relationships. An appropriate solver is applied for the resulting mixed-integer linear or nonlinear programming (MILP/MINLP) problem. The approach is theoretically guaranteed to find an optimal solution if one exists. The disadvantage is that the solver algorithm may take an unreasonable amount of time. Practitioners may use problem-specific simplifications in the formulation to get faster solutions without eliminating critical components of the scheduling model. Constraint programming is a similar approach except that the problem is formulated only as a set of constraints and the goal is to arrive at a feasible solution rapidly. Multiple solutions are possible with this method. Agent-based modeling describes the batch process and constructs a feasible schedule under various constraints. By combining with mixed-integer programming or simulated-based optimization methods, this approach could achieve a good balance between the solution efficiency and the schedule performance. A new development and framework addresses how to exploit the aggregation of several digital twins, representing different physical assets and their autonomous decision-making, together with a global digital twin, in order to perform production scheduling optimization. See also Advanced planning and scheduling Gantt chart Kanban Manufacturing process management Resource-Task Network Single-machine scheduling Schedule (project management) Scheduling (computing) Stochastic scheduling References Further reading Blazewicz, J., Ecker, K.H., Pesch, E., Schmidt, G. und J. Weglarz, Scheduling Computer and Manufacturing Processes, Berlin (Springer) 2001, Herrmann, Jeffrey W., editor, 2006, Handbook of Production Scheduling, Springer, New York. McKay, K.N., and Wiers, V.C.S., 2004, Practical Production Control: a Survival Guide for Planners and Schedulers, J. Ross Publishing, Boca Raton, Florida. Co-published with APICS. Pinedo, Michael L. 2005. Planning and Scheduling in Manufacturing and Services, Springer, New York. Conway, Richard W., Maxwell, William L., Miller, Louis W., Theory of Scheduling, Dover Publications June 2003, Brucker P. Scheduling Algorithms. Heidelberg, Springer. Fifth ed. Production economics Production planning Production and manufacturing software Information technology management Enterprise resource planning terminology Business terms