Engineering:Advanced planning and scheduling

Short description: Manufacturing management process

Advanced planning and scheduling (APS, also known as advanced manufacturing) refers to a manufacturing management process by which raw materials and production capacity are optimally allocated to meet demand. APS is especially well-suited to environments where simpler planning methods cannot adequately address complex trade-offs between competing priorities. Production scheduling is intrinsically very difficult due to the (approximately) factorial dependence of the size of the solution space on the number of items/products to be manufactured.

Difficulty of production planning

Traditional production planning and scheduling systems (such as manufacturing resource planning) use a stepwise procedure to allocate material and production capacity. This approach is simple but cumbersome, and does not readily adapt to changes in demand, resource capacity or material availability. Materials and capacity are planned separately, and many systems do not consider material or capacity constraints, leading to infeasible plans. However, attempts to change to the new system have not always been successful, which has called for the combination of management philosophy with manufacturing.

Unlike previous systems, APS simultaneously plans and schedules production based on available materials, labor and plant capacity.

APS has commonly been applied where one or more of the following conditions are present:

1. make to order (as distinct from make to stock) manufacturing
2. capital-intensive production processes, where plant capacity is constrained
3. products 'competing' for plant capacity: where many different products are produced in each facility
4. products that require a large number of components or manufacturing tasks
5. production necessitates frequent schedule changes which cannot be predicted before the event

Advanced planning & scheduling softwares, such as MangoGem, Decision Brain or SAP, enables manufacturing scheduling and advanced scheduling optimization within these environments. APS functionality is available both as standalone software and as modules within larger enterprise resource planning (ERP) systems. The choice between off-the-shelf APS packages and custom-built optimization solutions depends on the complexity of the manufacturing environment and the degree to which standard software can accommodate the specific constraints and objectives of the operation.

Solution methods

APS systems rely on a variety of algorithmic techniques drawn from operations research (OR) and artificial intelligence (AI) to generate feasible and near-optimal production schedules.

Mathematical programming

Mixed-integer linear programming (MILP) is widely used in APS for planning problems where decisions involve discrete choices (e.g., which products to assign to which production lines) combined with continuous variables (e.g., production quantities). Commercial solvers such as CPLEX and Gurobi are commonly embedded in APS platforms to solve these formulations. However, for detailed shop-floor scheduling with complex sequencing constraints, pure MILP formulations can become computationally intractable as problem size increases.

Constraint programming

Constraint programming (CP) offers an alternative paradigm that is particularly effective for scheduling problems involving complex temporal and resource constraints. CP models the problem as a set of variables with finite domains, linked by constraints that must be simultaneously satisfied. Global constraints such as the cumulative constraint and the no-overlap constraint allow efficient reasoning about resource capacity and sequencing. CP-based approaches have been successfully applied to scheduling problems with sequence-dependent setup times and alternative resources.

Hybrid approaches

Modern APS systems increasingly combine techniques from both OR and CP. One important line of research involves embedding linear programming relaxations within constraint propagation to strengthen domain filtering. This approach uses reduced-cost information from LP relaxations to prune infeasible values from variable domains, resulting in tighter bounds and faster convergence. Similarly, cutting plane techniques from integer programming have been integrated into CP solvers to tighten relaxation bounds during search.

Other hybrid strategies include column generation with CP-based subproblem solvers, which has been applied to vehicle routing and scheduling problems with time windows, and the combination of local search metaheuristics with constraint-based reasoning.

Heuristic and metaheuristic methods

For very large-scale industrial problems where exact methods are impractical, APS systems often employ heuristic approaches such as priority dispatching rules (e.g., shortest processing time, earliest due date), genetic algorithms, simulated annealing, and tabu search. These methods sacrifice guarantees of optimality in exchange for the ability to produce good solutions within practical time limits. In many industrial settings, hybrid methods that combine metaheuristics with problem-specific constraint propagation yield the best trade-off between solution quality and computational speed.

Planning horizons

APS systems typically address decision-making across three planning horizons, each requiring different modeling approaches and levels of detail:

• Strategic planning (months to years): involves long-term decisions such as capacity investment, facility location, and workforce dimensioning. These problems are often formulated as mixed-integer programs.
• Tactical planning (weeks to months): covers medium-term decisions including production lot sizing, inventory targets, and sales and operations planning (S&OP). Aggregate models are used to balance demand forecasts against available capacity.
• Operational scheduling (hours to days): generates detailed production sequences at the shop-floor level, assigning specific operations to machines and time slots while respecting all constraints. This is the level where constraint programming and hybrid optimization methods are most commonly applied.

The quality of strategic and tactical decisions constrains what can be achieved at the operational level; for example, even an optimal schedule cannot compensate for a fundamental shortage of skilled labor or machine capacity that should have been addressed at the strategic level.

Further reading

• (in German) Supply Chain Management and Advanced Planning - Concepts, Models, Software and Case Studies, Heidelberg: Springer-Verlag, 2000, ISBN 3-540-67682-1