities and scheduled on each facility subject to release dates and deadlines. Some of the tasks assigned to a gi...

• Type: Journal
• Year: 2007
• Where: IOR
• Authors: John N. Hooker
• Keywords: Cumulative Scheduling, IOR 2007, Mixed Integer Linear, Problems